The reaction ( ) is investigated in solution

CHEMISTRY · Multi-part · AP · Chemistry · Kinetics · Kinetics

Problem

The reaction

P + Q + R \to \text{products}

(

20^\circ\text{C}

) is investigated in solution. Concentrations are measured in moles per liter, and

R

is maintained at a constant initial concentration of

0.25\,\text{M}

in all experiments. The collected data are shown below.

Experiment	$[P]_0$ ( $\text{M}$ )	$[Q]_0$ ( $\text{M}$ )	$[R]_0$ ( $\text{M}$ )	Initial rate ( $\text{M s}^{-1}$ )
1	0.12	0.25	0.25	$6.0 \times 10^{-5}$
2	0.24	0.25	0.25	$1.2 \times 10^{-4}$
3	0.24	0.50	0.25	$4.8 \times 10^{-4}$

Assume the rate law can be expressed as

\text{rate} = k[P]^a[Q]^b[R]^c

. (a) Determine the order of the reaction with respect to

P

and to

Q

, justifying each value quantitatively. (b) Because the concentration of

R

is held constant, explain how its order

c

can or cannot be deduced from the data provided. (c) Write the rate law that is consistent with the data and calculate the numerical value and units of the rate constant

k

using Experiment 1. (d) Determine the units of

k

you obtained in part (c) by dimensional analysis and verify that they are consistent with the overall order of the reaction. (e) Calculate the initial rate that would be observed if

[P]_0 = 0.60\,\text{M}

and the experimenter wishes to achieve an initial rate of

6.0 \times 10^{-3}\,\text{M s}^{-1}

by adjusting

[Q]_0

while keeping

[R]_0

unchanged at

0.25\,\text{M}

. What value of

[Q]_0

is required?

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