What volume of a 2.00 M stock solution of NaOH is required to prepare 50.0 mL of 0.400 M NaOH? (LO 4.4) (a) 15.0 mL (b) 1.00 mL (c) 10.0 mL (d) 4.00 mL

Verified step by step guidance

1. Identify the formula for dilution: \( C_1V_1 = C_2V_2 \), where \( C_1 \) and \( V_1 \) are the concentration and volume of the stock solution, and \( C_2 \) and \( V_2 \) are the concentration and volume of the diluted solution.
2. Substitute the known values into the equation: \( (2.00 \, \text{M})(V_1) = (0.400 \, \text{M})(50.0 \, \text{mL}) \).
3. Solve for \( V_1 \) by dividing both sides of the equation by \( 2.00 \, \text{M} \).
4. Calculate the value of \( V_1 \) to find the volume of the stock solution needed.
5. Compare the calculated \( V_1 \) with the given options to determine the correct answer.

Key Concepts

Molarity (M)

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L). Understanding molarity is crucial for dilutions and preparing solutions, as it allows chemists to quantify how much solute is present in a given volume of solvent.

Dilution Equation

The dilution equation, often expressed as M1V1 = M2V2, relates the molarity and volume of a concentrated solution (M1 and V1) to the molarity and volume of the diluted solution (M2 and V2). This equation is essential for calculating how much of a stock solution is needed to achieve a desired concentration in a specific volume.

Volume Conversion

Volume conversion is the process of changing the volume measurement from one unit to another, such as from milliliters to liters. In the context of molarity and dilution, it is important to ensure that all volume measurements are in the same units to accurately apply the dilution equation and calculate the required volumes.