A gas mixture contains 0.60 mol of N2, 0.10 mol of H2, 0.20 mol of CH4. Calculate the pressure of the gas mixture and the partial pressure of each constituent gas if the mixture is in a 6.0 L vessel at 27C.
What is the:
Total pressure
Pressure of H2
Pressure of N2
Pressure of CH4
THANKS!!
There are a couple ways to do this but both depend upon the same process.
#1 way.
a) Use n = individual mols listed in the problem, use PV = nRT and solve for Peach as pN2, pH2, pCH4.
b) Then find ptotal = pN2 + pH2 + pCH4.
#2 way.
a. Add mols of individual gases to find ntotal, the use PV = nRT and substitute the conditions of the problem; solve for Ptotal (since you used ntotal).
b. Calculate mols fraction of each gas.
You know total mols from above,
XN2 = (pN2/total mols) = ?
XCH4 = (pCH4/total mols) = ?
XH2 = (pH2/total mols)
c. pH2 = XH2*Ptotal
pN2 = XN2*Ptotal
pCH4 = XCH4*Ptotal
#1 is easier because it's all the same formula; #2 is more interesting because you use something different. Mole fraction is important.
To calculate the total pressure and partial pressures of the constituents in the gas mixture, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres, atm)
V = volume (in liters, L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin, K)
First, let's calculate the total pressure of the gas mixture.
Step 1: Convert the temperature from Celsius to Kelvin.
T(K) = T(°C) + 273.15
T(K) = 27 + 273.15 = 300.15 K
Step 2: Calculate the total moles of the gas mixture.
Total moles = n(N2) + n(H2) + n(CH4)
Total moles = 0.60 mol + 0.10 mol + 0.20 mol = 0.90 mol
Step 3: Substitute the values into the ideal gas law equation.
PV = nRT
P * 6.0 L = 0.90 mol * (0.0821 L·atm/mol·K) * 300.15 K
Step 4: Solve for P (total pressure).
P = (0.90 mol * 0.0821 L·atm/mol·K * 300.15 K) / 6.0 L
P ≈ 3.6 atm
So, the total pressure of the gas mixture is approximately 3.6 atm.
Next, we can calculate the partial pressure of each constituent gas.
Step 1: Calculate the moles of each gas.
n(H2) = 0.10 mol
n(N2) = 0.60 mol
n(CH4) = 0.20 mol
Step 2: Calculate the partial pressure of each gas using the ideal gas law equation.
P(H2) = (n(H2) * 0.0821 L·atm/mol·K * 300.15 K) / 6.0 L
P(N2) = (n(N2) * 0.0821 L·atm/mol·K * 300.15 K) / 6.0 L
P(CH4) = (n(CH4) * 0.0821 L·atm/mol·K * 300.15 K) / 6.0 L
Calculating each partial pressure:
P(H2) = (0.10 mol * 0.0821 L·atm/mol·K * 300.15 K) / 6.0 L ≈ 0.41 atm
P(N2) = (0.60 mol * 0.0821 L·atm/mol·K * 300.15 K) / 6.0 L ≈ 2.44 atm
P(CH4) = (0.20 mol * 0.0821 L·atm/mol·K * 300.15 K) / 6.0 L ≈ 0.81 atm
Therefore, the partial pressures are:
Pressure of H2 ≈ 0.41 atm
Pressure of N2 ≈ 2.44 atm
Pressure of CH4 ≈ 0.81 atm
Please note that these values are approximate due to rounding.