Chapter 16, Problem 47A

In the gas-phase reaction, $I_2+C{l}_2\to 2ICl,[I_2]$ changesfrom 0.400M at 0.00 min to 0.300M at 4.00 min.Calculate the average reaction rate in moles of $I_2$ consumedper liter per minute.

Interpretation Introduction

Interpretation:

The average reaction rate in moles of ${\text{I}}_{\text{2}}$ consumed per liter per minute needs to be determined for the reaction,

${\text{I}}_{\text{2}}\text{+}{\text{Cl}}_{\text{2}}\to {\text{2ICl}}_{\text{2}}$

Concept introduction:

In a chemical reaction, the reactants are written on the left side of the equation and the product is written on the right side.

The average rate of a reaction can be given by the formula,

Average reaction rate $\text{=}-\frac{\text{Δ}\left[\text{reactant}\right]}{\text{Δt}}$

Here, $\text{Δ}\left[\text{reactant}\right]$ = change in the concentration of the reactant

Answer to Problem 47A

The average reaction rate for the moles of ${\text{I}}_{\text{2}}$ consumed per liter per minute is $\text{0}\text{.250}\frac{\text{min}}{\text{L}\text{min}}$

Explanation of Solution

Given in the reaction,

${\text{I}}_{\text{2}}\text{+}{\text{Cl}}_{\text{2}}\to {\text{2ICl}}_{\text{2}}$, ${\text{[I}}_{\text{2}}]$ changes from 0.400 M at 0.00 min to 0.300 M at 4.00 min.

For this reaction,

Average reaction rate $\text{=}-\frac{\text{Δ}\left[\text{reactant}\right]}{\text{Δt}}$

Where, the change in the concentration of the reactant is given by $\text{Δ}\left[\text{reactant}\right]$ and $\text{Δt}$ is the change in time.

So, as ${\text{[I}}_{\text{2}}]$ changes from 0.400 M at 0.00 min to 0.300 M at 4.00 min in the reaction,

Therefore,

$\begin{array}{c}\text{Δ}\left[\text{reactant}\right]\text{=Δ}\left[{\text{I}}_{\text{2}}\right]\\ \text{=0}\text{.300}\text{M}-\text{0}\text{.44}\text{M}\\ \text{=}-\text{0}\text{.100}\text{M}\end{array}$

The change in time is $\text{Δt=}\text{4}\text{.00}\text{min}-\text{0}\text{.00}\text{min=}\text{4}\text{.00}\text{min}$.

So, now we can use these values to calculate the average reaction rate.

Average reaction rate $\text{=}-\frac{\text{Δ}\left[\text{reactant}\right]}{\text{Δt}}$

$\begin{array}{c}\text{=}\frac{\text{Δ}\left[{\text{I}}_{\text{2}}\right]}{\text{Δt}}\\ \text{=}\frac{-\text{0}\text{.100}\text{M}}{\text{4}\text{.00}\text{min}}\\ \text{=}\frac{\text{0}\text{.100}}{\text{4}\text{.00}}\frac{\text{mol}}{\text{L}\text{min}}\\ \text{=0}\text{.0250}\frac{\text{min}}{\text{L}\text{min}}\end{array}$

Therefore, the average reaction rate is $\text{0}\text{.250}\frac{\text{min}}{\text{L}\text{min}}$

Conclusion

The average rate of the reaction is $\text{0}\text{.250}\frac{\text{min}}{\text{L}\text{min}}$