Question

Hydrogen peroxide solution for hair bleaching is usually prepared by mixing \(5.0\) g of hydrogen peroxide \(\left(\mathrm{H}_{2} \mathrm{O}_{2}\right.\), molecular weight \(=34 \mathrm{~g} /\) mole \()\) per \(100 \mathrm{ml}\) of solution. What is the molarity of this solution?

Short answer

The molarity of the hydrogen peroxide solution can be calculated as follows: Molarity = (number of moles) / (volume in liters) Molarity = \(\frac{5.0 \, g}{34 \, g/mol} \div 0.1 \, L\) Molarity = \(\frac{0.147 \, mol}{0.1 \, L}\) Molarity = \(1.47 \, mol/L\)

Step-by-step solution

Calculate the number of moles of hydrogen peroxide

We're given 5.0 g of hydrogen peroxide (H₂O₂), and its molecular weight is 34 g/mol. To find the number of moles, we'll divide the mass of hydrogen peroxide by its molecular weight: Number of moles = (mass of hydrogen peroxide) / (molecular weight of hydrogen peroxide) Number of moles = (5.0 g) / (34 g/mol)

Convert volume to liters

The volume of the solution is given in milliliters (mL), but we need to convert it to liters (L) for molarity calculations. To do this, recall that 1 L = 1000 mL: Volume in liters = (100 mL) * (1 L / 1000 mL) Volume in liters = 0.1 L

Calculate molarity

Finally, we'll divide the number of moles of hydrogen peroxide by the volume of the solution in liters to find the molarity: Molarity = (number of moles) / (volume in liters) Molarity = (5.0 g / 34 g/mol) / (0.1 L) Now, calculate the molarity of the hydrogen peroxide solution.

Key concepts

Hydrogen Peroxide

Hydrogen peroxide () is commonly known as a disinfectant and bleaching agent. It's used in various concentrations for different purposes, with hair bleaching being one of them. This clear liquid is composed of hydrogen and oxygen, and it's known for its ability to release oxygen upon decomposition, which is why it works well as a bleach. When using hydrogen peroxide for hair bleaching, it's very important to accurately calculate its concentration, to prevent any damage to the hair or scalp. In lower concentrations, it's also used for wound cleaning and as a mouth rinse.

Molar Mass

The molar mass of a substance is the mass of one mole of its particles, usually expressed in grams per mole (). For hydrogen peroxide (), the molar mass is calculated by summing the atomic masses of its constituent atoms: 2 hydrogen atoms and 2 oxygen atoms. This value is critical in converting mass to moles which is a key step in various calculations including molarity. Understanding molar mass allows us to measure quantities of chemicals in the lab accurately, making it a cornerstone concept in chemistry.

Mole Concept

The mole concept is a fundamental principle in chemistry, enabling chemists to count atoms, molecules, or other particles in a given sample. One mole is defined as the amount of a substance that contains exactly particles, which is Avogadro's number. By calculating moles, we bridge the gap between the small, particle scale of atoms and the large, observable scale of grams. This concept is applied in the exercise to convert from the mass of hydrogen peroxide to the number of its moles, a necessary step for finding the solution's molarity.

Solution Concentration

Solution concentration is a measure of the amount of solute present in a given amount of solution or solvent. Molarity is one of the most common units of concentration and is defined as the number of moles of solute per liter of solution (). To calculate it, one needs to know both the amount of substance in moles and the total volume of the solution in liters. The concept is widely used in chemistry to prepare solutions with precise concentrations for various applications such as reactions, titrations, and in our case, hair bleaching.