Gas Laws
Introduction
Many phenomenon familiar to you are caused by gases that fill the atmosphere. Your are able to hear the sound of thunder. Aircrafts can fly in air and you can feel the sea breeze because of certain physical properties of gases. Liquids, solids and gases respond to pressure and temperature differently. This is because density, kinetic energy and the number of molecules contained in a fixed volume is different for each state of matter. Many gaseous substances are used in chemistry. Scientists have hence formulated many rules about the nature of gases and also ways to measure the properties of gases. Scientists have formulated these rules by observing how gases behave in different situations and linking this to their properties. Based on these laws, changes observed in gaseous substances that are used or produced in chemical experiments can be explained: Various measures for gases are also needed to explain the experiments.
You know that ice, water and steam can be changed from one state to another. How does the following changes occur?
Steam to water
Water to ice
Ice to water
The above changes are due to the differ in temperature level.
Let us see what happens to the molecular arrangement when such a change occurs. A diagrammatic representation of the molecular arrangement in the three states of matter is given below:
- Is the molecular arrangement in the three states same?
- In which state are the molecules very closely packed?
- In which are the molecules very far apart?
- In which state is the molecular force of attraction very weak? In which state is the force of attraction very strong and why?
- Compare the movement of molecules in gas, liquid and solid and note down your inferences.
- On the basis of motion of molecules explain in which state does diffusion take place easily? In steam or in ice?
Write the answers of the above question in their science diary.
From the statement given below select and write down those applicable to gases in science diary.
- Freedom for movement of molecules is limited.
- Molecules are far apart.
- Molecules are closely packed.
- Molecules can move about to some extent.
- Molecular motion is very great.
- Intermolecular force of attraction is very great.
- Intermolecular force of attraction is very weak.
The above three states contains equal number of molecules. But they have different volume due to the molecular arrangement. The volume is high in the case of gases.
You know that density is the mass per unit volume. If the volume of 2 g of matter in solid, liquid and gas is 4, 4.6 and 400 mL respectively, find out the density. Compare the densities of solids, liquids and gases and complete the table.
Solid | Liquid | Gas |
Density is higher than liquids and gases | Density is less than solids | Density is less than solids and liquids |
Find out the reason why gases have much lower densities and make notes in your science diary.
In gaseous state large inter molecular space is present. This vacant space contains another molecules.
The molecules are in a state of constant, rapid motion in all directions and during their motion they collide with one another and also with the walls of the containing vessel. As a result, walls of the containing vessel experience an outward force. This force per unit area on the walls is called pressure is expressed in the unit atmosphere(atm).
On increasing the temperature of the gas, the molecule motion and kinetic energy of molecules increases. What happens if the temperature is decreased and an external pressure is applied? On the basis of the following, discuss and prepare notes.
- Kinetic energy of molecules
- Molecular motion
- Disorder of molecules
- Intermolecular space
When gas molecules come closer, the molecular motion decreases and the molecular arrangement then resembles that of liquid. So gases can be liquefied.
Gas Laws
From the above, it is clear that physical behaviour of gases can be described in terms of temperature, volume and pressure. These characteristics of a gas are inter related and these relations are explained in gas laws.
Boyle’s Law
Presentation
Apply pressure on a gas filled balloon, the volume is changed. The reason of that is discussed here.
The experiment of the application of pressure on syringe filled with gas is diagrammatically represented below:
Pressure P(atmosphere pressure) | P1 1 | P2 1.5 | P3 2 | P4 2.5 | P5 3 |
Volume V (Litres) | V1 24.46 | V2 16.306 | V3 12.23 | V4 9.78 | V5 8.153 |
From the above table shows that increase in pressure, the volume of the gas decreases. This relationship is known as Boyle’s Law.
According to Boyle’s Law the volume of a given mass of a gas is inversely proportional to its pressure at constant temperature.
The mathematical relationship between volume and pressure is given below:
V α 1
P
To remove the proportionality sign, multiply with constant
ie. V = constant x 1
P
Find out the value of PV from the above table and record in the below table
ie. PV = a constant
P1V1 | P2V2 | P3V3 | P4V4 | P5V5 | |
PV |
Two factors influence the value of PV
- Amount of gas changes
- Temperature changes
From the above table the quantitative relationship between the four variables P1, V1 P2 and V2 is found to be P1V1 = P2V2. This is another statement of Boyle’s Law.
