# The following reaction is observed in a lab experiment: A + 2B -> C + D In this experiment, it required 750 s for the concentration of C to change from 0.333 M to 0.750 M. What is the rate of the reaction?

May 25, 2016

$\text{rate" = 5.6 * 10^(-4)"M}$

#### Explanation:

The rate of a reaction is simply a measure of how the concentration of the reactants or the concentration of the products changes over time.

In order to express the rate of a reaction, you must essentially figure out the change that takes place in the concentration of the reactants or of the products per unit of time.

Usually, this unit of time is the second, $\text{s}$.

Your chemical reaction looks like this

$\text{A" + 2"B" -> "C" + "D}$

If you take $\left[\text{C}\right]$ to be the concentration of $\text{C}$, and $t$ to be the time of the reaction, you can say that the rate of this reaction in terms of the change in concentration of $\text{C}$ will be

color(blue)(|bar(ul(color(white)(a/a)"rate" = (Delta["C"])/(Deltat)color(white)(a/a)|)))

In your case, you know that the concentration of $\text{C}$ increases from $\text{0.333 M}$ to $\text{0.750 M}$ in a total of $\text{750 s}$. The change in the concentration of $\text{C}$ will thus be

Delta["C"] = "0.750 M" - "0.333 M"

Delta["C"] = "0.417 M"

The rate of the reaction will thus be

"rate" = "0.417 M"/"750 s" = color(green)(|bar(ul(color(white)(a/a)5.6 * 10^(-4)"M s"^(-1)color(white)(a/a)|)))

The answer is rounded to two sig figs.

This tells you that as the reaction proceeds, the concentration of $\text{C}$ will increase by $5.6 \cdot {10}^{- 4} \text{M}$ per second.