A gas occupies 255 mL at 479.6 Torr and 21.0 °C. When the pressure is changed to 558.6 Torr, what temperature is needed to maintain the same volume?
To solve this problem, we can use the combined gas law, which states:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures, respectively
V₁ and V₂ are the initial and final volumes, respectively
T₁ and T₂ are the initial and final temperatures, respectively
We are given:
P₁ = 479.6 Torr
V₁ = 255 mL
P₂ = 558.6 Torr
V₂ = 255 mL
Our objective is to find T₂. We can rearrange the equation to solve for T₂:
T₂ = (P₂ * V₂ * T₁) / (P₁ * V₁)
Substituting the values:
T₂ = (558.6 Torr * 255 mL * 21.0 °C) / (479.6 Torr * 255 mL)
Now, let's calculate T₂:
T₂ = (558.6 * 255 * 21.0) / (479.6 * 255)
= (299371.7) / (122408.8)
≈ 2.445 °C
Therefore, to maintain the same volume when the pressure is changed to 558.6 Torr, the temperature needed is approximately 2.445 °C.