Question

If [A] is the concentration of A at any time t and [A]₀ is the concentration at t = 0, then for the 1^st order reaction, the rate equation can be written as ____________.

Options

• k = `2.303/"t" log_10  (["A"])/(["A"]_0)`

• [A] = [A]₀ e^−kt

• k = `2.303/"t" log_10  (["A"]_0)/(["A"]_0 - ["A"])`

• k = `2.303/"t" log_10  (["A"]_0 - ["A"])/(["A"]_0)`

Answer 1

If [A] is the concentration of A at any time t and [A]₀ is the concentration at t = 0, then for the 1^st order reaction, the rate equation can be written as [A] = [A]₀ e^−kt.

Explanation:

For the first order reaction, the rate equation can be written as,

k = `2.303/"t" log_10  (["A"]_0)/(["A"]_"t")`

∴ kt = `ln  (["A"]_0)/(["A"]_"t")`

Taking antilog on both sides,

[A] = [A]₀ e^−kt