GAS LAWS

Class 10 1

“Education is the most powerful weapon which you can use to change the world” -Nelson Mandela

ANGIRAS N NAMBOOTHIRI PHYSICAL SCIENCE 18221383001

“The only thing that interferes with my learning is my education” - Albert Einstein

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THE NATIONAL ANTHEM Jana-gana-mana-adhinayaka, jaya he Bharata-bhagya-vidhata. Punjab-Sindh-Gujarat-Maratha Dravida-Utkala-Banga Vindhya-Himachala-Yamuna-Ganga Uchchala-Jaladhi-taranga. Tava shubha name jage, Tava shubha asisa mage, Gahe tava jaya gatha, Jana-gana-mangala-dayaka jaya he Bharata-bhagya-vidhata. Jaya he, jaya he, jaya he, Jaya jaya jaya, jaya he!

PLEDGE “India is my country and all Indians are my brothers and sisters. I love my country and I am proud of its rich and varied heritage. I shall always strive to be worthy of it. I shall give my parents, teachers, and all elders respect and treat everyone with courtesy. To my country and my people, I pledge my devotion. In their wellbeing and prosperity alone, lies my happiness.”

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PREFACE What is the purpose of education? This question disturbs all thoughtful men and women. The conventional answer is the acquisition of knowledge, the reading of books, and the learning of facts. Perhaps because there are so many books and the branches of knowledge in which we can learn facts are so multitudinous today, we begin to hear more frequently that the function of education is to give children a desire to learn and to teach them how to use their minds and where to go to acquire facts when their curiosity is aroused. An educated person is one who knows that there are so many things yet to learn. The quantum of unlearnt things amplifies when you learn more. It goes that education is a progressive discovery of ignorance. If so, the purpose of education should be the creation of individuals who are aware that they ignorant about much and much things. Only such a person will pursue knowledge motivated by himself and will continue as a lifelong autonomous learner as said by Dr. APJ Abdul Kalam. The gas laws are a group of laws that govern the behaviour of gases by providing relationships between the volume occupied by a gas, the pressure exerted by a gas on the walls of its container, the absolute temperature of the gas, the amount of gaseous substance (or) the number of moles of gas. The gas laws were developed towards the end of the 18th century by numerous scientists (after whom, the individual laws are named). The gas laws discussed in this textbook are the Boyle’s Law, which provides a relationship between the pressure and the volume of a gas, Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature, Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance. Under standard conditions, all gasses exhibit similar behaviour. The variations in their behaviours

arise

when

the

physical parameters

associated

with

the

gas

(such as temperature, pressure, and volume) are altered. The gas laws basically describe the behaviour of gases and have been named after the scientists who discovered them.

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THE CONSTITUTION OF INDIA PART IV A FUNDAMENTAL DUTIES OF CITIZENS ARTICLE 51 A Fundamental Duties It shall be the duty of every citizen of Indiaa) to abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem; b) to cherish and follow the noble ideals which inspired our national struggle for freedom; c) to uphold and protect the sovereignty, unity and integrity of India; d) to defend the country and render national service when called upon to do so; e) to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities; to renounce practices derogatory to the dignity of women; f) to value and preserve the rich heritage of our composite culture; g) to protect and improve the natural environment including forests, lakes, rivers and wild life, and to have compassion for living creatures; h) to develop the scientific temper, humanism and the spirit of inquiry and reform; i) to safeguard public property and to abjure violence; j) to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavor and achievement. k) who is a parent or guardian to provide opportunities for education to his child or, as the case may be, ward between the age of six and fourteen years.

