Suppose the order of reaction of a chemical reacting system is $n,$ that is$,$

$\frac{dC}{dt}=-k{C}^n$

where $C$ is the concentration of the reacting species. Show that the rate of change of mole fraction of reacting species, $d\frac{x}{d}t,$ is proportional to $-k{x}^n{}^{n-1}.$ What is the pressure dependence of $d\frac{x}{d}t?$ List your assumptions. Can we say that

$\frac{d}{dt}$prop$-k{}^n{}^{n-1}$

where $$ is the reaction progess variable defined by Eq$.(1-12)$ in Chapter $1?$