# Which of the following is correct expression for an irreversible nth order reaction?

$\begin{array}{1 1} kt = \large\frac{n}{n-1}\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big) \\ kt = \large\frac{1}{n}\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big) \\ kt = \large\frac{1}{n-1}\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big) \\ kt = (n-1)\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big)\end{array}$

Answer: $kt = \large\frac{1}{n-1}$$\big($$\large\frac{1}{[A]^{n-1}}$$- \large\frac{1}{[A_0]^{n-1}}$$\big)$
Given: $nA \overset{k} \rightarrow \text{Products}$
Rate Equation: $-\large\frac{d[A]}{dt}$$= k[A]^n = n\large\frac{d[P]}{dt} Integrating, we get: \large\frac{1}{[A]^{n-1}}$$ - \large\frac{1}{[A_0]^{n-1}}$$= (n-1)kt \Rightarrow kt = \large\frac{1}{n-1}$$\big($$\large\frac{1}{[A]^{n-1}}$$ - \large\frac{1}{[A_0]^{n-1}}$$\big)$
edited Jul 26, 2014