Problem 100 - Chemistry: The Central Science

Question

A \(35.0\) -mL sample of \(1.00 M\) KBr and a \(60.0\) -mL sample of \(0.600 \mathrm{M} \mathrm{KBr}\) are mixed. The solution is then heated to evaporate water until the total volume is \(50.0 \mathrm{~mL}\). What is the molarity of the KBr in the final solution?

Step-by-Step Solution

Answer

The molarity of KBr in the final solution after mixing the two samples and evaporating water to a total volume of 50.0 mL is approximately 1.42 M.

Step 1: Determine the moles of KBr in each sample

Calculate the moles of KBr in both samples using the formula: moles = Molarity × Volume For the 35.0 mL sample with 1.00 M KBr: moles = (1.00 mol/L) × (35.0 mL) × (1 L/1000 mL) moles = 0.035 mol For the 60.0 mL sample with 0.600 M KBr: moles = (0.600 mol/L) × (60.0 mL) × (1 L/1000 mL) moles = 0.036 mol

Step 2: Calculate the total moles of KBr

Add the moles of KBr from both samples together: Total moles = moles (sample 1) + moles (sample 2) Total moles = 0.035 mol + 0.036 mol Total moles = 0.071 mol

Step 3: Find the final concentration of KBr

The total volume of the resulting solution is 50.0 mL. Apply the formula for molarity: Molarity = moles / Volume Molarity of KBr in the final solution = (0.071 mol) / (50.0 mL × 1 L/1000 mL) Molarity of KBr = \(\frac{0.071}{0.050}\) mol/L Molarity of KBr in the final solution ≈ 1.42 M

Key Concepts

Moles Calculation

To calculate the moles of a substance in a solution, we use the relationship between molarity, volume, and the number of moles. Molarity, abbreviated as M, refers to the concentration of a solution in terms of moles of solute per liter of solution. The formula to calculate moles is given by:\[moles = ext{Molarity} \times ext{Volume}\]Where "Volume" should be in liters to match the molarity units. For example, in the given problem, we calculate moles for a 35.0 mL sample of 1.00 M KBr. Convert the volume from milliliters to liters:- 35.0 mL = 35.0 × (1 L/1000 mL) = 0.035 L.Using the formula: - moles = 1.00 mol/L × 0.035 L = 0.035 mol.Similarly, for a 60.0 mL sample of 0.600 M KBr:- convert 60.0 mL to liters: 60.0 × (1 L/1000 mL) = 0.060 L.- calculate moles: 0.600 mol/L × 0.060 L = 0.036 mol.These calculations tell us how much KBr is present in each sample in terms of moles.

Molarity Formula

Molarity is a measure of the concentration of a solute in a solution. It reflects the number of moles of solute per liter of solution, denoted as mol/L or M. The formula to determine molarity is written as:\[ ext{Molarity} = \frac{ ext{moles of solute}}{ ext{volume of solution in liters}}\]In the provided exercise, you need to determine the molarity of KBr in the final mixed solution. Here's how it's done:1. **Calculate Total Moles of Solute:** Gather the moles from the two solutions: - Sample 1 provided 0.035 mol - Sample 2 provided 0.036 mol - Total moles = 0.035 mol + 0.036 mol = 0.071 mol2. **Determine Final Volume:** The final solution's volume after water evaporation is 50.0 mL, convert it to liters: - 50.0 mL × (1 L/1000 mL) = 0.050 L3. **Apply the Molarity Formula:** Use the total moles and final volume in the molarity formula: - Molarity = 0.071 mol / 0.050 L = 1.42 MThis calculation gives us the concentration of KBr in the final solution after mixing and evaporation.

Volume Conversion

When dealing with molarity and chemical calculations, it's crucial to ensure that all volume measurements are in the same units, often liters, to ensure consistency with molarity units, which are mol/L. In our example, we must convert milliliters (mL) to liters (L) because the molarity is given in mol/L. The conversion factor we use is: - 1 L = 1000 mL To convert mL to L: - Simply divide the volume in mL by 1000. For example, converting 35.0 mL to L: - 35.0 mL × (1 L/1000 mL) = 0.035 L Similarly, convert the final volume of 50.0 mL: - 50.0 mL × (1 L/1000 mL) = 0.050 L Using consistent units ensures clarity and accuracy when applying formulas, like calculating molarity, which requires volumes in liters.