Question

The concentration of hydrogen peroxide in a solution is determined by titrating a \(10.0\) -mL sample of the solution with permanganate ion. $$ \begin{array}{r} 2 \mathrm{MnO}_{4}^{-}(a q)+5 \mathrm{H}_{2} \mathrm{O}_{2}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow \\ 2 \mathrm{Mn}^{2+}(a q)+5 \mathrm{O}_{2}(g)+8 \mathrm{H}_{2} \mathrm{O}(l) \end{array} $$ If it takes \(14.8 \mathrm{~mL}\) of \(0.134 \mathrm{M} \mathrm{MnO}_{4}^{-}\) solution to reach the equivalence point, what is the molarity of the hydrogen peroxide solution?

Short answer

The concentration (molarity) of the hydrogen peroxide solution is \(0.4963\,M\).

Step-by-step solution

Identify the given data and what we need to find

We are given the information: - Volume of the hydrogen peroxide solution: \(10.0\,mL\) - Volume of the permanganate solution: \(14.8\,mL\) - Concentration of the permanganate solution: \(0.134\,M\) We need to find the molarity(concentration) of the hydrogen peroxide solution.

Convert volumes to liters

We need to convert the given volumes from milliliters to liters for further calculations using unit conversion factors: \(Volume_{H_2O_2} = 10.0\,mL \times \frac{1\,L}{1000\,mL} = 0.010\,L\) \(Volume_{MnO_4^-} = 14.8\,mL \times \frac{1\,L}{1000\,mL} = 0.0148\,L\)

Calculate the moles of permanganate ion

Now, we can find out the moles of permanganate ion (\(MnO_4^-\)) using the volume and concentration of the titrant solution: \(Moles_{MnO_4^-} = Volume_{MnO_4^-}\times Concentration_{MnO_4^-}\) \(Moles_{MnO_4^-} = 0.0148\,L \times 0.134\,M = 0.0019852\,mol\)

Use stoichiometry to find moles of hydrogen peroxide

Using the stoichiometry from the balanced chemical equation, we can find the moles of hydrogen peroxide: \(2\,MnO_4^-(aq) + 5\,H_2O_2(aq) + 6\,H^+(aq) \rightarrow 2\,Mn^{2+}(aq) + 5\,O_2(g) + 8\,H_2O(l)\) From the balanced equation, it is clear that \(2\,mol\,MnO_4^-\) are consumed for every \(5\,mol\,H_2O_2\): \(Moles_{H_2O_2} = \frac{5}{2} \times Moles_{MnO_4^-}\) \(Moles_{H_2O_2} = \frac{5}{2} \times 0.0019852\,mol = 0.004963\,mol\)

Calculate the concentration (molarity) of hydrogen peroxide

Now that we have the moles of hydrogen peroxide and the volume of the hydrogen peroxide solution, we can calculate the concentration (molarity) using the formula: \(Molarity_{H_2O_2} = \frac{Moles_{H_2O_2}}{Volume_{H_2O_2}}\) \(Molarity_{H_2O_2} = \frac{0.004963\,mol}{0.010\,L} = 0.4963\,M\) So, the concentration (M) of the hydrogen peroxide solution is \(0.4963\,M\).