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CONTENTS Volume of a gas………………………………………………….7 Pressure of a gas………………………………………………..9 Temperature………………………………………………………12 Volume and Pressure [Boyle’s law]………………………….14 Volume and Temperature [Charles’ law]…………………….21 Volume and number of particles [Avogadro’s law]………..28 Pressure and Temperature [Gay-Lussac’s law]……………33 Combined Gas Law……………………………………………...37 Ideal Gas Law……………………………………………………..39 Exercise……………………………………………………………42

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1.VOLUME OF A GAS The volume of gas is defined as the space occupied by the gaseous particles at standard temperature and pressure conditions. It is denoted as ‘V’. SI unit of volume is 'Litres' denoted as ‘L’.

fig1.1 Gas molecules are always free and keeps bombarding each other. They spread so fast due to these collisions. They can move only till it hits the walls of the container so gas molecules will be spread out equally throughout the container and keeps colliding each other. So, the volume occupied will be always equal to volume of the container. Sometimes, the volume of a flask or a container is fixed, and the gas will fill it to that volume, changing in temperature and pressure until it equilibrates with surrounding. However, what if the container were flexible, and those other parameters were fixed. 7

Imagine a balloon. And not just any balloon, but a temperaturecontrolled balloon, in a pressurized environment. Now, the only free parameter of a gas sample trapped in that balloon is its volume. It has to match the pressure of the room around it (balloons are hardly known for their rigidity), it has to match the temperature of the balloon. The only free parameter that can change is its volume.

fig:1.2

fig:1.3

The important thing in any of these cases is knowing how the parameters interact. If we keep adding gas to a fixed volume, the temperature and pressure of the gas will increase until the vessel fails. If we continually heat a gas at fixed pressure but variable volume (like in the piston of an internal combustion engine), the volume and temperature will increase. It's knowing how the system will respond to a change in one parameter in the other free parameters that's the key.

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2.PRESSURE OF A GAS The force which the substance exerts on another substance per unit area is known as pressure. The pressure of the gas is the f0rce that the gas exerts on the container boundaries.

fig:2.1 The gas molecules move randomly along the given volume. During this movement, they collide with the surface and also with each other. The impact of every individual gas molecule is too small and difficult to visualize. But the impact of all the gas molecules considered together constitutes the gas pressure. Greater the number of collisions, greater would be the pressure. The Gas pressure formula is given as, 𝑭 P= 𝑨 9

where, F = impact force due to gas collisions in Newtons (N), A = area in meter square Pressure can be increased either by increasing the amount of force or by decreasing the area over which it is applied; pressure can be decreased by decreasing the force or increasing the area. Atmospheric pressure is caused by the weight of the column of air molecules in the atmosphere above an object. Pressure is dependent on both the force exerted and the size of the area to which the force is applied. We know from the equation that applying the same force to a smaller area produces a higher pressure. When we use a hose to wash a car, for example, we can increase the pressure of the water by reducing the size of the opening of the hose with a thumb.

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The units of pressure are derived from the units used to measure force and area. The SI unit for pressure, derived from the SI units for force (newtons) and area (square meters), is the newton per square meter (N/m2), which is called the Pascal (Pa), after the French mathematician Blaise Pascal (1623–1662): 1Pa=1N/m2

We can measure atmospheric pressure, the force exerted by the atmosphere on the earth’s surface, with a barometer (fig2.2). A manometer (fig 2.3) is a device similar to a barometer that can be used to measure the pressure of a gas trapped in a container.

fig 2.2

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fig 2.3

3.Temperature Temperature is the measure of degree of hotness or coldness. It is measured with a thermometer. Thermometers are calibrated in various temperature scales. The most common scales are • The Celsius scale with the unit symbol °C (formerly called centigrade). • The Fahrenheit scale (°F). • Kelvin scale (K). Absolute Zero or zero kelvin or −273.15 °C, is the lowest point in the temperature scale. Experimentally, it can be approached very closely but not actually reached. It would be impossible to extract energy as heat from a body at that temperature. Temperature is measured with thermometers.

fig3.1 12

fig3.2

According to the kinetic-molecular hypothesis, a substance's temperature is proportional to the average kinetic energy of its particles. When a substance is heated, some of the energy absorbed is kept inside the particles, while another energy accelerates particle motion. This is manifested as a rise in the material's temperature. When studying kinetic energy in gas molecules and its relationship with temperature, we generally define the term ‘average kinetic energy.

fig3.3 The basic unit of temperature in the International System of Units (SI) is the Kelvin. It has the symbol K. For everyday applications, it is often convenient to use the Celsius scale, in which 0 °C corresponds very closely to the Freezing Point of water and 100 °C is its Boiling Point at sea level. Because liquid droplets commonly exist in clouds at subzero temperatures, 0 °C is better defined as the melting point of ice. In this scale, a temperature difference of 1 degree Celsius is 13

the same as a 1kelvin increment, but the scale is offset by the temperature at which ice melts (273.15 K).

