Step-by-step 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