Since, the molecules rebound from the wall, the component of velocity perpendicular to wall is reversed,  while its velocity parallel to wall does not change. The change in velocity of molecules is parallel to normal N. The magnitude of charge is

                         $\left|\Delta \overrightarrow{\text{v}}\right|=2v\text{cos}\theta$

The change in momentum of a molecule is

                         $\left|\Delta \overrightarrow{\text{p}}\right|=m\left|\Delta \overrightarrow{\text{v}}\right|$

                          $=2mv\text{cos}\theta$

in the direction of normal N. Let n be the number of molecules per unit volume.The number of molecules arriving at an area A of the wall per unit time is the number in a slanted cylinder whose length is equal to the velocity v and whose cross-section is $\mathrm{A} \cos \mathrm{\theta }$

       Number of molecules $=\mathrm{n}\left(\mathrm{Av} \cos \mathrm{\theta }\right)$.

Each molecule suffers a change of momentum $2\mathrm{mv} \cos \mathrm{\theta }$. Change of momentum of the stream of gas in a direction perpendicular to wall is equal to $\left(\mathrm{nAv} \cos \mathrm{\theta }\right)\times \left(2\mathrm{mv} \mathrm{cos\theta }\right)=2 \mathrm{An} {\mathrm{mv}}^2{\cos }^2\mathrm{\theta }$.

Hence, force exerted by stream of gas on the wall.

                        $\mathrm{F}=2\text{A}\mathrm{n}{\text{mv}}^2{\text{cos}}^2\mathrm{\theta }$

This is also the force exerted by gas molecules on the wall.

                        $\text{Pressure}=\frac{\text{Normal force}}{\text{Area}}$

                            $=\frac{\mathrm{F}}{\mathrm{A}}$

                            $=2\mathrm{n}\mathrm{m}\mathrm{v}{}^2{\text{cos}}^2\mathrm{\theta }$