Hydrogen gas is confined within a closed vessel at 1 atm ( 100 kPa ) and 300 K . Assume that the molecules strike the wall with their mean speed, making an average angle of 45^ with the wall. Calculate the number of molecules striking each square metre of the wall per second.

Step-by-step solution

Mean speed of hydrogen molecules is given by: v = 8RT M Substituting the given values: v = 8 8.314 300 2 10⁻³ 1782 m/s Mass of one hydrogen molecule is: m = M N_A = 2 10⁻³ 6.022 10²³ 3.32 10⁻²⁷ kg When a molecule strikes the wall at an angle of 45^ with the wall, the component of velocity perpendicular to the wall is v 45^ = v 2 . The change in momentum of each molecule upon elastic collision is: p = 2 m v_ = 2 m ( v 2 ) = 2 m v Let n be the number of molecules striking per unit area per second. The total change in