Answer:
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of a gas sample. The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure
V2 = Final volume
T2 = Final temperature
Let's solve the problem step by step:
Step 1: Convert the temperatures to Kelvin.
Given: T1 = 25°C, T2 = 125°C
Convert them to Kelvin:
T1 = 25°C + 273.15 = 298.15 K
T2 = 125°C + 273.15 = 398.15 K
Step 2: Determine the initial and final volumes.
Given: V1 = V2 = 20.0 L
Step 3: Substitute the values into the combined gas law equation.
For the initial condition (P1, V1, T1):
(P1 * V1) / T1 = (P2 * V2) / T2
For the final condition (P2, V2, T2):
(P2 * V2) / T2 = (P2 * 20.0) / 398.15
Step 4: Solve for P2.
(P1 * V1 * T2) / (V2 * T1) = P2
For the initial condition:
P1 = 2.00 atm (hydrogen)
V1 = 20.0 L
T1 = 298.15 K
Substituting these values:
P2 = (2.00 * 20.0 * 398.15) / (20.0 * 298.15) = 2.67 atm
So, at 25°C, the pressure in the tank is approximately 2.67 atm.
For the final condition (T2 = 398.15 K):
P2 = (2.00 * 20.0 * 398.15) / (20.0 * 398.15) = 2.00 atm
So, at 125°C, the pressure in the tank is 2.00 atm.
Please note that the volume remains constant in this problem, so it doesn't affect the pressure calculations.