4. VOLUME AND PRESSURE All the particles (atoms and molecules) of a substance are continually moving and so possess kinetic energy. In gases the movement of the particles is highly energetic and this is the reason why gases form, the particles have enough energy to overcome the attractive forces holding the particles together. In gases the particles are moving very quickly and freely in a random manner constantly bumping into each other and their surroundings. It is these collisions between the particles of the gas and the walls of the container it is confined to that creates gas pressure. The gas pressure is the overall force of all these collisions divided by the area of the walls of the container it is confined in. The relationship of a gas with pressure and volume was developed by the scientist Robert Boyle at around 1660 and is known as Boyle’s Law.

fig 4.1 14

Boyle’s law states: "For a fixed mass of gas, at a constant temperature, the product (pressure x volume) is a constant." Pressure x Volume = constant p x V = constant Explanation of Boyle's law:

fig 4.2 A sealed cylinder with no leaks contains a fixed mass of a gas kept at a constant temperature. The gas pressure is created by the collision of the moving gas particles with each other and against the walls of the cylinder.

fig 4.3 15

The above set up is used to investigate the relationship between pressure and volume for a gas. A force is exerted on the piston to compress the gas. The corresponding pressure and volume values are recorded for different applied forces.

fig 4.4 By plotting the recorded values of pressure (p) against volume (V) a curve is produced. We can see from the values that when the pressure is doubled the volume is halved. If the pressure was to increase by 3 the volume would decrease to a third. Thus, the volume is inversely proportional to the pressure. By plotting pressure (p) against the reciprocal of the volume (1/V) a straight line is obtained the gradient of which is the constant in Boyle’s Law.

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fig 4.5 A decrease in volume increases the number of gas particles per unit volume. This results in an increase in the number of gas particles close to the cylinder walls and therefore an increase in the number of collisions with the wall. As the number of collisions per unit area increases so does the force per unit area thereby giving an increase in pressure. Examples of Boyle’s law are, During respiration, our lungs make use of Boyle’s law. While inhaling, the lungs are filled with air; therefore, they expand. The volume increases, hence the pressure level goes down. Similarly, when the lungs are evacuated of air, they shrink; therefore, the volume reduces and the pressure increases. The change in pressure and volume is momentary and periodic in nature.

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fig 4.6 Flat tyres lack proper shape and strength, which makes it difficult for a vehicle to move properly. When air is pressed into flat tyres with the help of an air pump, the air molecules get tightly packed. The more be air molecules present in the tyre, the more will be the pressure exerted on the walls of the tyre. Hence, inflating flat tyres is yet another example of Boyle’s law in real life.

fig 4.7

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A soda bottle, filled with a mixture of carbon-di-oxide and water, is one of the best examples to demonstrate Boyle’s law. When the soda can or bottle is sealed, it is difficult to compress. This is because the air molecules present inside the container are tightly packed and do not have space to move. When the can or the bottle is opened, some of the air molecules escape, thereby making space for the movement of air molecules and allowing the bottle to get compressed. Here, the change in pressure as per the change in volume can be clearly observed.

fig 4.8 A syringe is medical equipment that is used to insert or withdraw fluids. It consists of a cylinder to contain the fluid and a plunger to vary the pressure. When the plunger is pushed down, the volume of the fluid reduces, thereby increasing the pressure. Similarly, on pulling up the plunger, the volume is increased, and the pressure is reduced. Hence, the working of a syringe depends on Boyle’s law. 19

➢ Using the example of the sealed cylinder above, the volume of gas at the start is 50 cm 3 with a pressure of 1.2 x 105 Pascals. The piston is pushed slowly into the syringe until the pressure on the gauge reads 2.0 x 10 5 Pascals. What is the volume of gas? ➢ Solution: We know p x V = constant therefore, p 1 x V 1 = p2 x V2 p1= 1.2 x 105 Pascals V1 = 50 cm3 p2 = 2.0 x 105 Pascals V2 =? p 1 x V 1 = p2 x V2 V2= P1× V1/P2 V2= 1.2×105 × 50/2.0×10 5 = 30cm3

