Question

The initial rate of reaction doubles as the concentration of one of the reactants is quadrupled. What is the order of this reaction? If a reactant has a -1 order, what happens to the initial rate when the concentration of that reactant increases by a factor of two?

Short answer

The order of the reactant is 0.5.

The initial rate of reaction becomes 0.5 times.

Step-by-step solution

The formula for the Rate of reaction

As we know, $\mathrm{Rate}=\mathrm{k}[\mathrm{Reactant}{]}^{\mathrm{a}}$ (i)

Where a is the order of reactant

Solving the equations

According to question, $2\mathrm{Rate}=\mathrm{k}[4\mathrm{Reactant}{]}^{\mathrm{a}}$... (ii)

Dividing eq.(i) by eq.(ii), we get a = 0.5

Making equation of rate of reaction for 2nd part

According to question, $\mathrm{Initial}\mathrm{rate}=\mathrm{k}[\mathrm{Reactant}{]}^{-1}$ (iii)

Comparing eq. (i) and eq. (iii), we get

Initial rate = 0.5 x Rate