Step-by-step explanation:
We have a sample of gas that has a temperature of 24°C and an unknown volume. The same sample at the same pressure has a volume of 464 mL at 81°C. We have to find the initial volume.
To solve our problem we can apply the formula that shows us the relationship between the volume and temperature of a gas sample at constant pressure.
V₁/T₁ = V₂/T₂
Where V₁ and T₁ are the initial temperature and volume and V₂ and T₂ are the final volume and temperature. We already know some of these values, but we have to convert the temperatures from °C to Kelvins, because we have to work with an absolute temperature scale (to not divide by zero).
V₁ = ?
T₁ = (273.15 + 24) K
T₁ = 297.15 K
V₂ = 464 mL
T₂ = (273.15 + 81) K
T₂ = 354.15 K
Finally we can replace these values in the formula and solve it for V₁ to get the answer to our problem.
V₁/T₁ = V₂/T₂
V₁ = V₂ * T₁/T₂
V₁ = 464 mL * 297.15 K/(354.15 K)
V₁ = 389 mL
Answer: the initial volume was 389 mL.