Question

The integrated rate equation for first-order reaction, A → product, is ______.

Options

• k = `1/"t" ln  (["A"]_0)/(["A"]_"t")`

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

• k = - `1/"t" ln  ["A"]_"t"/["A"]_0`

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

Answer 1

The integrated rate equation for first order reaction, A → product, is `underline("k" = - 1/"t" ln  ["A"]_"t"/["A"]_0)`.

Explanation:

The integrated rate equation for first-order reaction, A → product is k = - `1/"t" ln  ["A"]_"t"/["A"]_0`.

For 1st order reactions, R → P

Rate = `(- "d"["R"])/"dt" = "k"["R"]`

On integrating this equation, we get

ln[R] = - kt + I     ...(i)

At t = 0, R = [R]₀ , ln[R]₀ = - k × 0 + I

ln[R]₀ = l

Substituting the value of I in (i) and on rearrangement, we get

ln[R] = - kt + lnR₀

and, `"k" = 1/"t" ln  ["R"]_0/(["R"])`