Question

Houschold 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 g/mL.)

Short answer

The molarity of the 3.0% household hydrogen peroxide solution is approximately 0.891 M.

Step-by-step solution

Determine the mass of hydrogen peroxide in a specific volume

Assuming we have 100 g of the household hydrogen peroxide solution, 3.0% by mass means there are 3 g of hydrogen peroxide (H2O2) since \(3.0\% \times 100 \text{g} = 3 \text{g of H2O2)}\).

Calculate the volume of the solution

Using the density formula \(\text{density} = \frac{ \text{mass}}{\text{volume}}\), we can rearrange to find the volume: \(\text{volume} = \frac{\text{mass}}{\text{density}}\). With a mass of 100 g and a density of 1.01 g/mL, the volume is \( \frac{100 \text{g}}{1.01 \text{g/mL}} \approx 99.01 \text{mL}\).

Convert the mass of hydrogen peroxide to moles

The molar mass of H2O2 is approximately 34.0147 g/mol (2*1.0079 for hydrogen and 2*15.999 for oxygen). The number of moles of H2O2 is given by\(\frac{3 \text{g}}{34.0147 \text{g/mol}} \approx 0.0882 \text{moles of H2O2}\).

Calculate the molarity of the solution

Molarity is defined as moles of solute per liter of solution. Convert the volume from milliliters to liters by dividing by 1000: \(\frac{99.01 \text{mL}}{1000} = 0.09901 \text{L}\). Then, calculate the molarity: \(\frac{0.0882 \text{moles}}{0.09901 \text{L}} \approx 0.8909 \text{M}\), rounded to three significant figures.

Key concepts

Solution Concentration

Understanding the concentration of solutions is critical when working with any chemical reactions. Solution concentration refers to the amount of a solute that is dissolved in a given quantity of solvent. In chemistry, one common measurement of concentration is molarity, which is expressed as moles of solute per liter of solution (mol/L or M).

When dealing with household hydrogen peroxide, for example, which is an aqueous solution containing 3.0% hydrogen peroxide by mass, we calculate molarity to understand how concentrated the hydrogen peroxide is. To do so, one must know both the amount of solute (hydrogen peroxide) in moles and the total volume of the solution in liters. Molarity is vital in labs because it allows chemists to predict the outcomes of reactions, understand formula stoichiometry, and prepare desired solution strengths for various applications.

Converting Mass to Moles

One fundamental aspect of chemistry is knowing how to convert between mass and moles. A mole is a unit of measure that allows chemists to count particles, such as atoms and molecules, by weighing them. The bridge between mass and moles is the molar mass, which is the mass of one mole of a substance and is measured in grams per mole (g/mol).

For instance, when dealing with a 3.0% hydrogen peroxide solution, you need to first identify the mass of hydrogen peroxide present, and then use its molar mass to find the number of moles. Hydrogen peroxide (H2O2) has a molar mass of 34.0147 g/mol, which can be calculated from the atomic weights of hydrogen and oxygen. This conversion is crucial for calculating molarity, as molarity is defined in terms of moles.

Density and Volume Relationship

The density of a substance is its mass per unit volume (g/mL or g/cm³ for liquids). Understanding the relationship between density and volume is important for precision in preparing solutions. This relationship allows us to determine the volume of a particular mass of liquid if its density is known.

In the context of our example, given the density of the hydrogen peroxide solution, we can find the total volume of the solution we are working with, which is necessary when calculating molarity. The formula to find volume given the mass and density is \(\text{volume} = \frac{\text{mass}}{\text{density}}\). Using the density of 1.01 g/mL and a mass of 100 g, we find a volume of approximately 99.01 mL, which gets converted to liters in the final molarity calculation.