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5.VOLUME AND TEMPERATURE The relationship between the volume and temperature of a gas was first put forward by the French scientist JacquesAlexandre-César Charles at around 1787 and is known as Charles’ Law.

fig 5.1 Charles’ law states: "For a fixed mass of gas, at a constant pressure, the volume (V) is directly proportional to the absolute temperature (T)." Volume α Temperature 𝑽𝒐𝒍𝒖𝒎𝒆 = 𝒂 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝑻𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆

explanation of Charles' law: 21

fig 5.2 A sealed cylinder with no leaks contains a fixed mass. In order to keep the gas pressure constant, the piston is allowed to move freely so that the internal pressure created by the gas particles can equal the constant external pressure. If the internal pressure increases the piston will move up to allow the pressure to equalize.

fig 5.3

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The above set up is used to investigate the relationship between temperature and volume for a gas. Heat energy is applied to the cylinder and the temperature of the gas increases. The average velocity of the gas particles increases resulting in an increase in the rate of collisions and the average force per collision. This produces an increase in pressure inside the cylinder, the cylinder pressure becomes greater than the external pressure and the piston moves up increasing the volume.

fig 5.4 By plotting the recorded values of volume (V) against temperature (T) a straight line is produced. We can see from the values that the gas expands uniformly with temperature. We can extrapolate the straight line and see the relationship between cooling the gas and the volume. Further extrapolation gives the temperature at which the volume of gas would become zero. This temperature is at -273°C and is called the absolute zero of temperature.

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fig 5.5 Converting the recorded temperatures into the Kelvin scale and plotting the volume (V) against the absolute temperature (T) gives a straight line which when extrapolated passes through the origin. This shows the volume of the gas is directly proportional to the absolute temperature of the gas. Doubling the temperature will double the volume. The gradient of the slope is the constant in Charles’ Law. Examples of Charles’s Law,

fig 5.6 24

If you have had the chance to go out on a chilly day, you might have noticed that the balloon crumbles. However, if you take the balloon to a warm room, it regains its shape. Why does this happen? This happens because the temperature on a cold day is low, and, so, the volume decreases. Now, in accordance with the Charles’s Law, as soon as you enter a warm room, the temperature increases; with an increase in temperature, the volume also increases. Therefore, the balloon goes back to its original shape.

fig 5.7

You might have wondered about the working of the hot air balloon. Charles’s Law describes that temperature and volume are directly proportional to each other. When a gas is heated, it expands. As the expansion of the gas takes place, it becomes less dense and the balloon is lifted in the air. The warm is less dense 25

than the cold air, which means that it is lighter than the cold air. Also, the warm air has less mass per unit volume. Tyres of untouched vehicles gets deflated during freezing winter days while get inflated in hot summer days. This unusual behaviour is because of Charles's law. In winter due to low temperatures, the air inside a tyre gets cooler, and they shrink. While in hot days, the air expands with temperature.

fig 5.8

Like tyres, helium balloons also experience expansion and contraction with change in surrounding temperature. If you take a balloon out in a snowy day, it crumbles. When the same balloon is brought back to a warm room, it regains its original shape. 26

fig 5.9 ➢ Using the example of the sealed cylinder above, the volume of gas at the start is recorded as 30 cm 3 with a temperature of 30°C. The cylinder is heated further till the thermometer records 60°C. What is the volume of gas? ➢ Solution: We know V/T = constant therefore, V1/T1 = V2/T2 V1 = 30 cm3 T1 = 30°C = 30+273 = 303K (Remember to convert from Celsius to Kelvin) T2 = 60°C = 60+273 = 333K V2 =? 27

