Problem 17 - Chemistry Matter and Change

Question

Calculate the molarity of 1.60 \(\mathrm{L}\) of a solution containing 1.55 \(\mathrm{g}\) of dissolved \(\mathrm{KBr}\) .

Step-by-Step Solution

Answer

The molarity of the solution is 0.00813 M.

Step 1: Identify the formula for molarity

Molarity \((M)\) is defined as the number of moles of solute per liter of solution. The formula for molarity is given by \( M = \frac{n}{V} \), where \(n\) is the number of moles of the solute and \(V\) is the volume of the solution in liters.

Step 2: Calculate moles of solute

To find the number of moles of \( \text{KBr} \), use the formula: \( n = \frac{ ext{mass}}{ ext{molar mass}} \). For \( \text{KBr} \), the molar mass is approximately \(119.0 \text{ g/mol}\) (Potassium: 39.1 \text{ g/mol}, Bromine: 79.9 \text{ g/mol}). Calculate \( n = \frac{1.55 \text{ g}}{119.0 \text{ g/mol}} = 0.0130 \text{ mol}\).

Step 3: Calculate the molarity of the solution

Substitute the number of moles \( n = 0.0130 \text{ mol} \) and the volume \( V = 1.60 \text{ L} \) into the molarity formula. \( M = \frac{0.0130 \text{ mol}}{1.60 \text{ L}} = 0.008125 \text{ M}\).

Step 4: Final answer

Express the molarity using appropriate significant figures based on the given data. \( M = 0.00813 \text{ M}\), considering three significant figures from the mass of \( \text{KBr} \) and the volume of the solution.

Key Concepts

Chemical calculations

Chemical calculations form the backbone of solving any quantitative queries in chemistry. They involve determining quantities such as the mass, volume, and number of moles involved in chemical reactions or solutions.

The key to mastering chemical calculations is understanding the relationship between different units and concepts.

• First, identify the quantities given and what is being asked for. In this case, you have the mass of the solute and the volume of the solution and need to find the molarity.
• Understanding the concept of significant figures is crucial, as it ensures precision and accuracy in chemical calculations. The values are often adjusted to match the significant digits of the given data to reflect measurement precision accurately.
• Learning the standard formulas, such as the molarity formula, helps to set up the problem correctly from the start.

Overall, being comfortable with chemical calculations enables more effective analysis and understanding of chemical systems.

Moles of solute

The concept of moles in chemistry provides a bridge between the atomic scale and the macroscopic scale we can observe and measure.

• The number of moles is a measure of the amount of substance, and it's based on Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules or atoms per mole.
• To find the moles of a solute, you need to divide the mass of the substance by its molar mass (mass of one mole of the substance). The formula is: \(n = \frac{\text{mass}}{\text{molar mass}}\).
• For instance, to find the moles of \(\text{KBr}\), we calculated \(n = \frac{1.55 \text{ g}}{119.0 \text{ g/mol}} = 0.0130 \text{ mol}\). Note how the units of grams cancel out, leaving moles as the unit.

Understanding how to calculate moles accurately is essential for determining how much of a chemical you have in a sample, which is crucial for reactions and solution preparation.

Solution concentration

Solution concentration isn't just about how much solute is in a solution, but more about knowing the precise amount per unit of volume.

• Molarity (\(M\)) is the most common unit for expressing concentration, which is defined as the number of moles of solute divided by the volume of the solution in liters: \(M = \frac{n}{V}\).
• For the solution in the exercise, with \(0.0130 \text{ mol}\) of \(\text{KBr}\) in \(1.60 \text{ L}\) of solution, rearranging the formula gives us \(M = \frac{0.0130 \text{ mol}}{1.60 \text{ L}} = 0.008125 \text{ M}\).
• Adjusting for significant figures, we express this as \(0.00813 \text{ M}\), showing that even in such a small concentration, precision matters.

Analyzing and calculating solution concentration help chemists design experiments and create reactions with exact known outcomes. Solution concentration is critical for dosing in pharmaceuticals, creating exact conditions for reactions and understanding how solutes interact in a solution.