Question #19873
8kg of gaseous N2 occupy 100 L flask at 300C. What's the pressure of the gas, using van der Waals equation? What's the pressure of the gas, using the ideal gas equation? What are the shortcomings of kinetic molecular theory that lead to the deviation in this calculation?
Expert's answer
1) The van der Waal'sequation is
[P + (n^2a)/V^2]*[V - nb] = nRT
P = (nRT/(V - nb)) - ((n^2a)/V^2)
For nitrogen, a = 1.408 and b = 0.03913. Plugging in these values, along with n
and V, we get
P is pressure in atm = ???
V is volume in L = 100L
n is mol = 8000/28 = 285,714
R is the universal gas constant = 0.08206
T is temperature in K = 300K
P = (nRT/(V - nb)) - ((n^2a)/V^2) = (( 285,714 * 0.08206 *300)/(100L - (
285,714 * 0.03913 ))) - ( 285,714 * 285,714 *1.408/100*100) = 67.79
atm = 6867.45 kPa
2) P = nRT/V = 285,714 *8.31*300/100 = 7122.85 kPa
3) This theory rejects the volumes of gases, considered them ideal.
[P + (n^2a)/V^2]*[V - nb] = nRT
P = (nRT/(V - nb)) - ((n^2a)/V^2)
For nitrogen, a = 1.408 and b = 0.03913. Plugging in these values, along with n
and V, we get
P is pressure in atm = ???
V is volume in L = 100L
n is mol = 8000/28 = 285,714
R is the universal gas constant = 0.08206
T is temperature in K = 300K
P = (nRT/(V - nb)) - ((n^2a)/V^2) = (( 285,714 * 0.08206 *300)/(100L - (
285,714 * 0.03913 ))) - ( 285,714 * 285,714 *1.408/100*100) = 67.79
atm = 6867.45 kPa
2) P = nRT/V = 285,714 *8.31*300/100 = 7122.85 kPa
3) This theory rejects the volumes of gases, considered them ideal.
