Calculating Temperature using the Combined Gas Law

Calculation of Temperature in Celsius

Question: Suppose that the volume of a particular sample of Cl2 is 718 mL at 675 mmHg and 48°C. At what temperature in Celsius will the volume be 2.0 L if the pressure is 159 kPa?

Answer:

This problem involves using the Combined Gas Law to calculate the final temperature when the volume and pressure of a gas change.

Step-by-step explanation:

This looks like a case where we can use the Combined Gas Law to calculate the temperature.

p₁V₁/T₁ = p₂V₂/T₂

Multiply both sides by T₂:

p₁V₁T₂/T₁ = p₂V₂

Multiply each side by T₁:

p₁V₁T₂ = p₂V₂T₁

Divide each side by p₁V₁:

T₂ = T₁ × p₂/p₁ × V₂/V₁

Data:

We must convert the pressures to a common unit. I have chosen atmospheres.

p₁ = 675 mmHg × 1atm/760 mmHg = 0.8882 atm

V₁ = 718 mL = 0.718 L

T₁ = 48 °C = 321.15 K

p₂ = 159 kPa × 1 atm/101.325 kPa = 1.569 atm

V₂ = 2.0 L

T₂ = ?

Calculation:

T₂ = 321.15 × 1.569/0.8882 × 2.0/0.718

T₂ = 321.15 × 1.766 × 2.786

T₂ = 321.15 × 1.569/0.8882 × 7.786

T₂ = 1580K

T₂ = 1580 + 273.15

T₂ = 1900 °C

Note: The answer can have only two significant figures because that is all you gave for the second volume of the gas.

Can the Combined Gas Law be used to calculate the temperature of a gas in different conditions?

Yes, the Combined Gas Law can be used to calculate the temperature of a gas when the volume and pressure change, given the initial conditions.