From the above relation, V2 = P1V1
P2
A gas occupies a volume of 5 L at 1 atmospheric pressure. What would be the volume of the gas at 2 atmospheric pressure if temperature is kept constant?
P1 = 1 atm V1 = 5L
P2 = 2 atm V2 = ?
According to Boyle’s Law
P1V1 = P2V2
V2 = P1V1 = 1x5 = 2.5L
P2 2
Robert Boyle (1627 – 1691)
Robert Boyle, son of a rich industrialist of Ireland
Charles Law
Presentation
When a balloon is exposed to sunlight, does the volume of the balloon change? Why does the balloon broken after sometime? The reason of that is discussed here.
The above figure shows that when temperature increases the intermolecular space of the molecules also increase that is volume increases.
The graphical representation is given below:
Temperature (T) | Volume (V) | V T |
253 263 303 313 | 92.5 96.15 110.16 113.81 |
From the above table shows that the value of V is constant.
T
The mathematical representation is given below:
V = constant
T
V = constant x T
V α T
The relationship between temperature of a gas and volume occupied by it at constant pressure was first experimentally studied by Jacques Charles.
According to Charles Law pressure remaining constant, the volume of a given mass of gas is directly proportional to its temperature on Kelvin scale.
According to this Law at constant pressure and number of moles of gas of volume V1 and V2 and their temperature T1 and T2 respectively the relationship between them is given below:
V1 = V2
T1 T2
Jacques Charles
The relationship between temperature of a gas and volume occupied by it at constant pressure was experimentally studied by Jacques Alexander Charles in 1787. On the basis of this he put forward a law which states that “at constant pressure, the volume of a given mass of gas increases or decreases by 1/273 of its original volume at 0˚C for each degree celcius rise or fall in temperature”. To get temperature value in degree celcius.
ie. 0˚C = 0 + 273 = 273 K
If the temperature of 2 L of a gas is increased from 300 K to 310 K at constant pressure, calculate the final volume.
T1 = 300 K, T2 = 310 K, V1 = 2L, V2 = ?
According to Charles Law V1 = V2
T1 T2
V2 = V1T2 = 2 x 310 = 2.066 L
T1 300
Avagadro’s Law
Avagadro proposed that under the same conditions of temperature and pressure the volume of a gas varies directly as the number of moles of the gas (n).
Mathematically V α n
V = Volume
n = Number of moles
Standard Temperature and Pressure (STP)
The volume of the gases is dependent on pressure and temperature. A standard measure of these values is needed to state the volume of gases. 273 K and 1 atmospheric pressure is taken as standard. These conditions are termed Standard Temperature and Pressure, abbreviated as STP.
Molar Volume
The volume of one mole of any gas is called molar volume. It has been experimentally proven that the volume of 1 mole of any gas at S.T.P is 22.4 litres.
Ideal Gas Equation
The above three laws may be combined to derive a general relationship.
According to Boyles Law V α 1 (n, T constant)
P
According to Charles Law V α T (n, P constant)
According to Avagadro’s Law V α n (P,T constant)
Combining the three
V α 1 x T x n
P
ie. V α nT or V = a constant x nT
P P
This constant is known as universal gas constant and is denoted as R.
Then V = R x n x T
P
PV = n x R x T
i.e., PV = nRT
This equation is called ideal gas equation. A gas that obeys the ideal gas equation strictly at all temperatures and pressures is called an ideal gas.
From the table given below, calculate
- PV
- Relation between P1V1 and P2V2 for each gas.
PV = nRT can also be written as PV = nR
T
If n and R are constant, then PV will also be a constant.
T
Gas | Pressure (P atm) | Volume (V) mL | Temperature T (K) | PV T |
Nitrogen | 1 (P1) 0.825 (P2) | 320 (V1) 482 (V2) | 273 (T1) 339 (T2) | |
Helium | 2.5(P1) 15.16 (P2) | 285(V1) 27.5 (V2) | 298 (T1) 1744.3 (T2) |
