Is the pressure of real gas greater than ideal gas?According to ideal gas equation pv=nRt and vanderwaals equation for real gas is (p+a/v ^2)(v-b)=Rt.Here p in vanderwalls equation accounts for pressure of ideal gas pressure. When we compare both ideal gas equation and real gas equation,we find that pressure of real gas is greater than pressure of ideal gas.But pressure of real gas is less than pressure of ideal gas because of the presence of inter molecular forces of attractions which causes inward drag of molecules of real gas resulting them to collide with a reduced pressure on the walls of the container.

The interesting thing (!) is that the pressure of real, or Van-der-Waals, gases can be either higher or lower than the pressure of the ideal gas, depending on the density of the real gas. At lower densities, during isothermal compression real gas first compresses easier that the ideal gas (because of molecular attraction -> lower pressure) and after a certain density is reached, real gas compresses harder than the ideal (because, when dense enough, gas molecules start repelling each other -> pressure goes up). Rewrite the VdW equation this way: P = RT/(V-b) - a/V^2, multiply by V: PV = RTV/(V-b) - a/V; then introduce density: d = M/V, here M - molecular mass of gas, so that: PV = RT/(1-b(d/M)) - a(d/M).

Plot PV as a function of density d and you will see that this function has a minimum. As d increases, PV first drops and then goes up.

Alternatively, you can compare real gas pressure P = RT/(V-b) - a/V^2 and ideal gas pressure P = RT/V with fixed values of a, b and T, but varying V. You will see that at some values of V, P(real) is higher than P(ideal), at other values of V, P(real) is lower than P(ideal).