Understanding Mole Fraction in Aqueous NaOH Solutions

When dealing with aqueous solutions of NaOH (sodium hydroxide), it is often necessary to determine the mole fraction of the solute (NaOH) in the solution. This article explores how to calculate the mole fraction of a solute, specifically in a 10 N aqueous NaOH solution, by examining the relationship between the mass of NaOH and water in the solution.

Calculating Mole Fraction: 10 N NaOH Solution

Consider a solution that contains 10 g of sodium hydroxide (NaOH) dissolved in 90 g of water. We aim to find the mole fraction of NaOH in this solution.

Step 1: Convert Mass to Moles

First, we need to determine the number of moles of NaOH and water in the solution.

For NaOH: 10 g NaOH 10 / 40 0.25 mol For water: 90 g H?O 90 / 18 5 mol

Now, we need to calculate the total moles in the solution.

Step 2: Calculate Total Moles

The total moles of the solution is the sum of the moles of NaOH and water:

Xa (moles of NaOH) / (moles of NaOH moles of water) 0.25 / (0.25 5) mol 0.25 / 5.25 ≈ 0.0476

Rewriting the Calculation with Additional Data

Using more detailed data, we can improve the accuracy of the calculation. Let's assume we are dealing with a 10 N NaOH solution.

Step 1: Density of 10 N Aqueous NaOH Solution

The density of a 10 N NaOH solution is approximately 1.10655 g/mL. This means that 1 L of the solution has a mass of 1106.55 g, of which 100 g is sodium hydroxide and the rest is water.

Step 2: Moles of NaOH and Water

We can now calculate the moles of NaOH and water in 1 liter of this solution:

100 g NaOH / 40.00 g/mol 2.50 mol NaOH 1106.55 g - 100 g 1006.55 g water 1006.55 g / 18.01 g/mol 55.86 mol water

The total moles in the solution is the sum of the moles of NaOH and water:

(2.50 mol NaOH 55.86 mol water) 58.36 mol total

Now, the mole fraction of NaOH can be calculated as:

XNaOH (moles of NaOH) / (total moles) 2.50 / 58.36 ≈ 0.043

And the mole fraction of water:

Xwater 1 - XNaOH 1 - 0.043 0.957

Therefore, the mole fraction of NaOH is approximately 0.043, and the mole fraction of water is 0.957.

Conclusion

In summary, when dealing with a 10 N aqueous NaOH solution, the mole fraction of NaOH can be calculated by accurately determining the moles of NaOH and water and then applying the mole fraction formula. This method allows us to better understand the composition of the solution and its properties.

Keywords: mole fraction, aqueous solution, NaOH, solute