Q.Derive an expression for a pressure exerted by a gas on the basis of kinetic theory of gases.

Sum the momentum transferred per collision over all molecules hitting a wall, per unit time and area, to get the pressure.

Consider $N$ gas molecules of mass $m$ each in a cubical container of side $L$ (volume $V=L^3$). Consider one molecule moving with velocity component $c_x$ perpendicular to a wall. On elastic collision with the wall, its momentum change is $2mc_x$. It returns to hit the same wall after time $2L/c_x$, so the average force it exerts on that wall is $\dfrac{2mc_x}{2L/c_x} = \dfrac{mc_x^2}{L}$.

Summing over all $N$ molecules, the total force on the wall is $\dfrac{m}{L}\sum c_x^2 = \dfrac{Nm\langle c_x^2\rangle}{L}$. Pressure = force/area:

$P = \frac{Nm\langle c_x^2\rangle}{L\cdot L^2} = \frac{Nm\langle c_x^2\rangle}{V}$ …