Question

If the collision frequency of a gas at 1 atm pressure is Z, then its collision frequency at 0.5 atm is:
A.$1.0Z$
B.$0.70Z$
C.$2Z$
D.$0.5Z$

Answer 1

Hint: The collision theory describes the gas-phase chemical reactions that occur when molecules collide with sufficient kinetic energy. Thus, the rate at which a chemical reaction occurs is equal to the frequency of effective collisions.
Collision frequency is usually defined as the number of collisions that takes place among molecules which are present in one centimetre cube of gas in one second. It is represented by Z . It varies inversely with the pressure.

Complete step by step answer:
Gas molecules collide with each other and with the wall of the container when they are in random motion. While moving they follow Brownian motion that is zig zag motion. These particles undergo perfectly elastic Collision, that is they take the shape of the container in which they collide. Gas molecules collide because they do not have intermolecular forces between them.
Collision frequency is represented by $\mathop Z\nolimits_{} $
Now let us see its relation with pressure
$Z \propto \dfrac{1}{P}$
So now,
\[\mathop Z\nolimits_1 \times \mathop P\nolimits_1 = \mathop Z\nolimits_2 \times \mathop P\nolimits_2 \]
\[\]
Now , $\mathop Z\nolimits_1 = Z$
          $\mathop P\nolimits_1 = 1atm$
         $ Z_1 = Z' $
         \[\mathop P\nolimits_2 {\text{ }} = {\text{ }}0.5{\text{ }}atm\;\]
$\mathop P\nolimits_1 = $ initial pressure
$\mathop P\nolimits_2 = $ final pressure
Now collision frequency at 0.5 atm is $\mathop Z\nolimits' $
$\mathop {Z \times 1 = \mathop Z\nolimits' \times 0.5}\nolimits_{} $

Now , \[\mathop Z\nolimits' = {\text{ }}\dfrac{Z}{{0.5}}\]
      $\mathop Z\nolimits' = \mathop {2Z}\nolimits_{} $

Our required answer is C that is $\mathop {2Z}\nolimits_{} $.


Note:
It explains why most reaction rates increase as concentration increases. When concentration of any reacting substance increases, the chances for collisions between molecules are increased due to more molecules per unit of volume resulting in faster reaction rate.
The collision frequency is the number of collisions that happen per second.
The more collisions per second there are, the more collisions can be effective and lead to product formation.