An ideal gas in a sealed container has an initial volume of 2.50 L. At constant pressure, it is cooled to 14.00 °C where its final volume is 1.85 L. What was the initial temperature?
(V1/T1) = (V2/T2)
Remember T must be in kelvin.
To find the initial temperature of the ideal gas, we can use the Combined Gas Law equation. The Combined Gas Law relates the initial and final states of a gas sample at constant pressure. It states:
(P1 * V1) / T1 = (P2 * V2) / T2
where:
P1 and P2 are the initial and final pressures respectively (since the problem states constant pressure, we can assume they are equal).
V1 and V2 are the initial and final volumes respectively.
T1 and T2 are the initial and final temperatures respectively.
In this problem, we have:
P1 = P2 (constant pressure)
V1 = 2.50 L
V2 = 1.85 L
T2 = 14.00 °C
Let's plug the given values into the equation:
(P1 * V1) / T1 = (P2 * V2) / T2
(P1 * 2.50) / T1 = (P2 * 1.85) / 14.00
Since P1 = P2, we can simplify the equation further:
(2.50) / T1 = (1.85) / 14.00
Now, we can solve for T1:
T1 = (2.50 * 14.00) / 1.85
T1 = 18.918918...
Rounding to the appropriate number of significant figures, the initial temperature is approximately 18.9 °C.