Finding the Volume of Solvent Needed for a Desired Molarity

In this article, we'll explore how to calculate the volume of solvent required to achieve a desired molarity for a solution. We'll provide practical examples to help you understand the concept clearly.
By Jamie

Understanding Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. It is a common unit of concentration used in chemistry. The formula for calculating molarity is:

\[ M = \frac{n}{V_{solution}} \]

Where:

  • M = molarity (mol/L)
  • n = number of moles of solute
  • V_{solution} = volume of solution in liters

To find the volume of solvent needed to achieve a specific molarity, we can rearrange the formula:

\[ V_{solution} = \frac{n}{M} \]

This means that if we know the amount of solute (in moles) and the desired molarity, we can find the volume of solvent required.

Example 1: Preparing a Sodium Chloride Solution

Problem:

You want to prepare a 0.5 M sodium chloride (NaCl) solution using 0.1 moles of NaCl. How much volume of solvent do you need?

Solution:

  1. Identify the given values:

    • Molarity (M) = 0.5 M
    • Moles of NaCl (n) = 0.1 moles

  2. Use the formula to calculate the volume:
    \[ V_{solution} = \frac{n}{M} = \frac{0.1 \, moles}{0.5 \, mol/L} = 0.2 \, L \]

  3. Convert liters to milliliters:
    \[ 0.2 \, L = 200 \, mL \]

Conclusion:

To achieve a 0.5 M solution of sodium chloride with 0.1 moles of solute, you need 200 mL of solvent.

Example 2: Preparing a Glucose Solution

Problem:

You need to create a 1.5 M glucose (C6H12O6) solution using 0.75 moles of glucose. What volume of solvent is required?

Solution:

  1. Identify the given values:

    • Molarity (M) = 1.5 M
    • Moles of glucose (n) = 0.75 moles

  2. Use the formula to calculate the volume:
    \[ V_{solution} = \frac{n}{M} = \frac{0.75 \, moles}{1.5 \, mol/L} = 0.5 \, L \]

  3. Convert liters to milliliters:
    \[ 0.5 \, L = 500 \, mL \]

Conclusion:

To prepare a 1.5 M glucose solution with 0.75 moles of solute, you will need 500 mL of solvent.

Key Takeaways

  • Molarity is a crucial concept in chemistry for expressing concentration.
  • By knowing the number of moles of solute and the desired molarity, you can easily calculate the volume of solvent required.
  • Always ensure to convert the final volume to your desired units (liters or milliliters) for practical application.