Question

What volume of \(2.06 \mathrm{M} \mathrm{KMnO}_{4},\) in liters, contains \(322 \mathrm{g}\) of solute?

Short answer

0.989 liters of 2.06 M KMnO4 is needed.

Step-by-step solution

Calculate Molar Mass of KMnO4

Firstly, we need to find the molar mass of potassium permanganate (\( ext{KMnO}_4\)). Calculate it by adding the atomic masses of all elements: \(\text{K} = 39.10\ \text{g/mol}, \text{Mn} = 54.94\ \text{g/mol}, \text{O} = 16.00\ \text{g/mol}\). The molar mass of \(\text{KMnO}_4\) is thus \(39.10 + 54.94 + 4 \times 16.00 = 158.04\ \text{g/mol}\).

Calculate Moles of Solute

Next, use the molar mass to find the number of moles of \(\text{KMnO}_4\) in \(322\ \text{g}\). Use the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). So, \(\text{moles} = \frac{322}{158.04} = 2.037\, \text{mol}\).

Calculate Volume of Solution Needed

Now that we know the moles of solute, we can use the molarity formula to find the volume of \(\text{KMnO}_4\). Molarity is given by the formula \(\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\). Rearranging gives \(\text{volume} = \frac{\text{moles of solute}}{\text{Molarity}}\). So, \(\text{volume} = \frac{2.037}{2.06} = 0.989\, \text{L}\).

Key concepts

Molar Mass Calculation

Calculating molar mass is essential in solution chemistry because it allows us to determine how much of a compound is needed to achieve a desired concentration in a solution. The molar mass is the sum of the atomic masses of all atoms in a molecule. For example, to compute the molar mass of potassium permanganate (KMnO₄), we add together the molar masses of potassium (K), manganese (Mn), and oxygen (O):
- Potassium (K) contributes 39.10 g/mol.
- Manganese (Mn) contributes 54.94 g/mol.
- Each Oxygen (O) contributes 16.00 g/mol, and since there are four oxygen atoms, we multiply 16.00 by 4 to get 64.00 g/mol.
Adding these together, the molar mass of KMnO₄ is 158.04 g/mol. Once calculated, this value is used to relate the mass of a compound to the number of moles, which is a measure of the quantity of substance.

Potassium Permanganate

Potassium permanganate, represented as KMnO₄, is a chemical compound composed of potassium, manganese, and oxygen. Known for its striking deep purple color, KMnO₄ is often used in chemistry as an oxidizing agent. It's highly soluble in water and dissociates into K⁺ and MnO₄⁻ ions when dissolved.
KMnO₄ has a variety of applications beyond the laboratory:

• It serves as a disinfectant and antiseptic in medical and sanitation practices.
• In aquariums, it's used to treat certain types of fish diseases.
• In water treatment facilities, it's utilized to treat iron and hydrogen sulfide.

Given its oxidizing properties, it's important to handle KMnO₄ with care, as it can stain skin and surfaces and may cause an exothermic reaction if not mixed properly.

Molarity Formula

Molarity is a key concept in solution chemistry that describes the concentration of a solution. Defined as the number of moles of solute per liter of solution, molarity is expressed as moles per liter (mol/L), often abbreviated as M.
The formula to calculate molarity is:
\[\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}\]
To find how much volume of a solution is needed for a specific concentration, you can rearrange the formula:
\[\text{Volume (L)} = \frac{\text{Moles of solute}}{\text{Molarity}}\]
In practice, understanding and using the molarity formula allows chemists to prepare solutions of exact concentrations needed for experiments or production processes. It's vital for ensuring reactions occur under controlled and predictable conditions.