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A 38.3 L sample of gas at 30.4°C and 273.5 mm Hg expands to 256.9 L at 18.2°C. What is the new gas pressure?

A. 39.1 mm Hg
B. 24.4 mm Hg
C. 42.5 mm Hg
D. 2.44 mm Hg

Answer :

Explanation:

We have a sample of gas that at 30.4 °C and 273.5 mmHg of pressure occupies 38.3 L. The gas expands to 256.9 L at 18.2 °C.

We are working with a gas and we know the initial conditions of temperature, pressure and volume, and know the final temperature and volume but not the pressure. We can apply the following formula.

P₁ * V₁/T₁ = P₂ * V₂/T₂

Where P₁, V₁ and T₁ are the initial conditions and P₂, V₂ and T₂ are the final conditions. We know the values of them, and we can convert the temperature from °C to K.

P₁ = 273.5 mmHg

V₁ = 38.3 L

T₁ = (30.4 + 273.15) K

T₁ = 303.55 K

P₂= ?

V₂ = 256.9 L

T₂ = (18.2 + 273.15)

T₂ = 291.35 K

We can replace these values in the formula and solve it for the final volume.

P₁ * V₁/T₁ = P₂ * V₂/T₂

P₂ = (P₁ * V₁ * T₂)/(T₁ * V₂)

P₂ = (273.5 mmHg * 38.3 L * 303.55 K)/(291.35 K * 256.9 L)

P₂ = 42.5 mmHg

Answer: c. 42.5 mmHg

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