Gay-Lussac's Law

Formula and Derivation

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

Or, P1T2 = P2T1

Solved Exercises on Gay-Lussac’s Law

Exercise 1

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,

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.

Exercise 2

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.

Initial pressure, P1 = 3 atm

Initial temperature, T1 = 300K

Final temperature, T2 = 900 K

Therefore, final pressure (P2) = (P1T2)/T1 = (3 atm*900K)/300K = 9 atm.

Frequently Asked Questions – FAQs

What is Gay Lussac’s law formula?

The law of Gay-Lussac is a variant of the ideal gas law where the volume of gas is held constant. The pressure of a gas is directly proportional to its temperature while the volume is kept constant. P / T = constant or Pi / Ti = Pf / Tf are the standard calculations for Gay-Lussac ‘s law.

What does Charles law state?

The physical theory known as Charles’ law states that a gas’s volume equals a fixed value as determined on the Kelvin scale compounded by its temperature.

What is the importance of Gay Lussac’s law?

The meaning of this gas law is that it illustrates that rising a gas’s temperature induces a relative increase in its pressure (assuming that the volume does not change). Likewise, reducing the temperature allows the strain to decrease proportionally.

How does Avogadro’s law apply to everyday life?

The Law of Avogadro states that the amount of the gas is directly proportional to the number of gas moles. You are driving more molecules of gas into it when you blow up a football.

What are the applications of Avogadro’s law?

The relationship between a gas’s relative vapour density and its relative molecular mass is defined. Establishes the relationship between the volume of a gas at STP and gram molecular weight.

Avogadro's Law

where P is the pressure, T is the absolute temperature, and k₃ is another proportionality constant.

Avogadro's Law states that the volume occupied by an ideal gas is directly proportional to the number of molecules of the gas present in the container. This gives rise to themolar volume of a gas, which at STP (273.15 K, 100 kPa) is about 22.7 l/mol.

where n is equal to the number of molecules of gas (or the number of moles of gas).