Answer to Question #141157 in General Chemistry for mike

Question

State the order of reaction with respect to a reactant, R, if:
a). the rate of reaction doubles when [R] doubles
b). the rate of reaction is unchanged when [R] triples
c). the rate of reaction reduces by a factor of four when [R] is halved.

Answer 1

State the order of reaction with respect to a reactant, R, if:

a) the rate of reaction doubles when [R] doubles

b) the rate of reaction is unchanged when [R] triples

c) the rate of reaction reduces by a factor of four when [R] is halved

Solution

 $v_R=-d[R]/dt=k[R]^n$ - rate equation [1]

a) $v_1=v_2/2$ and $[R_1]=[R_2]/2$

Hense 

$k[R_1]^n=k[R_2]^n/2$

$([R_1]/[R_2])^n=1/2$

$n=log_{[R_1] \above{2pt} [R_2]}0,5= log_{1 \above{2pt} 2}0,5=1$

b) $v_1=v_2$ and $[R_1]=[R_2]/3$

Hence

$k[R_1]^n=k[R_2]^n$

$([R_1]/[R_2])^n=1$

$n=log_{[R_1] \above{2pt} [R_2]}1=0$

c)$v_1=4v_2$ and $[R_1]=2[R_2]$

Hence

$k[R_1]^n=4k[R_2]^n$

$([R_1]/[R_2])^n=4$

$n=log_{[R_1] \above{2pt} [R_2]}4= log_{2}4=2$

Answer: a) $n=1$, b) $n=0$, c) $n=2$

Reference: https://en.wikipedia.org/wiki/Rate_equation