Question

Household hydrogen peroxide is an aqueous solution containing \(3.0 \%\) hydrogen peroxide by mass. What is the molarity of this solution? (Assume a density of \(1.01 \mathrm{~g} / \mathrm{mL}\).)

Short answer

The molarity of the 3.0% hydrogen peroxide solution is approximately 0.888 M.

Step-by-step solution

Calculate the Mass of Hydrogen Peroxide in 1 Liter of Solution

To get the mass of hydrogen peroxide in 1 liter of solution, first convert the volume to milliliters, 1000 ml. Multiply the volume by the solution's density (1.01 g/mL) to get the mass of the solution in grams. Then, multiply the mass of the solution by the percentage of hydrogen peroxide (3.0%) to find the mass of hydrogen peroxide in grams.

Convert the Mass of Hydrogen Peroxide to Moles

Using the molar mass of hydrogen peroxide (H2O2), which is 34.0147 g/mol, convert the mass of hydrogen peroxide obtained in the first step to moles by dividing the mass by the molar mass.

Calculate the Molarity of the Solution

Molarity (M) is defined as the number of moles of solute per liter of solution. Use the moles of hydrogen peroxide calculated in step 2 and divide by the volume of the solution in liters (since we are considering a 1 liter solution) to find the molarity of the hydrogen peroxide solution.

Key concepts

Solution Concentration

Understanding solution concentration is essential when working with chemical solutions, such as the molarity of a hydrogen peroxide solution discussed in our exercise. Molarity, denoted by the letter M, is a measure of the concentration of a solute in a solution. It indicates the number of moles of a solute that is present per liter of solution.

When a problem gives you a percentage concentration, like the 3.0% hydrogen peroxide by mass, it's telling you how much solute is in the solution by mass compared to the total mass of the solution. To determine the molarity, you'll need to consider the volume of the solution and the mass of the solute within that volume.

For example, if we have a 1 liter (or 1000 ml) solution of hydrogen peroxide with a density of 1.01 g/ml, we can calculate the total mass of the solution and then find out how much of that mass is hydrogen peroxide. By doing this, we convert a percentage concentration into a more usable form for molarity calculations since molarity is focused on the moles of solute per liter of solution, not directly on the mass percentages.

Molar Mass Calculation

To accurately calculate the molarity of a solution, one must also understand how to determine the molar mass of the solute. The molar mass is the weight in grams of one mole of a substance. Each element on the periodic table has an atomic mass, and the molar mass of a compound is the sum of the atomic masses of each element in it, multiplied by the number of atoms of that element in the compound.

In the case of hydrogen peroxide, with the chemical formula H₂O₂, its molar mass is calculated by adding the molar mass of two hydrogen atoms (about 1.01 g/mol each) to that of two oxygen atoms (about 16.00 g/mol each). This calculation yields a molar mass of approximately 34.0147 g/mol for hydrogen peroxide. This is a crucial step because knowing the molar mass allows us to convert the mass of hydrogen peroxide into moles, which is a necessary part of finding the solution's molarity.

Converting Mass to Moles

The conversion of mass to moles is a fundamental concept in chemistry and a key step in calculating molarity. To convert the mass of a substance to moles, you use the molar mass of that substance as a conversion factor. This is because the molar mass tells us how much one mole of that substance weighs.

By dividing the mass of the substance by its molar mass, you obtain the number of moles. For instance, if we calculate that we have a certain mass of hydrogen peroxide in a solution, we use the previously calculated molar mass of hydrogen peroxide (\(34.0147 \text{ g/mol}\)) to find out how many moles of hydrogen peroxide this mass equates to. This conversion from mass to moles allows us to then plug this value into the molarity formula and thus complete the calculation of the solution's concentration.