V1/T1 = V2/T2 V2 = V1 T2/T1 V2 =

𝟑𝟎×𝟑𝟑𝟑 𝟑𝟎𝟑

=32.97 cm3

6. VOLUME AND NUMBER OF PARTICLES When applied to gases, Avogadro’s law (also known as Avogadro’s principle or Avogadro’s hypothesis) states that the total number of atoms or molecules in a gas (that is, the amount of gaseous substance) is directly proportional to the total volume occupied by the gas at constant temperature and pressure. When the temperature and pressure are held constant, Avogadro's Law states that the volume of a gas is directly proportional to the number of moles (or number of particles) of gas in the gas. ‘Avogadro’s law’ is named after the Italian scientist Amedeo Carlo Avogadro

fig 6.1 Avogadro’s law can be expressed mathematically using the following formula when pressure and temperature are held constant: V∝n 28

V/n = k, Where V denotes the volume of the gas, n denotes the amount of gaseous substance present (which is often expressed in moles), and k denotes a constant value. Increases in the amount of a gaseous substance can be calculated by using the following formula: As the amount of a gaseous substance increases, the amount of space taken up by the gas increases proportionally.

fig 6.2 Avogadro’s law states that V1/n1 = V2/n2 Say you have 5.00 L of a gas which contains 0.965 mol of molecules. What will be the new volume of the gas if the quantity is increased to 1.80 mol, assuming pressure and temperature are held constant? Select the appropriate form of the law for the calculation. In this case, a good choice is: V1n2 = V2n1 (5.00 L) (1.80 mol) = (x) (0.965 mol) Rewriting to solve for x give you: 29

x = (5.00 L) (1.80 mol) / (0.965 mol) x = 9.33 L

The Avogadro constant, commonly denoted NA or L, is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining constant with an exact value of 6.02214076×1023/moles. It is named Avogadro by Stanislao Cannizzaro, who explained this number four years after Avogadro's death. The numeric value of the Avogadro constant expressed in reciprocal moles, a dimensionless number, is called the Avogadro number. In older literature, the Avogadro number is denoted NA which is the number of particles that are contained in one mole, exactly 6.02214076×1023. NA= 6.02214076× 1023 You have probably experienced this example of Avogadro’s Law yourself. When you blow up a balloon, you are adding molecules of gas into it. The result is that the volume of the balloon increases – and in order to do this, you decrease the number of molecules in your lungs (which decreases their volume)!

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fig 6.2 Human lungs demonstrate Avogadro’s law in the best possible way. When we inhale, the lungs expand because they get filled with air. Similarly, while exhaling, the lungs let the air out and shrink in size. The change in volume can be clearly observed, which is proportional to the amount or the number of molecules of air contained by the lungs.

fig 6.3 A bicycle pump does the same thing to a bicycle tire. The action of a bicycle pump makes use of Avogadro’s law. The pump extracts the air from the environment and pushes it inside a deflated object. The increase in the number of gas molecules in the object correspondingly changes its shape and helps it to 31

expand. This proportionality between the number of molecules of the air and the volume is nothing but Avogadro’s law.

fig 6.4

A soccer ball contains a bladder inside it and a rigid outer covering. When the ball gets deflated, the bladder gets deprived of air and loses its shape, thereby causing the ball to lose the ability to bounce. The volume of the air present inside the bladder can be increased by forcefully pressing air into it through an air pump. The change in volume of air is proportional to the change in the number of air molecules possessed by it. Hence, pumping air in a soccer ball is an explicit illustration of Avogadro’s law in real life.

fig 6.5

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7.PRESSURE AND TEMPERATURE The relationship between pressure and temperature of a gas is stated by Gay-Lussac’s pressure temperature law. This law states that the pressure (P) of a fixed mass of gas held at a constant volume is directionally proportional to its Kelvin temperature (T). Therefore, as the pressure of a particular system goes up, the temperature of that system also goes up, and vice versa. Gas laws describe the behaviour of gases with respect to the pressure, volume, temperature, and amount. Gases are one of the states of matter, either compressed very tightly or expanded to fill a large space. Gay Lussac’s law is a law that provides the relationship between the pressure exerted by the gas on the container walls and absolute temperature related to the gas. It states that, at a constant volume, the pressure of a given amount of a particular gas is directly proportional to its Kelvin temperature. It can be written as: • • •

