Question

consider this balanced equation:
mathrm{h}_{2} mathrm{o}_{2}(a q)+3 mathrm{i}^{-}(a q)+2 mathrm{h}^{+}(a q)
ightarrow mathrm{i}_{3}^{-}(a q)+2 mathrm{h}_{2} mathrm{o}(l)
in the first 10.0 seconds of the reaction, the concentration of ( mathrm{i}^{-} ) dropped from ( 1.000 mathrm{m} ) to ( 0.868 mathrm{m} ).
determine the rate of change in the concentration of ( mathrm{i}^{-} ).
calculate the average rate of this reaction in this time interval.
determine the rate of change in the concentration of ( mathrm{h}^{+}left(deltaleftmathrm{h}^{+}
ight / delta t
ight) ) during this time interval.

Explanation:

Step1: Find the rate of change of \(I^-\)

The formula for the rate of change is \(\text{Rate of change}=\frac{\Delta\text{Concentration}}{\Delta t}\).
For \(I^-\), \(\Delta[I^-]=0.868 - 1.000=- 0.132\space M\) and \(\Delta t = 10.0\space s\).
So, rate of change of \(I^-\) is \(\frac{\Delta[I^-]}{\Delta t}=\frac{-0.132\space M}{10.0\space s}=- 0.0132\space M/s\)

Step2: Use the stoichiometry of the reaction

From the balanced equation \(H_2O_2(aq)+3I^-(aq)+2H^+(aq)\to I_3^-(aq)+2H_2O(l)\), the stoichiometric ratio between \(H^+\) and \(I^-\) is \(2:3\).
Let the rate of change of \(H^+\) be \(\frac{\Delta[H^+]}{\Delta t}\) and rate of change of \(I^-\) be \(\frac{\Delta[I^-]}{\Delta t}\)
We know that \(\frac{\Delta[H^+]}{\Delta t}=\frac{2}{3}\times\frac{\Delta[I^-]}{\Delta t}\)

Step3: Calculate the rate of change of \(H^+\)

Substitute \(\frac{\Delta[I^-]}{\Delta t}=-0.0132\space M/s\) into the above formula.
\(\frac{\Delta[H^+]}{\Delta t}=\frac{2}{3}\times(- 0.0132\space M/s)=-0.0088\space M/s\)

Step4: Calculate the average rate of the reaction

The average rate of the reaction \(r\) can be expressed in terms of the rate of change of reactants. Using the formula \(r =-\frac{1}{3}\frac{\Delta[I^-]}{\Delta t}\) (based on the stoichiometry of the reaction where the coefficient of \(I^-\) is \(3\))
Substitute \(\frac{\Delta[I^-]}{\Delta t}=-0.0132\space M/s\)
\(r=-\frac{1}{3}\times(-0.0132\space M/s)=0.0044\space M/s\)

Answer:

• Rate of change of \(I^-\): \(-0.0132\space M/s\)
• Rate of change of \(H^+\): \(-0.0088\space M/s\)
• Average rate of the reaction: \(0.0044\space M/s\)