Some hydrogen gas is enclosed within a chamber being held at 200 whose volume is 0.0250 . Initially, the pressure in the gas is (14.8 ). The chamber is removed from the heat source and allowed to cool until the pressure in the gas falls to . At what temperature does this occur?
To solve this problem, we can use the ideal gas law equation: PV=nRT.
Given:
Initial temperature, T1 = 200 K
Initial pressure, P1 = 14.8 atm
Initial volume, V1 = 0.0250 L
Final pressure, P2 = unknown (given as blank)
Final temperature, T2 = unknown (what we need to find)
We need to find the final temperature (T2) when the pressure (P) falls to the given final pressure (P2).
First, let's find the value of n, the number of moles of hydrogen gas.
n = PV / RT
Using the initial conditions:
n = (14.8 atm * 0.0250 L) / (0.0821 atm L/(mol K) * 200 K)
n = 0.018 mol (rounded to three decimal places)
Next, we can use the ideal gas law equation to find the final temperature (T2).
P1V1 / T1 = P2V2 / T2
Rearranging the equation:
T2 = (P2V2 * T1) / (P1V1)
Substituting the known values:
T2 = (P2 * 0.0250 L * 200 K) / (14.8 atm * 0.0250 L)
Now, we can solve for T2 by substituting the given final pressure, P2, into the equation.
Therefore, the final temperature T2 when the pressure falls to P2 can be calculated by the equation above.