Question

(a) Define Collision frequency.

(b) Write the units of

(i) first order reaction and (ii) zero order reaction

Hint:

Collision frequency is the number of collisions per unit volume per second. Units of k: first order is s^-1, zero order is mol L^-1 s^-1.

Answer 1

Step 1: Understanding the Question:
Part (a) asks for a definition from collision theory. Part (b) asks for the units of the rate constant \(k\) for first and zero order reactions.

Step 2: Collision frequency (a):
In collision theory, a reaction needs molecules to collide first. The number of such collisions is counted per unit volume and per unit time.
Collision frequency (Z) is the number of collisions per second per unit volume of the reaction mixture.
It depends on temperature and on the concentration of the reactants.

Step 3: Units of the rate constant (b):
For a reaction of order \(n\), the rate is \(\mathrm{rate} = k[A]^n\). So the unit of \(k\) is the unit of rate divided by the unit of concentration to the power \(n\).
\[ \text{unit of } k = \frac{\mathrm{mol\ L^{-1}\ s^{-1}}}{(\mathrm{mol\ L^{-1}})^{n}} \]

Step 4: First order reaction (b)(i):
Put \(n = 1\).
\[ k = \frac{\mathrm{mol\ L^{-1}\ s^{-1}}}{\mathrm{mol\ L^{-1}}} = \mathrm{s^{-1}} \]

Step 5: Zero order reaction (b)(ii):
Put \(n = 0\). The concentration factor is 1.
\[ k = \mathrm{mol\ L^{-1}\ s^{-1}} \]

Final Answer:
(a) Collision frequency is the number of collisions per unit volume per second. (b)(i) First order: \(\mathrm{s^{-1}}\). (ii) Zero order: \(\mathrm{mol\ L^{-1}\ s^{-1}}\). \[ \boxed{k_1 : \mathrm{s^{-1}};\quad k_0 : \mathrm{mol\ L^{-1}\ s^{-1}}} \]