The uncatalyzed conversion of to products follows the rate law ( rate _ un = k_ un…

CHEMISTRY · Subjective · A Level · Chemistry · Rate equations · Rate equations

Problem

The uncatalyzed conversion of

X

to products follows the rate law

\text{rate}_{\text{un}} = k_{\text{un}}[X]^2

with

k_{\text{un}} = 1.5\times10^{-3}\,\text{M}^{-1}\text{s}^{-1}

25^{\circ}\text{C}

. In the presence of catalyst

C

, an alternative pathway obeys

\text{rate}_{\text{cat}} = k_{\text{cat}}[C][X]

with

k_{\text{cat}} = 2.0\times10^{2}\,\text{M}^{-1}\text{s}^{-1}

. A reaction mixture at

25^{\circ}\text{C}

initially contains

[X] = 0.80\,\text{M}

and

[C] = 1.0\times10^{-3}\,\text{M}

. Calculate the initial overall rate of disappearance of

X

(include appropriate units).