A 2.0 L container is filled with hydrogen gas (H2) at 2.0 atm pressure and 273 K. It is then connected to an empty 1.0 L container, and the two containers equilibrate. Calculate the final pressure of hydrogen gas assuming ideal behavior.
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To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
We are given:
Initial volume of hydrogen = 2.0 L
Final volume of hydrogen = 2.0 L + 1.0 L = 3.0 L
Initial pressure of hydrogen = 2.0 atm
Temperature of hydrogen gas = 273 K
First, let's calculate the number of moles of hydrogen in the 2.0 L container using the ideal gas law equation:
n1 = (P1 * V1) / (R * T)
n1 = (2.0 atm * 2.0 L) / (0.0821 L*atm/mol*K * 273 K)
n1 = 0.146 moles
Now, let's calculate the number of moles of hydrogen in the final equilibrated system. Since the final pressure and temperature will be the same as the initial pressure and temperature, the moles of hydrogen will remain constant.
n_total = n1 + n2
n_total = 0.146 moles
The total number of moles of hydrogen in the final system will be 0.146 moles.
Now, let's calculate the final pressure using the ideal gas law equation:
P_total = (n_total * R * T) / V_total
P_total = (0.146 moles * 0.0821 L*atm/mol*K * 273 K) / 3.0 L
P_total = 0.408 atm
Therefore, the final pressure of hydrogen gas when the two containers equilibrate is 0.408 atm.
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