Calculating the Mass of NaOH Required for a 0.5M Aqueous Solution

Understanding how to calculate the mass of a substance required to prepare a specific molarity of a solution is essential in many scientific and industrial processes. This article will guide you through the calculation of the mass of NaOH (Sodium Hydroxide) needed to make 500 mL of a 0.5 M aqueous solution. We will explore various methods to ensure clarity and accuracy.

Method 1: Basic Formula Approach

The most straightforward method to determine the mass of NaOH required is by using the formula:

mass molarity x volume x molar mass

Molarity (M): 0.5 M Volume (V): 500 mL 0.5 L Molar Mass (Mr) of NaOH: 22.99 g/mol (Na) 15.999 g/mol (O) 1.008 g/mol (H) ≈ 40.00 g/mol

Plugging in the values:

mass 0.5 M x 0.5 L x 40.00 g/mol

mass 0.5 x 0.5 x 40.00 10.00 g

Hence, you need 10.00 grams of NaOH to make 500 mL of a 0.5 M aqueous solution.

Method 2: Simplified Calculation

A simpler approach involves breaking down the problem into smaller steps using the concept of moles:

Volume of NaOH: 500 mL Molarity of the aqueous solution: 0.5 M Molar Mass of NaOH: 40.0 g/mol

First, calculate the moles of NaOH required:

n M x V 0.5 M x (0.5 L) 0.25 moles

Next, use the molar mass to find the mass:

Mass n x Mr 0.25 moles x 40.0 g/mol 10.0 g NaOH

Therefore, 10 grams of NaOH is the required amount.

Method 3: Using Mole Concept Formula

Equation: n cV

This method involves using the formula for number of moles:

n cV

Concentration (c): 0.5 M Volume (V): 0.5 L

Calculate the number of moles:

n 0.5 M x 0.5 L 0.25 moles

Using the formula for mass (n m/Mr), where:

Number of moles (n): 0.25 moles Molecular Mass (Mr) of NaOH: 40 g/mol

Rearrange the formula to solve for mass (m):

m n x Mr 0.25 moles x 40 g/mol 10 g

Thus, 10 grams of NaOH is needed to prepare the solution.

Conclusion

Using any of these methods, you can determine that to prepare 500 mL of a 0.5 M aqueous solution of NaOH, you need 10 grams of the compound. This calculation is crucial for various applications, ranging from laboratory experiments to industrial processing. Mastering these calculations can enhance your understanding of chemical solutions and aid in accurate measurements.

Keywords

NaOH - Sodium Hydroxide Molarity - The concentration of a solution expressed as the number of moles of solute per liter of solution Aqueous Solution - A solution in which the solvent is water Molar Mass - The mass of one mole of a substance Chemical Calculation - Calculations involving the relationships between chemical quantities