a sample of air has a volume of 140.0 mL at 67 degrees C. At what temperature will its volume be 50.0 mL at constant pressure?
V1/T1 = V2/T2
T1 and T2 must be in Kelvin.
To solve this problem, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant.
Charles's Law can be represented by the equation:
V₁ / T₁ = V₂ / T₂
Where:
V₁ = initial volume
T₁ = initial temperature
V₂ = final volume
T₂ = final temperature
In this case, we're given:
V₁ = 140.0 mL
T₁ = 67°C
V₂ = 50.0 mL
Let's plug in these values and solve for T₂:
140.0 mL / (67 + 273) K = 50.0 mL / T₂
To convert Celsius to Kelvin, we add 273 to the temperature value.
(140.0 mL / 340 K) = (50.0 mL / T₂)
Next, we can cross-multiply to solve for T₂:
140.0 mL * T₂ = 50.0 mL * 340 K
140.0 T₂ = 17,000
Now, divide both sides by 140.0 to isolate T₂:
T₂ = 17,000 / 140.0
T₂ ≈ 121.4 K
Therefore, at constant pressure, the temperature at which the air sample's volume will be 50.0 mL is approximately 121.4 K.