Question

A solution of hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), is titrated with a solution of potassium permanganate, \(\mathrm{KMnO}_{4}\). The reaction is $$ \begin{array}{c} 5 \mathrm{H}_{2} \mathrm{O}_{2}(a q)+2 \mathrm{KMnO}_{4}(a q)+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \\ 5 \mathrm{O}_{2}(g)+2 \mathrm{MnSO}_{4}(a q)+\mathrm{K}_{2} \mathrm{SO}_{4}(a q)+8 \mathrm{H}_{2} \mathrm{O}(l) \end{array} $$ It requires \(51.7 \mathrm{~mL}\) of \(0.145 \mathrm{M} \mathrm{KMnO}_{4}\) to titrate \(20.0 \mathrm{~g}\) of the solution of hydrogen peroxide. What is the mass percentage of \(\mathrm{H}_{2} \mathrm{O}_{2}\) in the solution?

Short answer

The mass percentage of H2O2 in the solution is 3.19%.

Step-by-step solution

Calculate Moles of KMnO4

We begin by calculating the moles of potassium permanganate (KMnO4) used in the titration. Given that the concentration of KMnO4 is 0.145 M and the volume used is 51.7 mL, we first convert this volume to liters: \(51.7 \, \text{mL} = 0.0517 \, \text{L}\). The moles of KMnO4 are calculated using the formula: \(\text{moles} = \text{volume} \times \text{concentration}\). Thus, \(\text{moles of } \mathrm{KMnO_4} = 0.0517 \, \text{L} \times 0.145 \, \text{M} = 0.0075065 \, \text{moles}\).

Use Reaction Stoichiometry

From the balanced chemical equation, we see that 2 moles of KMnO4 react with 5 moles of H2O2. Let \(x\) be the moles of H2O2. From the stoichiometry, \(2\, \text{moles of KMnO4: 5\, moles of H2O2}\), thus, \(5/2 = x/0.0075065\). Solving for \(x\) gives \(x = \frac{5}{2} \times 0.0075065 = 0.01876625\, \text{moles of } \mathrm{H_2O_2} \).

Calculate Mass of H2O2

We now calculate the mass of the hydrogen peroxide that reacted. The molar mass of H2O2 is approximately 34.02 g/mol. The mass of H2O2 is given by the moles of H2O2 multiplied by its molar mass: \(\text{mass} = \text{moles} \times \text{molar mass}\). This yields \( \text{mass of } \mathrm{H_2O_2} = 0.01876625 \, \text{moles} \times 34.02 \, \text{g/mol} = 0.638 \text{g} \).

Calculate Mass Percentage of H2O2

Finally, we find the mass percentage of H2O2 in the solution. The mass percentage is calculated by dividing the mass of H2O2 by the total mass of the solution and then multiplying by 100%. Thus, \(\text{mass percentage of } \mathrm{H_2O_2} = \left(\frac{0.638 \text{g}}{20.0 \text{g}}\right) \times 100\% = 3.19\%\).

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationships between the different substances involved in a chemical reaction. When performing calculations in stoichiometry, one must consider the moles and coefficients indicated in a chemical equation. This is critical in determining how much of each reactant is needed or how much product will be formed.

During the titration of hydrogen peroxide with potassium permanganate, the reaction equation provides the stoichiometric coefficients. These coefficients indicate that 2 moles of KMnO4 react with 5 moles of H2O2. By understanding this stoichiometric relationship, we can accurately calculate the moles of hydrogen peroxide that reacted based on the moles of KMnO4 used in the titration.

To perform such calculations, the following key points can be helpful:

• Identify the balanced chemical equation.
• Note the ratios in which reactants combine and products form.
• Convert volumes to moles using concentration data when solutions are involved.

By applying these principles, stoichiometry allows us to quantitatively analyze chemical reactions and prepare them with exact proportions.

Chemical Reactions

In chemistry, a chemical reaction is a process in which substances, known as reactants, are transformed into different substances, called products. Each chemical reaction can be described using a chemical equation, which shows the reactants on the left side and the products on the right, separated by an arrow.

The reaction between hydrogen peroxide (H2O2) and potassium permanganate (KMnO4) is a classic example used in titrations. The balanced chemical equation:\[5 \text{ H}_2\text{O}_2 (aq) + 2 \text{ KMnO}_4 (aq) + 3 \text{ H}_2\text{SO}_4 (aq) \rightarrow 5 \text{ O}_2 (g) + 2 \text{ MnSO}_4 (aq) + \text{ K}_2\text{SO}_4 (aq) + 8 \text{ H}_2\text{O} (l)\]This equation illustrates a redox reaction, where electrons are transferred from hydrogen peroxide to potassium permanganate, resulting in the formation of oxygen, manganese(II) sulfate, potassium sulfate, and water. Each component in the reaction plays a specific role, with sulfuric acid acting as the medium to facilitate electron transfer.

Understanding chemical reactions includes knowing:

• The reactants and products involved.
• The state of each substance (e.g., aqueous, solid, gas).
• The type of reaction (such as redox, acid-base, etc.).

This lays the foundation for further calculations and understanding the nature of changes at a molecular level.

Mass Percentage

Mass percentage is a way to express the concentration of a component in a mixture or solution. It defines the fraction of the total mass that a particular substance makes up, providing insight into its proportion in the overall mixture.

In the context of the titration exercise, the mass percentage of hydrogen peroxide (H2O2) is calculated to determine how concentrated the H2O2 is in the solution relative to the total mass of the solution. The formula for mass percentage is:\[\text{Mass percentage of H}_2\text{O}_2 = \left(\frac{\text{mass of H}_2\text{O}_2}{\text{total mass of solution}}\right) \times 100\%\]Using the mass of H2O2 found from stoichiometry calculations and the given mass of the solution, this calculation reveals that the solution contains 3.19% of hydrogen peroxide by mass.

Key points to remember include:

• Accurate measurement of mass for both the component and the total solution.
• Expressing the result as a percentage to understand the solution's makeup.
• Utilization of mass percentage in quality control and product specifications in various industries.

This provides valuable information for evaluating solution strength and uses in practical applications.

Molar Mass

The concept of molar mass is instrumental in chemistry for converting between the mass of a substance and the number of moles. Molar mass is defined as the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms present in the molecule.

For hydrogen peroxide (H2O2), each molecule contains two hydrogen atoms and two oxygen atoms. The atomic mass of hydrogen is about 1.01 g/mol, and for oxygen, it is approximately 16.00 g/mol. Thus, the molar mass of H2O2 can be computed as follows:\[\text{Molar mass of } \text{H}_2\text{O}_2 = 2 \times 1.01 + 2 \times 16.00 = 34.02 \text{ g/mol}\]Understanding molar mass is crucial for:

• Converting grams to moles and vice-versa in chemical calculations.
• Facilitating stoichiometric calculations in reactions and processes.
• Predicting yields and quantities in chemical production.

By comprehending and applying molar mass, chemists can accurately measure and predict the amounts of substances involved in chemical reactions.