Problem 69 - General Chemistry

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?

Step-by-Step Solution

Answer

The molarity of the solution is 0.101 M.

Step 1: Calculate Moles of Solute

First, we need to find the moles of potassium permanganate (\(\text{KMnO}_4\)). The molar mass of \(\text{KMnO}_4\) is the sum of the atomic masses of potassium (\(39.10\ g/mol\)), manganese (\(54.94\ g/mol\)), and oxygen (\(16.00\ g/mol\) \( \times 4\)). This gives \[Molar\ Mass = 39.10 + 54.94 + (16.00 \times 4) = 158.04\ g/mol.\] Now, calculate the moles of \(\text{KMnO}_4\): \(\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{0.798\ g}{158.04\ g/mol} = 0.00505\ mol.\)

Step 2: Convert Volume to Liters

The volume of the solution is given in milliliters (\(50.0\ \text{mL}\)). We need to convert this into liters by dividing by 1000, since there are 1000 milliliters in one liter: \[\text{Volume in Liters} = \frac{50.0}{1000} = 0.0500\ \text{L}.\]

Step 3: Calculate Molarity

Molarity is defined as the number of moles per liter of solution. Use the formula for molarity: \(M = \frac{\text{Moles of Solute}}{\text{Liters of Solution}}\). So, the molarity \(M\) of \(\text{KMnO}_4\) is: \[M = \frac{0.00505\ \text{mol}}{0.0500\ \text{L}} = 0.101\ \text{mol/L}.\] Thus, the molarity of the \(\text{KMnO}_4\) solution is \(0.101\ M\).

Key Concepts

Understanding Potassium Permanganate

Potassium permanganate, with the chemical formula \( \mathrm{KMnO}_4 \), is a well-known chemical compound used in various applications, including as a disinfectant and in chemical analyses. This compound is composed of potassium \( (\mathrm{K}) \), manganese \( (\mathrm{Mn}) \), and oxygen \( (\mathrm{O}) \) atoms. Each molecule of potassium permanganate contains one atom of potassium, one atom of manganese, and four atoms of oxygen. Because of this specific composition, it's crucial to understand and calculate the molar mass accurately, which brings us to the next topic.

Exploring Moles of Solute

Calculating the number of moles of solute is a fundamental step in determining the concentration of a solution. A mole is a unit in chemistry that refers to \( 6.022 \times 10^{23} \) entities, which can be atoms, molecules, or ions depending on the context. In our case, to calculate the moles of potassium permanganate, we use the relation between mass and molar mass with the formula:

• Moles = \( \frac{\text{Mass of compound}}{\text{Molar Mass}} \)

For potassium permanganate, the moles are obtained by dividing the given mass \( (0.798 \mathrm{~g}) \) by its molar mass \( (158.04 \mathrm{~g/mol}) \). This gives \( 0.00505 \mathrm{~mol} \) of \( \mathrm{KMnO}_4 \). This number tells us the amount of potassium permanganate that's available in the solution to react or interact with other substances.

Simplifying Molar Mass Calculation

The molar mass of a compound is an essential concept in chemistry as it transforms between the mass of the substance and the moles. For potassium permanganate \( (\mathrm{KMnO}_4) \), calculating the molar mass involves:

• Potassium \((\mathrm{K}) : 39.10 \mathrm{~g/mol}\)
• Manganese \((\mathrm{Mn}) : 54.94 \mathrm{~g/mol}\)
• Oxygen \((\mathrm{O}) : 16.00 \mathrm{~g/mol}\) for each of the four atoms

Adding these values gives the total molar mass of \( 158.04 \mathrm{~g/mol} \). This molar mass enables us to calculate the number of moles required for any given mass of potassium permanganate. Understanding the molar mass is crucial for various calculations in chemistry that involve converting between mass and moles.

Understanding Volume Conversion

When working with solutions, it's vital to ensure that all units are consistent, especially volume units. The original problem states the volume as \( 50.0 \mathrm{~mL} \), which needs to be converted into liters. Volume conversion is straightforward:

• 1 liter = 1000 milliliters

Therefore, to convert \( 50.0 \mathrm{~mL} \) to liters, divide by 1000, resulting in \( 0.0500 \mathrm{~L} \). This conversion is necessary since molarity, a common measure of concentration, is expressed in moles per liter \( (\mathrm{mol/L}) \). Keeping units consistent prevents mix-ups and errors in chemical calculations.

Defining Aqueous Solution

An aqueous solution is a type of solution where water is the solvent. The term 'aqueous' comes from 'aqua', which means water. This means that potassium permanganate is dissolved in water to form the solution in this exercise. Aqueous solutions are essential in chemistry because water is often a convenient and effective solvent due to its polarity and ability to dissolve a wide range of substances. The properties of the solute, like potassium permanganate in this case, can change significantly when it goes from a solid to being dissolved in an aqueous solution. This nature of solutions opens up various experimental and analytical possibilities in science.