Chapter 3: Rate Laws

Relative Rates of Reaction

The Reaction:

\[2A + 3B \rightarrow 5C\]

is carried out in a reactor. If at a particular point, the rate of disappearance of A is 10 mol/dm³/s, what are the rates of B and C?

Solution

The Reaction:

\[2A + 3B \rightarrow 5C\]

reactor. If at a particular point, the rate of disappearance of A is 10 mol/dm³/s, what are the rates of B and C?

The rate of disappearance of A, -r_a, is

\[-r_a = 10 \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}}\]

or the rate of formation of species A is

\[r_a = -10 \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}}\]

The relative rates are

\[\frac{r_a}{-2} = \frac{r_b}{-3} = \frac{r_c}{5}\]

The rate of formation of species B is

\[r_b = \frac{-3}{-2}(r_a) = \frac{3}{2}r_a\]

\[r_b = \frac{3}{2} \left(-10 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \right) = -15 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}}\]

The rate of disappearance of B, -r_b , is

\[-r_b = 15 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}}\]

The rate of formation of C, -r_c, is

\( r_c = \frac{5}{-2}(r_a) = \frac{5}{-2} \left( -10 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \right) \)

\( r_c = 25 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \)

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