a 1.00 vessel at 0 degrees celcius contains 0.17 mols n2 1.0 mols h2 and 1.0 mols CH4 calculate the pressure of the gas mixture and the partial pressure of each constituent gas in the mixture.
Ptotal= ?
Pn2=?
Ph2=?
PCH4?
The easy way to do this is to use PV = nRT for each gas (that will be the partial pressure of each), then add all of them for the total pressure.
To calculate the pressure of the gas mixture and the partial pressure of each constituent gas in the mixture, we need to apply the ideal gas law.
The ideal gas law equation is given by:
PV = nRT
Where:
P = Pressure of the gas
V = Volume of the container
n = Number of moles of the gas
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature in Kelvin
First, let's start by converting the temperature from Celsius to Kelvin.
Given:
Temperature (T) = 0 degrees Celsius
To convert from Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
T(K) = 0 + 273.15
T(K) = 273.15 K
Now, let's calculate the pressure of the gas mixture using the total number of moles and the ideal gas law.
Given:
Total moles of gases (n_total) = 0.17 mol N2 + 1.0 mol H2 + 1.0 mol CH4 = 2.17 mol
Using the ideal gas law equation:
P_total = (n_total * R * T) / V
Assuming the volume (V) is 1.00 L (as given in the problem):
P_total = (2.17 mol * 0.0821 L·atm/mol·K * 273.15 K) / 1.00 L
P_total ≈ 50.83 atm
Therefore, the pressure of the gas mixture (P_total) is approximately 50.83 atm.
Now, let's calculate the partial pressure for each constituent gas using the mole fractions and the pressure of the gas mixture (P_total).
Given:
Moles of N2 (n_N2) = 0.17 mol
Moles of H2 (n_H2) = 1.0 mol
Moles of CH4 (n_CH4) = 1.0 mol
Mole fraction (X) of a gas is calculated by dividing the number of moles of that gas by the total number of moles of all gases.
Mole fraction of N2 (X_N2) = n_N2 / n_total
X_N2 = 0.17 mol / 2.17 mol ≈ 0.0784
Mole fraction of H2 (X_H2) = n_H2 / n_total
X_H2 ≈ 0.4619
Mole fraction of CH4 (X_CH4) = n_CH4 / n_total
X_CH4 ≈ 0.4619
Now, let's calculate the partial pressure for each gas by multiplying the mole fraction of each gas by the total pressure of the gas mixture (P_total).
P_N2 = X_N2 * P_total
P_N2 ≈ 0.0784 * 50.83 atm ≈ 3.99 atm
P_H2 = X_H2 * P_total
P_H2 ≈ 0.4619 * 50.83 atm ≈ 23.44 atm
P_CH4 = X_CH4 * P_total
P_CH4 ≈ 0.4619 * 50.83 atm ≈ 23.44 atm
Therefore, the partial pressure of N2 (P_N2) is approximately 3.99 atm, the partial pressure of H2 (P_H2) is approximately 23.44 atm, and the partial pressure of CH4 (P_CH4) is approximately 23.44 atm.