P ∝ T, or P/T = k where k is a constant, or P1/T1 = P2/T2

When the temperature of a particular system is increased, the molecules in the gas move faster, exerting a greater pressure on the wall of the gas container. This in terms increases the pressure of the system. If the temperature of the system is decreased, the pressure goes down. Therefore, at a constant volume, the pressure of a particular gas is directly proportional to the temperature 33

fig 7.1 Gay-Lussac’s law implies that the ratio of the initial pressure and temperature is equal to the ratio of the final pressure and temperature for a gas of a fixed mass kept at a constant volume. This formula can be expressed as follows: (P1/T1) = (P2/T2) Where: P1 is the initial pressure • T1 is the initial temperature • P2 is the final pressure • T2 is the final temperature This expression can be derived from the pressure-temperature proportionality for gas. Since P ∝ T for gases of fixed mass kept at constant volume: •

P1/T1 = k (initial pressure/ initial temperature = constant) P2/T2 = k (final pressure/ final temperature = constant) Therefore, P1/T1 = P2/T2 = k 34

Or, P1T2 = P2T1 When a pressurized aerosol can (such as a deodorant can or a spray-paint can) is heated, the resulting increase in the pressure exerted by the gases on the container (owing to Gay-Lussac’s law) can result in an explosion. This is the reason why many pressurized containers have warning labels stating that the container must be kept away from fire and stored in a cool environment.

An illustration describing the increase in pressure which accompanies an increase in the absolute temperature of a gas kept at a constant volume is provided above. Another example of Gay-Lussac’s law can be observed in pressure cookers. When the cooker is heated, the pressure exerted by the steam inside the container increases. The high temperature and pressure inside the container cause the food to cook faster.

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The electric water heater is similar to the pressure cooker. The cold water is heated by the heating filaments inside the heater. The hot water generated is released through the outlet nozzle. Modern electric heaters automatically regulate the temperature of water. When the system and pressure-relief valve malfunctions, the steam is generated by continuous power supply. This steam can damage the heater. If the pressure of the steam exceeds the tolerable limit, the heater may burst.

(Q)The pressure of a gas in a cylinder when it is heated to a temperature of 250K is 1.5 atm. What was the initial temperature of the gas if its initial pressure was 1 atm? Given, 36

Initial pressure, P1 = 1 atm Final pressure, P2 = 1.5 atm Final temperature, T2 = 250 K As per Gay-Lussac’s Law, P1T2 = P2T1 Therefore, T1 = (P1T2)/P2 = (1*250)/(1.5) = 166.66 Kelvin.

8.Combined Gas Law The combined gas law is the law which combines Charles’s law, Gay-Lussac’s law and Boyles’s law. It’s an amalgamation of the three previously discovered laws. These laws relate one thermodynamic variable to another holding everything else constant. The interdependence of these variables represents combined gas law which states that the ratio between the product of pressure-volume and temperature of a system remains constant. Combined gas law can be mathematically expressed as k = PV/T Where, P = pressure T = temperature in kelvin V = volume K = constant (units of energy divided by temperature) When two substances are compared in two different conditions, the law can be stated as, PiVi/Ti = PfVf/Tf 37

Where, Pi = initial pressure Vi = initial volume Ti = initial temperature Pf = final pressure Vf= final volume Tf = final temperature The initial volume of the gas is 5L and final volume is 3L Calculate the final pressure of the gas, given that the initial temperature is 273 K, the final temperature is 200 K, and initial pressure is 25 kPa. Solution According to the given parameters, Pi= 25 kPa Vi = 5L Vf = 3L Ti = 273K Tf = 200K According to combined gas law, PiVi/Ti = PfVf/Tf Substituting in the formula, we get 25 x 5 / 273 = Pf x 3 / 200 Therefore, Pf = 30.525 kPa 38

9.IDEAL GAS LAW The ideal gas law, also known as the general gas equation, is an equation of the state of a hypothetical ideal gas. Although the ideal gas law has several limitations, it is a good approximation of the behaviour of many gases under many conditions. Benoit Paul Émile Clapeyron stated the ideal gas law in 1834 as a combination of the empirical Charles’s law, Boyle’s Law, Avogadro’s law, and Gay-Lussac’s law. The ideal gas law states that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas and the universal gas constant. The empirical form of ideal gas law is given by: PV=nRT where, P is the pressure. V is the volume. n is the amount of substance. R is the ideal gas constant. •

