1.00 mol of NH2 is stored at 77 oC in a 7.00 L container. Use the van der Waals equation to determine the pressure exerted by the 1.00 mol of NH2. (a= 4.17 atm.L2/mol2 and b= 0.0371L/mol. (R = 0.08206 L.atm/mol.K)
The van der Waals equation is:
(P + a(n/V)^2)(V-nb) = nRT
where P is the pressure, n is the number of moles, V is the volume, T is the temperature, a and b are the van der Waals constants, and R is the gas constant.
Substituting the given values:
P + (4.17 atm.L^2/mol^2)((1.00 mol)/(7.00 L))^2)(7.00 L - (1.00 mol)(0.0371 L/mol)) = (1.00 mol)(0.08206 L.atm/mol.K)(77 + 273.15)K
P + (4.17 atm.L^2/mol^2)(0.02053 mol^2/L^2)(6.963 L) = 24.684 atm
P + 0.0595 atm = 24.684 atm
P = 24.624 atm
Therefore, the pressure exerted by the 1.00 mol of NH2 is 24.624 atm.
To determine the pressure exerted by 1.00 mol of NH2 using the van der Waals equation, follow these steps:
Step 1: Write down the van der Waals equation:
(P + a(n/V)^2)(V - nb) = nRT
Where:
P = pressure in atm
a = van der Waals constant for the gas (given: 4.17 atm.L^2/mol^2)
n = number of moles of gas (given: 1.00 mol)
V = volume of the container in liters (given: 7.00 L)
b = van der Waals constant for the gas (given: 0.0371 L/mol)
R = ideal gas constant (given: 0.08206 L.atm/mol.K)
T = temperature in Kelvin (given: 77 °C)
Step 2: Convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 77 + 273.15
T(K) = 350.15 K
Step 3: Plug in the values into the van der Waals equation:
(P + a(n/V)^2)(V - nb) = nRT
(P + (4.17 atm.L^2/mol^2)(1.00 mol / 7.00 L)^2)(7.00 L - (0.0371 L/mol)(1.00 mol)) = (1.00 mol)(0.08206 L.atm/mol.K)(350.15 K)
Simplifying the equation:
(P + (4.17 atm.L^2/mol^2)(0.02041 mol^2/L^2))(7.00 L - 0.0371 L) = 0.08206 L.atm/mol.K * 350.15 K
(P + 0.1691 atm)(6.9629 L) = 28.7433 L.atm
Step 4: Multiply through the parentheses:
6.9629 P + 1.176 atm = 28.7433 L.atm
Step 5: Isolate the pressure term:
6.9629 P = 27.5673 L.atm
Step 6: Divide both sides by 6.9629 to solve for P:
P = 27.5673 L.atm / 6.9629 L
P ≈ 3.9576 atm
The pressure exerted by 1.00 mol of NH2 is approximately 3.96 atm.