An ideal gas in a sealed container has an initial volume of 2.45 L. At constant pressure, it is cooled to 23.00 °C where its final volume is 1.75 L. What was the initial temperature?
To solve this problem, we can use the combined gas law, which relates the initial and final states of a gas system. The combined gas law equation is as follows:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 and P2 are the initial and final pressures (assuming constant pressure)
V1 and V2 are the initial and final volumes
T1 and T2 are the initial and final temperatures
In this problem, we are given the initial and final volumes (V1 = 2.45 L and V2 = 1.75 L), and the final temperature (T2 = 23.00 °C). We need to find the initial temperature (T1).
Now, to use the combined gas law equation, we need to know the values of the initial and final pressures. However, the problem statement does not provide that information.
To proceed, we can assume that the pressure remains constant throughout the process. This is a common assumption when dealing with problems involving ideal gases and constant pressure conditions.
So, let's assume the pressure is constant (P1 = P2).
Now, we can simplify the combined gas law equation and solve for T1:
(V1 / T1) = (V2 / T2)
Multiplying both sides by T1, we have:
V1 = (V2 / T2) * T1
Isolating T1, we can rearrange the equation to solve for it:
T1 = (V1 * T2) / V2
Now we can substitute the given values:
T1 = (2.45 L * 23.00 °C) / 1.75 L
Calculating this expression gives us the answer:
T1 = 32.13 °C
Therefore, the initial temperature of the gas in the sealed container was approximately 32.13 °C.