# 6.11: Chemical Reaction Rate

Drag racing is a sport where two cars start from a dead stop and drive as fast as they can down a quarter-mile strip. At the end of the strip are timers that determine both elapsed time (how long did it take for them to cover the quarter mile) and top speed (how fast they were going as they went through the timer chute). Both pieces of data are important. One car may accelerate faster and get ahead that way, while the other car may be slower off the line, but can get up to a higher top speed at the end of the run.

## Chemical Reaction Rate

Chemical reactions vary widely in the speeds with which they occur. Some reactions occur very quickly. If a lighted match is brought in contact with ligher fluid or another flammable liquid, it erupts into flame instantly and burns fast. Other reactions occur very slowly. A container of milk in the refrigerator will be good to drink for weeks before it begins to turn sour. Millions of years were required for dead plants under Earth's surface to accumulate and eventually turn into fossil fuels such as coal and oil.

Chemists need to be concerned with the rates at which chemical reactions occur. Rate is another word for speed. If a sprinter takes $$11.0 \: \text{s}$$ to run a $$100 \: \text{m}$$ dash, his rate or speed is given by the distance traveled divided by the time.

$\text{speed} = \frac{\text{distance}}{\text{time}} = \frac{100 \; \text{m}}{11.0 \: \text{s}} = 9.09 \: \text{m/s}$

The sprinter's average running rate for the race is $$9.09 \: \text{m/s}$$. We say that it is his average rate because he did not run at that speed for the entire race. At the very beginning of the race, while coming from a standstill, his rate must be slower until he is able to get up to his top speed. His top speed must then be greater than $$9.09 \: \text{m/s}$$ so that taken over the entire race, the average ends up at $$9.09 \: \text{m/s}$$.

Chemical reactions can't be measured in units of meters per second, as that would not make any sense. A reaction rate is the change in concentration of a reactant or product with time. Suppose that a simple reaction were to take place in which a $$1.00 \: \text{M}$$ aqueous solution of substance $$\ce{A}$$ was converted to substance $$\ce{B}$$.

$\ce{A} \left( aq \right) \rightarrow \ce{B} \left( aq \right)$

Suppose that after 20.0 seconds, the concentration of $$\ce{A}$$ had dropped from $$1.00 \: \text{M}$$ to $$0.72 \: \text{M}$$ as $$\ce{A}$$ was slowly being converted to $$\ce{B}$$. We can express the rate of this reaction as the change in concentration of $$\ce{A}$$ divided by time.

$\text{rate} = -\frac{\Delta \left[ \ce{A} \right]}{\Delta t} = -\frac{\left[ \ce{A} \right]_\text{final} - \left[ \ce{A} \right]_\text{initial}}{\Delta t}$

A bracket around a symbol or formula means the concentration in molarity of that substance. The change in concentration of $$\ce{A}$$ is its final concentration minus its initial concentration. Because the concentration of $$\ce{A}$$ is decreasing over time, the negative sing is used. Thus, the rate for the reaction is positive and the units are molarity per second or $$\text{M/s}$$.

$\text{rate} = -\frac{0.72 \: \text{M} = 1.00 \: \text{M}}{20.0 \: \text{s}} = -\frac{-0.28 \: \text{M}}{20.0 \: \text{s}} = 0.014 \: \text{M/s}$

The molarity of $$\ce{A}$$ decreases by an average rate of $$0.014 \: \text{M}$$ every second. In summary, the rate of a chemical reaction is measured by the change in concentration over time for a reactant or product. The unit of measurement for a reaction rate is molarity per second $$\left( \text{M/s} \right)$$.

## Summary

• The reaction rate indicates how fast the reaction proceeds.