Question

An aqueous solution is made from \(0.798 \mathrm{~g}\) of potassium permanganate, \(\mathrm{KMnO}_{4}\). If the volume of solution is \(50.0 \mathrm{~mL},\) what is the molarity of \(\mathrm{KMnO}_{4}\) in the solution?

Short answer

The molarity of the KMnO4 solution is 0.101 M.

Step-by-step solution

Calculate the Molar Mass of KMnO4

To find the molarity, we first need the molar mass of KMnO4. Calculate the molar mass by summing the atomic masses of all elements in the compound.- Potassium (K): 39.10 g/mol- Manganese (Mn): 54.94 g/mol- Oxygen (O): 16.00 g/mol (each, 4 total)The molar mass of KMnO4 is: \[39.10 + 54.94 + 4(16.00) = 158.04 \text{ g/mol}\]

Calculate Moles of KMnO4

Use the mass of KMnO4 given and its molar mass to calculate the number of moles.Given mass of KMnO4: 0.798 gNumber of moles is calculated by:\[\text{Moles of } \mathrm{KMnO_4} = \frac{0.798 \text{ g}}{158.04 \text{ g/mol}} \approx 0.00505 \text{ mol}\]

Convert Volume from mL to L

The volume of the solution is given in milliliters; to find molarity, it must be in liters.Given volume: 50.0 mLConvert this to liters:\[50.0 \text{ mL} = 0.0500 \text{ L}\]

Calculate Molarity of the Solution

Molarity is calculated by dividing the moles of solute by the volume of solution in liters.Using the moles of KMnO4 calculated and the converted volume:\[\text{Molarity} = \frac{0.00505 \text{ mol}}{0.0500 \text{ L}} = 0.101 \text{ M}\]

Final Answer

The molarity of the KMnO4 solution is 0.101 M.

Key concepts

Potassium Permanganate

Potassium permanganate, chemically represented as \( \mathrm{KMnO}_{4} \), is a dark purple compound used widely in various chemical applications. It comprises potassium \((K)\), manganese \((Mn)\), and oxygen \((O)\). This compound is replete with uses in industrial and laboratory settings due to its oxidizing properties.
One of the most common uses of potassium permanganate is as a disinfectant and water purification substance. Additionally, it plays a role in organic synthesis and as a titrant in analytical chemistry. When dissolved in water, it imparts a characteristic purple color, making even small concentrations visible.
Understanding the chemistry and application of potassium permanganate helps to grasp the significance of calculating its concentration in solutions, which is essential for its effective utilization in various processes.

Molar Mass

The molar mass is pivotal in chemistry, serving as a bridge between the mass of a compound and the amount of substance, often quantified in moles. In the case of potassium permanganate \((\mathrm{KMnO}_{4})\), determining its molar mass involves summing the atomic masses of its constituent atoms.
- **Potassium \((K)\):** 39.10 g/mol
- **Manganese \((Mn)\):** 54.94 g/mol
- **Oxygen \((O)\):** Each atom contributes 16.00 g/mol, with four atoms combining for a total of 64.00 g/mol
When the atomic masses are added, the molar mass of \(\mathrm{KMnO}_{4}\) sums to 158.04 g/mol. This calculation is crucial for subsequently converting given mass to moles, paving the way for further calculations such as molarity.

Solution Volume

In concentration calculations, solution volume is extremely important. Volume measurements are often required to be in liters, as molarity relies on a liter-based system. Here, the given volume was 50.0 mL. To convert milliliters to liters, we use this simple conversion: 1 mL is equal to 0.001 L.
Therefore, the solution volume of 50.0 mL converts to \(0.0500 \text{ L}\). This volume transformation is indispensable so that molarity can be correctly calculated, aligning the units of moles and liters for accurate computation of solution concentration.

Concentration Calculation

The calculation of concentration, specifically molarity, is a key skill in chemistry. Molarity (\text{M}) is defined as the number of moles of solute per liter of solution. It allows chemists to express how much solute is present in a given volume of solution, which is vital for carrying out reactions and preparing solutions with precise concentrations.
Here, by knowing the moles of \(\mathrm{KMnO}_{4}\) (0.00505 mol) and the volume of the solution in liters (0.0500 L), the calculation of molarity proceeds as:
\[\text{Molarity} = \frac{0.00505 \text{ mol}}{0.0500 \text{ L}} = 0.101 \text{ M} \].
Obtaining the correct molarity is crucial for scientific experiments, ensuring that chemicals react in the right proportions and under the correct conditions. The concept extends to various complex and real-world applications, from pharmacology to environmental science.