Question

What is the mole fraction of NaOH in an aqueous solution that contains 22.8$\mathrm{\%}\mathrm{NaOH}$ by mass?

Short answer

The mole fraction of NaOH in the aqueous solution is approximately 0.117.

Step-by-step solution

Convert the mass percentage to grams

We are given a solution that is 22.8% NaOH by mass. Let's assume we have 100 g of the solution (it is convenient to work with 100 g because percentage values will translate directly into grams). Then, the mass of NaOH in the solution will be 22.8 g, and the mass of water in the solution will be 100 g - 22.8 g = 77.2 g.

Calculate the moles of NaOH and water

Now we need to convert the mass of NaOH and water to moles. To do this, we'll use the molar masses of NaOH and water. Molar mass of NaOH = 40 g/mol (23 g/mol for Na + 16 g/mol for O + 1 g/mol for H) Molar mass of water = 18 g/mol (16 g/mol for O + 2 g/mol for H) Using the molar masses, we can calculate the moles: Moles of NaOH = (22.8 g)/(40 g/mol) = 0.57 mol Moles of water = (77.2 g)/(18 g/mol) = 4.29 mol

Calculate the mole fraction of NaOH

We can now calculate the mole fraction of NaOH in the solution using the formula: Mole fraction of NaOH = (moles of NaOH)/(moles of NaOH + moles of water) Mole fraction of NaOH = (0.57 mol)/(0.57 mol + 4.29 mol) = 0.117 The mole fraction of NaOH in the aqueous solution is approximately 0.117.

Key concepts

Understanding Mass Percentage

Mass percentage is a way to express the concentration of a component in a mixture. It tells us how much of the component is present, relative to the total mass of the mixture. In chemistry, this is often used to specify the concentration of a solute in a solution.
To calculate mass percentage, you use the formula:

• Mass percentage = $\left(\frac{\text{mass of solute}}{\text{total mass of solution}}\right)\times 100\mathrm{\%}$

In our example, if we are dealing with 22.8% NaOH solution by mass, it means that in 100 grams of the solution, 22.8 grams is NaOH.
This method of expressing concentration is very useful because it allows chemists to quickly understand how "concentrated" or "diluted" a solution is. It's a straightforward approach that helps in preparing solutions with precise concentrations.

Deciphering Molar Mass

Molar mass is a crucial concept in chemistry, representing the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and serves as a bridge between the mass of a substance and the amount of substance present on a molecular level.
To find the molar mass of a compound, simply sum the atomic masses of all the elements in the molecular formula.

• For NaOH, the molar mass is calculated as: 23 g/mol (Na) + 16 g/mol (O) + 1 g/mol (H) = 40 g/mol.
• For water (H₂O), it's: 16 g/mol (O) + 2 × 1 g/mol (H) = 18 g/mol.

Understanding molar mass allows us to convert between the amount of substance (in moles) and its mass (in grams). This conversion is fundamental in performing stoichiometric calculations, which are pivotal in reacting amount predictions and chemical reaction analyses.

Mole Calculation Made Simple

Moles serve as the standard unit for quantifying chemical substances. They allow chemists to count particles, such as atoms, molecules, or ions, using Avogadro's number $6.022\times {10}^{23}$. Mole calculations relate directly to the molar mass of a substance.
The basic formula for converting grams to moles is:

• Moles = $\frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

In our example, we calculate the moles of NaOH and water in the solution as follows:

• Moles of NaOH = $\frac{22.8}{40}\approx 0.57$ mol.
• Moles of water = $\frac{77.2}{18}\approx 4.29$ mol.

These calculations help in determining the mole fraction, which signifies the proportion of each component within the solution. It's an efficient way to express the ratio between parts in a mixture.

Exploring Aqueous Solution Chemistry

Aqueous solution chemistry deals with solutions where water is the solvent. Water is termed the "universal solvent" due to its ability to dissolve numerous substances. This branch of chemistry is crucial for understanding numerous natural and industrial processes.
In an aqueous solution, solutes like NaOH dissociate into ions when dissolved, impacting the solution’s properties, such as conductivity and reactivity. Such solutions are essential in a variety of chemical reactions.
For instance, the mole fraction calculated from mole calculations is important for predicting how substances will behave when mixed. This helps chemists design reactions and understand how concentrations affect reaction rates and product formation.

• It’s crucial for titration processes, where known concentrations are used to determine unknown ones.
• Aqueous solubility also influences how nutrients are absorbed in biological systems and how pollutants interact in environmental contexts.

Knowledge of aqueous solution chemistry is indispensable in fields ranging from environmental science to pharmaceutical development.