Question

What are the main characteristics of a first order reaction?

State the important characteristics of a first order reaction.

Answer 1

1. The rate of a first-order reaction is directly proportional to the concentration of the reactant.
   Rate ∝ [A]
   When the concentration is doubled, the rate also gets doubled.
2. The rate constant of a first-order reaction has the units of time⁻¹. Thus, the units of k are s⁻¹, min⁻¹, hour⁻¹, etc.
3. A first-order reaction obeys the following equations.
   [A] = [A]₀ e^−kt
   \[\ce{k = \frac{2.303}{t} log_10 \frac{[A]_0}{[A]}}\]
   \[\ce{\frac{2.303}{t} log_10 \frac{a}{a - x}}\]
   The meaning of the various terms involved in these equations is the same as discussed earlier.
4. For a first-order reaction, log₁₀ [A] plotted against t is a straight line. This line’s slope is determined by
   slope = \[\ce{\frac{k}{2.303}}\]
5. A first-order reaction's half-life is unaffected by the starting concentration. It is totally dependent on the reaction's rate constant value. The two are connected in that
   \[\ce{t_{1/2} = \frac{0.693}{k}}\]
6. The initial concentration has no effect on how long it takes for any fraction of a first-order reaction to finish. Here is one way to show this.
   For a first-order reaction,
   \[\ce{t = \frac{2.303}{k} log_10 \frac{a}{a - x}}\]
   Suppose the time required for the completion of n^th fraction of the reaction is t_1/n. Therefore,
   \[\ce{x = \frac{a}{n}}\] and t = t_1/n
   Substituting the values, we get
   \[\ce{t_{1/n} = \frac{2.303}{k} log_10 \frac{a}{a - \frac{a}{n}}}\]
   \[\ce{= \frac{2.303}{k} log_10 \frac{1}{1 - \frac{1}{n}}}\]
   \[\ce{t_{1/n} = \frac{2.303}{k} log_10 \frac{n}{n - 1}}\]

Answer 2

1. The rate of reaction, or rate ∝ [A], is directly proportional to the reactant concentration.
2. The rate constant has the units of time⁻¹.
3. A first order reaction obeys eqs. [A] = [A]₀ e^−kt, \[\ce{k = \frac{2.303}{t} log_10 \frac{[A]_0}{[A]}}\] and \[\ce{k = \frac{2.303}{t} log_10 \frac{a}{a - x}}\].
4. A plot of log₁₀[A] against tis a straight-line with a slope equal to −k/2.303.
5. The half-life of a first order reaction is independent of the initial concentration.
6. The time taken for the completion of any fraction of a first order reaction is independent of initial concentration.