# Rate Constants and Reaction Mechanisms

One-way reactions are dependent only on the concentration of reactants, not products. In such cases, the rate at which C( the product) forms in the reaction:

A + Bà C can be expressed as

Rate = k[A]m[B]n,

Where [A] = concentration of A in moles/L;

[B] = concentration of B in moles/L;

m and n are determined experimentally, and k can be found from the resulting graph.

Example 1: Suppose that for the reaction 2A + Bà C , experiments revealed that m = 2 and n =1, so that

Rate at which C forms = k[A]2[B]1,

What would happen to the rate at which C formed if…

a)       [A] tripled and [B] remained constant?

b)       [B] tripled and [A] remained constant?

c)       both reactants double in concentration?

d)  If under certain conditions it took 9 minutes for 1 mole of C to appear, how long would it take if the reaction was repeated with the same amount of B but twice the concentration of A?

Answer:

a)                   the rate would increase by a factor of 32 = 9 because the rate is proportional to the square of the concentration of A.

b)                   the rate would increase by a factor of 3.

c)                   The rate will get 22(2) = 8 times bigger.

d)                   9/22 = 2.25 minutes

The rate expression can rarely be predicted from the overall reaction, because the overall reaction does not reveal how the reaction actually takes place. The series of steps that actually lead to the deceptively simple overall result is known as the reaction mechanism.

Consider the overall reaction between nitrogen dioxide and carbon monoxide:

NO2 + CO à CO2 + NO

Experiments reveal that the rate at which CO2 forms is given by:

Rate = k [NO2]2

In other words the concentration of the reactant CO is almost irrelevant ( as long as it’s not zero!). But how can that be?

The actual mechanism will shed light on this mystery.

NO2 + NO2 à NO3 + NO ( very slow)

NO3 + CO à CO2 + NO2 (very fast)

Overall: NO2 + NO2+ NO3 + COà NO3 + NO + CO2 + NO2

Or canceling the common compounds on each side we get

NO2 + CO à CO2 + NO

The rate at which CO2 forms will be influenced by the slow step, not the fast step. It’s like if you take 2 seconds to wolf down your burger and fries but another 35 minutes to eat the rest of your meal: the yucky brussel sprouts and other vegetables, then the rate at which you finish your meal is determined by the rate at which you eat the yucky stuff.

So the slow step is NO2 + NO2 à NO3 + NO, so now it’s understandable why CO plays an unimportant role and that

Rate = k [NO2]2

# Exercises ( For Solutions: http://www.emsb.qc.ca/laurenhill/science/rate7soln.html)

1.                    The rate at which water is formed from hydrogen peroxide is given by

Rate = k[H2O2(aq)][I-1]

a.        What will happen to the rate if the concentration of iodide is halved and the peroxide concentration does not change?

b.       What would you have to do to the amount of iodide if the rate remained constant but the amount of peroxide tripled?

2.                    The rate at which HBr forms from its constituent elements is given by:

Rate = [H2][Br2]0.5

a.     If it took 2 hours for two moles of HBr to appear, how long would it take if the reaction was repeated by quadrupling the concentration of each reactant?

b.     If the rate tripled and the concentration of hydrogen was doubled, what was done to the concentration of bromine?

3.             Explain why the reaction mechanism is so important in determining the rate of a reaction.

4.          In an experiment that involved measuring the rate of a chemical reaction, 6.35 grams of solid copper reacted with a 1.0    mol/L solution of nitric acid.  The reaction lasted 1 min 40 s and occurred at room temperature.

What is the reaction rate in moles of copper per second (mol/s)?

5.     While studying the rate of various chemical reactions, a student measured the rate at which certain metals react with different acids.  One of the experiments involved combining a strip of solid magnesium, Mg(s), with a hydrochloric acid solution, HCl(aq).  The student made the following observations :

- Mass of the magnesium strip used                                                                 1.78 ´ 10-2 g

- Atmospheric pressure in the room                                                                 101.3 kPa

- Room temperature                                                                                             25.0°C

- Temperature of the acidic solution                                                                 25.0°C

- Duration of the reaction                                                                                   6 min 40 s

This chemical reaction is represented by the following equation :

Mg(s) + 2HCl(aq) ® MgCl2(aq) + H2(g)

Under these conditions, what is the average rate of production of H2(g)?