Gas Laws: Boyle’s, Charles’, Ideal gas equation and Dalton’s law of partial pressure

CONTENT

• Boyle’s law
• Charles’ law
• Ideal gas equation
• Dalton’s law of partial pressure

BOYLE’S LAW

It states that the volume of a fixed mass of gas is inversely proportional to the pressure provided the temperature remains constant.

Mathematically,

       V α 1/P

       V = k/P

       PV = k

Hence,               P₁V₁ = P₂V₂

EXPLANATION OF BOYLE’S LAW USING THE KINETIC THEORY

When the volume of fixed mass of gas is decreased, the molecules of the gas will collide with each other more rapidly. This gives rise to an increase in pressure. However, if molecules are farther apart the number of collisions for unit time decreases, resulting in a decrease in pressure.

CHARLES’ LAW

Charles’ law states that the volume of a fixed mass of gas at constant pressure is directly proportional to its temperature in the Kelvin scale.

EXPLANATION OF CHARLES’ LAW USING THE KINETIC THEORY

When a given gas is heated at constant pressure, the molecules acquire more kinetic energy and move faster. They collide with one another and with the walls of the container more frequently. To maintain the same number of collisions on the walls of container (i.e. keep the pressure constant) the volume of the gas increases.

EVALUATION

1. State Boyle’s law

2. Explain Charles’ law using the kinetic theory

GENERAL GAS EQUATION

Boyle’s and Charles’ laws are combined into a single expression known as the general gas equation which can be expressed mathematically as

   P₁V₁ = P₂V₂

     T₁T₂

IDEAL GAS EQUATION

This equation states that for an ideal gas PV/T is a constant.

That is, PV/T = R (R = molar gas constant)

             PV = RT

That is, for n mole of a gas, the equation becomes

             PV = nRT

DALTON’S LAW OF PARTIAL PRESSURE

This law state that in a mixture of gases which do not react chemically together, the total pressure exerted by the mixture of gases is equal to the sum of the partial pressure of the individual gases that make up the mixture.

GENERAL EVALUATION/REVISION

1. State Dalton’s of partial pressure.
2. Calculate the pressure at 27^oC of 16.0g O₂ gas occupying 2.50dm³
3. A certain mass of hydrogen gas collected over water at 10^oC and 760mmHg pressure has     a volume of 37cm³. Calculate the volume when it is dry at s.t.p (Saturated vapour     pressure of water at 10^oC =1.2mmHg)
4. Determine the number of electrons, protons and neutrons in each of the following: ³⁹K_19,       ^63.5Cu₂₉.
5. If an element R has isotopes 60% of ¹²R₆ and 40% ^xR₆ and the relative atomic mass is      12.4, find x.

READING ASSIGNMENT

New School Chemistry for Senior Secondary School by O.Y. Ababio, Pg 78-85.

WEEKEND ASSIGNMENT

1. Kelvin temperature can be converted into temperature by A.^oC = K-273 B. K + 273 C.^oC + 273/K D. K + 273/^oC
2. The pressure exerted by a gas is a result of the A. continuous random motion of its particle.

B. bombardment of the walls of the container by its molecules. C.expansion of the gas molecules

D. collision between the gas molecules.

• From the ideal gas equation, PV = nRT, the unit of n is A. atmdm³B. atmdm³/K C. mole D. K/mole
• What will be the new volume (V) if the new pressure is halved and the initial pressure      remain the same the sameA. 2P₁V₁ = P₂V₂B. P₁V₁ = 2P₂V₂C. P₁V₁/2= P₂V₂/2     D. P₁V₁ = P₂V₂/2
• A fixed mass of gas of volume 546cm3 at 0^oC is heated at constant pressure. What is     the volume of the gas at 2^oC? A. 550cm³B. 560cm³C. 570cm³D. 580cm³

THEORY

1. A given mass of nitrogen is 0.12dm³ at 60^oC and 1.01 x 10⁵Nm^-2. Find its pressure at the    same temperature if its volume is changed to 0.24dm³
2. 272cm3 of CO2 was collected over water at 15^oC and 782mmHg pressure. Calculate the     volume of dry gas at s.t.p (saturated vapour pressure of water at 15^oC is 12mmHg).