To calculate the volume of a gas at a different temperature, you can use the combined gas law, which states:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Where: P₁ = Initial pressure of the gas (assuming constant pressure) V₁ = Initial volume of the gas T₁ = Initial temperature of the gas P₂ = Final pressure of the gas (assuming constant pressure) V₂ = Final volume of the gas (to be determined) T₂ = Final temperature of the gas
Given: Initial temperature (T₁) = 27°C = 300K (converted to Kelvin) Initial volume (V₁) = 1 liter Final temperature (T₂) = 40°C = 313K (converted to Kelvin)
Assuming constant pressure, we can rearrange the equation to solve for V₂:
V₂ = (P₁ × V₁ × T₂) / (P₂ × T₁)
Since the problem does not provide pressure information and states "a gas sample was collected," we can assume the pressure is constant (as long as the gas is held under normal atmospheric pressure). Therefore, we can cancel out the pressure terms in the equation, and the equation simplifies to:
V₂ = (V₁ × T₂) / T₁
Substituting the values:
V₂ = (1 liter × 313K) / 300K
V₂ = 1.043 liters (rounded to three decimal places)
Therefore, the gas sample will occupy approximately 1.043 liters at 40°C.