# For reaction $X+Y\rightarrow Z$ the reaction rate is found to depend only upon concentration of X. A plot of $\large\frac{1}{[X]}$ vs time gives a straight line. What is rate law for this reaction?

$\begin{array}{1 1}(a)\;rate=k[X]\\(b)\;rate=k[X]^2\\(c)\;rate=k[X][Y]\\(d)\;rate=k[X]^2[Y]\end{array}$

Answer: Rate=$k[X]^2$
From the given diagram, when time $= 50s,\; \large\frac{1}{[X]}$$= 6 \rightarrow Equation of line=\large\frac{1}{[X]}$$-2=\large\frac{6-2}{50}$$(t-0) \large\frac{1}{[X]}$$=2+\large\frac{4t}{50}$
$\large\frac{1}{[X]}$$=2+\large\frac{2}{25}$$t$
Differentiating w.r.t [X]
$-\large\frac{-1}{[X]^2}=\frac{2}{25}\frac{dt}{d[X]}$
$\large\frac{d[X]}{dt}=-\frac{2}{25}$$[X]^2 rate=-\large\frac{d[X]}{dt}=\frac{2}{25}$$[X]^2=k[X]^2$
Rate=$k[X]^2$
edited Jul 24, 2014