Finding the Volume of Solvent Needed for a Desired Molarity

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.