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Chapter 19: Problem 65

The concentration of a hydrogen peroxide solution can be conveniently determined by titration against a standardized potassium permanganate solution in an acidic medium according to the following unbalanced equation: $$ \mathrm{MnO}_{4}^{-}+\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{O}_{2}+\mathrm{Mn}^{2+} $$ (a) Balance the above equation. (b) If \(36.44 \mathrm{~mL}\) of a \(0.01652 \mathrm{M} \mathrm{KMnO}_{4}\) solution are required to completely oxidize \(25.00 \mathrm{~mL}\) of a \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution, calculate the molarity of the \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution.

Short Answer

Expert verified
The balanced equation is: \(2MnO_4^- + 6H^+ + 5H_2O_2 \rightarrow 5O_2 + 2Mn^{2+} + 8H_2O\). The molarity of the \(H_2O_2\) solution is 0.0602 M

Step by step solution

01

Balance the chemical equation

To balance the reaction, it's important to notice that the manganese doesn't change in the reaction, but the oxygen and hydrogen does. After balancing the atoms on both sides, the balanced equation becomes: \n\[2MnO_4^- + 6H^+ + 5H_2O_2 \rightarrow 5O_2 + 2Mn^{2+} + 8H_2O\]
02

Understanding Molarity and its relation with volume and moles in a titration

Molarity (M) is defined as the number of moles of solute per liter of solution. In a titration like this one, the molarity and volume of one reactant are used to determine the moles, which can then be used to find the molarity of the other reactant through the balanced equation.
03

Calculate moles of \( KMnO_4 \)

First, the number of moles of \( KMnO_4 \) used is calculated by multiplying the volume by its molarity. The volume should be converted to liters, so 36.44 mL becomes 0.03644 L. Therefore, the moles of \( KMnO_4 \) used are \( 0.01652 M * 0.03644 L = 6.021 x 10^{-4} \, moles \)
04

Apply the stoichiometry from balanced equation

Stoichiometry from the balanced equation shows that 2 moles of \(MnO_4^-\) react with 5 moles of \(H_2O_2\). Therefore, the moles of \(H_2O_2\) that have reacted would be: \((6.021 x 10^{-4}\, moles * 5) / 2 = 1.505 x 10^{-3} \, moles \)
05

Calculate the molarity of \(H_2O_2\)

Finally, given that the moles of \(H_2O_2\) have been determined and the volume of \(H_2O_2\) solution used was given (25.00 mL = 0.02500 L), the molarity is calculated by dividing the moles by the volume. \n\[Molarity = 1.505 x 10^{-3}\, moles / 0.02500 L = 0.0602 M\]

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Most popular questions from this chapter

A galvanic cell is constructed by immersing a piece of copper wire in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{CuSO}_{4}\) solution and a zinc strip in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{ZnSO}_{4}\) solution. (a) Calculate the emf of the cell at \(25^{\circ} \mathrm{C}\) and predict what would happen if a small amount of concentrated \(\mathrm{NH}_{3}\) solution were added to (i) the \(\mathrm{CuSO}_{4}\) solution and (ii) the \(\mathrm{ZnSO}_{4}\) solution. Assume that the volume in each compartment remains constant at \(25.0 \mathrm{~mL}\). (b) In a separate experiment, \(25.0 \mathrm{~mL}\) of \(3.00 M \mathrm{NH}_{3}\) are added to the \(\mathrm{CuSO}_{4}\) solution. If the emf of the cell is \(0.68 \mathrm{~V},\) calculate the formation constant \(\left(K_{\mathrm{f}}\right)\) of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\).

A galvanic cell using \(\mathrm{Mg} / \mathrm{Mg}^{2+}\) and \(\mathrm{Cu} / \mathrm{Cu}^{2+}\) half-cell's operates under standard-state conditions at \(25^{\circ} \mathrm{C}\) and each compartment has a volume of \(218 \mathrm{~mL}\). The cell delivers 0.22 A for \(31.6 \mathrm{~h}\). (a) How many grams of \(\mathrm{Cu}\) are deposited? (b) What is the \(\left[\mathrm{Cu}^{2+}\right]\) remaining?

The zinc-air battery shows much promise for electric cars because it is lightweight and rechargeable: The net transformation is \(\mathrm{Zn}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{ZnO}(s)\) (a) Write the half-reactions at the zinc-air electrodes and calculate the standard emf of the battery at \(25^{\circ} \mathrm{C}\). (b) Calculate the emf under actual operating conditions when the partial pressure of oxygen is 0.21 atm. (c) What is the energy density (measured as the energy in kilojoules that can be obtained from \(1 \mathrm{~kg}\) of the metal) of the zinc electrode? (d) If a current of \(2.1 \times 10^{5} \mathrm{~A}\) is to be drawn from a zinc-air battery system, what volume of air (in liters) would need to be supplied to the battery every second? Assume that the temperature is \(25^{\circ} \mathrm{C}\) and the partial pressure of oxygen is \(0.21 \mathrm{~atm} .\)

Calculate the standard potential of the cell consisting of the \(\mathrm{Zn} / \mathrm{Zn}^{2+}\) half-cell and the SHE. What will the emf of the cell be if \(\left[\mathrm{Zn}^{2+}\right]=0.45 \mathrm{M}, \mathrm{P}_{\mathrm{H}_{2}}=2.0 \mathrm{~atm}\), and \(\left[\mathrm{H}^{+}\right]=1.8 \mathrm{M} ?\)

Calculate the standard emf of a cell that uses the \(\mathrm{Mg} / \mathrm{Mg}^{2+}\) and \(\mathrm{Cu} / \mathrm{Cu}^{2+}\) half-cell reactions at \(25^{\circ} \mathrm{C} .\) Write the equation for the cell reaction that occurs under standard-state conditions.
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