What is the molarity of a KCl solution made by diluting 75.0 mL of a 0.200 M solution to a final volume of 100.0 mL?

• A. 0.300 M
• B. 0.150 M
• C. 0.100 M
• D. 0.200 M

Answer: (B)

Verified step by step guidance

1. Start by understanding the concept of molarity, which is defined as the number of moles of solute per liter of solution. It is expressed as \( M = \frac{n}{V} \), where \( n \) is the number of moles and \( V \) is the volume in liters.
2. Recognize that this problem involves dilution, where the initial concentration and volume are used to find the final concentration after the solution is diluted. The formula for dilution is \( M_1V_1 = M_2V_2 \), where \( M_1 \) and \( V_1 \) are the initial molarity and volume, and \( M_2 \) and \( V_2 \) are the final molarity and volume.
3. Identify the given values: initial molarity \( M_1 = 0.200 \) M, initial volume \( V_1 = 75.0 \) mL, and final volume \( V_2 = 100.0 \) mL. Note that volumes should be converted to liters for calculations, so \( V_1 = 0.075 \) L and \( V_2 = 0.100 \) L.
4. Substitute the known values into the dilution equation: \( 0.200 \times 0.075 = M_2 \times 0.100 \). This equation will allow you to solve for the final molarity \( M_2 \).
5. Rearrange the equation to solve for \( M_2 \): \( M_2 = \frac{0.200 \times 0.075}{0.100} \). Calculate this expression to find the molarity of the diluted solution.