Reaction Rate and How to Measure It
An effervescent tablet dissolves in a glass in one minute, but an iron nail takes months to rust. Both are chemical reactions, so how can we say how fast each one is and compare them with a number?
Fast and slow reactions
Some reactions are almost instantaneous (the gunpowder in a rocket during the Independence Day festivities) and others take years (the corrosion of an iron fence). To compare them, it is not enough to say "fast" or "slow": we have to measure how much something changes in each unit of time.
What changes in a reaction? Over time, the reactants are used up and the products appear. That is why we measure how the concentration (mol/L) of a substance changes.
Average rate
If the concentration changes from $[\text{A}]_1$ to $[\text{A}]_2$ between times $t_1$ and $t_2$, the average rate is the change divided by the elapsed time.
The minus sign for the reactant is not a whim: $\Delta[\text{reactivo}]$ is negative (it is consumed), and we want the rate to be a positive number.
Hydrogen peroxide (the antiseptic known in Mexico as agua oxigenada) decomposes according to $2\ \text{H}2\text{O}2 \rightarrow 2\ \text{H}2\text{O} + \text{O}2$. In an…
Hydrogen peroxide (the antiseptic known in Mexico as agua oxigenada) decomposes according to $2\ \text{H}_2\text{O}_2 \rightarrow 2\ \text{H}_2\text{O} + \text{O}_2$. In an experiment its concentration drops from $0.80\ \text{mol}/\text{L}$ to $0.50\ \text{mol}/\text{L}$ in $60\ \text{s}$. Calculate the average rate of disappearance of hydrogen peroxide over that interval, including the units.
Rate and coefficients
In $2\ \text{H}_2\text{O}_2 \rightarrow 2\ \text{H}_2\text{O} + \text{O}_2$, 2 mol of peroxide are used up for every 1 mol of oxygen formed. So the peroxide disappears twice as fast as the $\text{O}_2$ appears.
That is why the measured rate depends on which substance you observe. To have a single reaction rate, we divide by the coefficient $\nu$ of each substance:
Reading tables and graphs
In the laboratory, the concentration is measured at different times and recorded in a table or plotted on a graph. The average rate is calculated by intervals, using the two data points that bound each one.
The curve of a reactant goes down, and it is steeper at the beginning. This means that the rate decreases over time: at the start there are many reactants, and little by little they run out. (With collision theory in the next section you will see why.)
In the decomposition of dinitrogen pentoxide, $2\ \text{N}2\text{O}5 \rightarrow 4\ \text{NO}2 + \text{O}2$, the concentrations shown in the table were measured. | $t$…
In the decomposition of dinitrogen pentoxide, $2\ \text{N}_2\text{O}_5 \rightarrow 4\ \text{NO}_2 + \text{O}_2$, the concentrations shown in the table were measured.
| $t$ (s) | $[\text{N}_2\text{O}_5]$ (mol/L) |
|---|---|
| 0 | 0.90 |
| 100 | 0.60 |
| 200 | 0.40 |
| 300 | 0.27 |
- a) Calculate the average rate of disappearance of $\text{N}_2\text{O}_5$ over the intervals from $0$ to $100\ \text{s}$ and from $200$ to $300\ \text{s}$. b) Explain why the rate is different in the two intervals.
How it is measured in practice
The rate is not measured directly: we measure a property that changes with the reaction and from it we obtain the concentration.
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Gas given off: the volume or the pressure (effervescent tablet, hydrogen peroxide with a catalyst).
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Color: if a reactant or product is colored, the intensity of the color indicates its concentration.
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Mass: a balance records the loss of mass when a gas escapes.
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Conductivity or pH of the solution.