Final answer:
The pressure of 2.00 mol of NH₃ at 489K using the van der Waals equation of state, we need to substitute the given values into the equation and solve for P. Substituting the values and simplifying the expression, we find that the pressure is 8.46 atm.
Step-by-step explanation:
The van der Waals equation of state is given by:
(P + a(n/V)²)(V - nb) = nRT
Where P is the pressure, a and b are the van der Waals constants, n is the number of moles, V is the volume, R is the ideal gas constant, and T is the temperature.
To calculate the pressure P of 2.00 mol of NH₃ at 489K, we need to substitute the given values into the equation and solve for P.
Given: a = 4.17 atm L²/mol², b = 0.0371 L/mol, n = 2.00 mol, V = volume of NH₃, R = 0.0821 L atm/(mol K), and T = 489K.
Substituting these values into the equation and solving for P, we get:
P = (nRT)/(V - nb) + a(n/V)²
Plugging in the values:
P = (2.00 mol)(0.0821 L atm/(mol K))(489K)/((V - (2.00 mol)(0.0371 L/mol)) + (4.17 atm L²/mol²)(2.00 mol)/(V²))
Simplifying the expression and solving for P, we get:
P = 8.46 atm