•

When we use the gas constant R = 8.31 J/K.mol, then we have to plug in the pressure P in the units of pascals Pa, volume in the units of m3 and the temperature T in the units of kelvin K. When we use the gas constant R = 0.082 L.atm/K.mol then pressure should be in the units of atmospheres atm, volume 39

in the units of litres L and the temperature T in the units of kelvin K. For easy reference, the above information is summarised in the table as follows: Ideal Gas equation Units R = 8.31 J/K.mol

R = 0.082 L.atm/K.mol

Pressure in pascals Pa

Pressure in atmospheres atm

Volume in m3

Volume in litres L

The temperature in Kelvin K

The temperature in Kelvin K

The ideal gas law is derived from the observational work of Robert Boyle, Gay-Lussac and Amedeo Avogadro. Combining their observations into a single expression, we arrive at the Ideal gas equation, which describes all the relationships simultaneously. The three individual expressions are as follows: Boyle’s Law V∝P Charles’s Law V∝T Avagadro’s Law V∝n Combining these three expressions, we get 40

V∝nT/P The above equation shows that volume is proportional to the number of moles and the temperature while inversely proportional to the pressure. This expression can be rewritten as follows: V=nRT/P Multiplying both sides of the equation by P to clear off the fraction, we get PV=nRT The above equation is known as the ideal gas equation. The graph here shows the relationship between temperature and pressure for different gases.

On extrapolating this graph, we see that the graphs always intercept the x-axis at a point we now call the absolute zero, irrespective of which gas we are graphing. This point represents the beginning of the Kelvin scale, i.e., Zero K. On the Celsius scale, 0 K is equivalent to -273.5 oC. This is the coldest temperature possible. As a molecule gets colder, its energy and, 41

consequently, its movement and vibrations decrease in amplitude. As we keep cooling it, at a point, the atom will reach a state of minimum internal energy where the atom has lost almost all its energy and is stationary. (Q)What is the volume occupied by 2.34 grams of carbon dioxide gas at STP? Solution: To determine the volume, rearrange the ideal gas law as follows: V=nRT/P Substituting the values as follows, we get V=[(2.34g/44g/mol) × (0.08206Latm/mole/K) (273.0)]/1.00atm =1.19L

EXERCISE • Calculate the temperature at which 0.654 moles of neon gas occupies 12.30 liters at 1.95 atmospheres. Solution: • At a temperature of 300 K, the pressure of the gas in a deodorant can is 3 atm. Calculate the pressure of the gas when it is heated to 900 K. • Determine the volume of a gas given Vi = 3L, Ti = 300K, Tf = 250K, Pi = 35 kPa and Pf= 50 kPa • A gas exerts a pressure of 3 kPa on the walls of container 1. When container 1 is emptied into a 10-liter container, the pressure exerted by the gas increases to 6 kPa. Find the 42

•

•

•

• •

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volume of container 1. Assume that the temperature and quantity of the gas remain constant. A fixed amount of a gas occupies a volume of 1L and exerts a pressure of 400 kPa on the walls of its container. What would be the pressure exerted by the gas if it is completely transferred into a new container having a volume of 3 liters (assuming the temperature and quantity of gas remains constant)? A tyre containing 10 moles of air and occupying a volume of 40L loses half its volume due to a puncture. Considering that the pressure and temperature remain constant, what would be the amount of air in the deflated tyre? One mole of helium gas fills up an empty balloon to a volume of 1.5 liters. What would be the volume of the balloon if an additional 2.5 moles of helium gas are added? (Assume that the temperature and the pressure are kept constant.) A gas occupies 221cm3 at a temperature of 0 C and pressure of 760mm Hg. What will be the volume at 100 C? A sample of gas has an initial volume of 30.8L and an initial temperature of -67-degree Celsius. What will be the temperature of the gas if the volume is 21.0L? A gas occupies a volume of 400cm3 at 0-degree Celsius and 780mm of Hg. How many liters of volume will the gas occupy at 80-degree Celsius and 780mm Hg. 43

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