Question

What is the mass of solute, in grams, in \(250 .\) mL. of a \(0.0125 \mathrm{M}\) solution of \(\mathrm{KMnO}_{4} ?\)

Short answer

The mass of the solute is 0.494 grams.

Step-by-step solution

Understand the Molarity Concept

Molarity ( M ) is defined as the number of moles of solute per liter of solution. In this problem, the molarity of the solution is given as 0.0125 M, which means there are 0.0125 moles of KMnO_4 in 1 liter of solution.

Convert Volume to Liters

The volume of the solution is provided in milliliters (mL). We need to convert it to liters because molarity is expressed in terms of liters. Given: 250 mL.Convert to liters: \( 250 \text{ mL} = 250 \times 10^{-3} \text { L} = 0.250 \text{ L} \)

Calculate the Moles of Solute

Using the molarity, calculate the moles of KMnO_4 in the given volume of solution. Equation: \( \text{Moles of KMnO}_4 = \text{Molarity} \times \text{Volume in liters} \)Substitute the given values: \( \text{Moles of KMnO}_4 = 0.0125 \text{ M} \times 0.250 \text{ L} = 0.003125 \text{ moles} \)

Determine the Molar Mass of KMnO_4

Use the periodic table to find the atomic masses of potassium (K), manganese (Mn), and oxygen (O). The molar mass of KMnO_4 is the sum of the atomic masses of its components. - K: 39.1 g/mol - Mn: 54.9 g/mol - O: 16.0 g/mol (since there are 4 oxygen atoms, 16.0 g/mol × 4 = 64.0 g/mol) Total molar mass of KMnO_4 = 39.1 + 54.9 + 64.0 = 158.0 g/mol.

Calculate the Mass of Solute in Grams

Multiply the number of moles by the molar mass to find the mass of KMnO_4 in grams.Equation: \( \text{Mass of KMnO}_4 = \text{Moles of KMnO}_4 \times \text{Molar mass} \)Substitute the values:\( \text{Mass of KMnO}_4 = 0.003125 \text{ moles} \times 158.0 \text{ g/mol} = 0.49375 \text{ grams} \)

Round the Mass to the Appropriate Significant Figures

The given values are to four significant figures, so round the result accordingly. The mass of KMnO_4 is approximately 0.494 grams, when rounded to three significant figures.

Key concepts

Understanding Molarity

Molarity is a fundamental concept in solution stoichiometry, representing the concentration of a solution. It is defined as the number of moles of solute in one liter of solution, symbolized as M. Molarity helps us determine how much solute is present in a specific volume of solution. For instance, a measurement of 0.0125 M means there are 0.0125 moles of solute, in this case, KMnO₄, in every liter the solution. This concept is crucial as it lays the groundwork for subsequent calculations involving volume and amount of substance. To accurately perform calculations, the volume should be in liters since molarity is expressed per liter. Converting milliliters to liters, as shown in our exercise, is an essential step.

The Role of Moles

Moles provide a way to express amounts of a chemical substance. A "mole" is a unit that scientists use to quantify very small entities like molecules, atoms, or particles. It helps simplify and standardize complex chemical calculations. In the exercise, the number of moles of KMnO₄ in the solution is determined by multiplying the molarity by the volume in liters: \[ \text{Moles of KMnO}_4 = \text{Molarity} \times \text{Volume in liters} \] For example, 0.0125 M \(\times\) 0.250 L results in 0.003125 moles of KMnO₄. Grasping the concept of moles allows you to traverse between mass, moles, and the number of particles in chemical equations seamlessly.

Calculating Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is obtained by summing the atomic masses of the elements present in a compound. This is crucial in moving from moles to grams in stoichiometry problems. For KMnO₄, the molar mass is computed by adding:

• Potassium (K): 39.1 g/mol
• Manganese (Mn): 54.9 g/mol
• Oxygen (O): 4 \(\times\) 16.0 g/mol = 64.0 g/mol

Adding these, we get a molar mass of 158.0 g/mol for KMnO₄. Understanding molar mass equips you to convert easily between the mass of a given sample and the amount of substance expressed in moles.

Significant Figures in Chemistry

Significant figures are vital in highlighting the precision of measurements and calculations in chemistry. They indicate which digits are meaningful, based on the precision of the measuring instrument or calculation method used. In the exercise, rounding the mass of KMnO₄ to three significant figures gives us 0.494 grams.

• The number of significant figures is determined by the measurement with the fewest significant digits involved in the calculation.
• For example, the volume 250 mL (0.250 L) and molarity 0.0125 M both have three significant figures, guiding our final answer.

Appropriately using significant figures avoids overestimating the precision of calculated results and provides a realistic reflection of uncertainty in scientific measurements.