Calculate the molarity of 8.25 mL of 0.0876 M KI diluted to 12.0 mL with water. Round your answer to 3 significant figures.

To calculate the molarity of the diluted solution, we can use the dilution formula: \[ C_1V_1 = C_2V_2 \] Where: - \(C_1\) is the initial concentration (molarity) of the solution, - \(V_1\) is the initial volume of the solution, - \(C_2\) is the final concentration (molarity) of the diluted solution, - \(V_2\) is the final volume of the solution. Given: - \(C_1 = 0.0876 \, \text{M}\) - \(V_1 = 8.25 \, \text{mL}\) - \(V_2 = 12.0 \, \text{mL}\) We need to find \(C_2\). 1. First, convert the volumes from mL to L: - \(V_1 = 8.25 \, \text{mL} = 0.00825 \, \text{L}\) - \(V_2 = 12.0 \, \text{mL} = 0.0120 \, \text{L}\) 2. Now, we can rearrange the dilution formula to solve for \(C_2\): \[ C_2 = \frac{C_1V_1}{V_2} \] 3. Substitute the known values into the equation: \[ C_2 = \frac{0.0876 \, \text{M} \times 0.00825 \, \text{L}}{0.0120 \, \text{L}} \] Now, let's calculate \(C_2\). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(0.0876\times 0.00825\right)}{0.012}\) - step1: Remove the parentheses: \(\frac{0.0876\times 0.00825}{0.012}\) - step2: Multiply the numbers: \(\frac{0.0007227}{0.012}\) - step3: Convert the expressions: \(\frac{\frac{7227}{10000000}}{\frac{3}{250}}\) - step4: Multiply by the reciprocal: \(\frac{7227}{10000000}\times \frac{250}{3}\) - step5: Reduce the numbers: \(\frac{2409}{40000}\times 1\) - step6: Multiply: \(\frac{2409}{40000}\) The calculation gives us: \[ C_2 = 0.060225 \, \text{M} \] Now, rounding this to three significant figures, we get: \[ C_2 \approx 0.0602 \, \text{M} \] Thus, the molarity of the diluted KI solution is **0.0602 M**.