Question

Calculate the mass percent \((\mathrm{m} / \mathrm{m})\) for the solute in each of the following solutions: a. \(75 \mathrm{~g}\) of \(\mathrm{NaOH}\) in \(325 \mathrm{~g}\) of \(\mathrm{NaOH}\) solution b. \(2.0 \mathrm{~g}\) of \(\mathrm{KOH}\) and \(20.0 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) c. \(48.5 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) in \(250.0 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) solution

Short answer

a) 23.08%, b) 9.09%, c) 19.4%

Step-by-step solution

- Understand the formula

Mass percent (m/m) is calculated using the formula: \[ \text{Mass percent} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 \]

- Calculate mass percent for part (a)

For part (a), the solute is NaOH. The mass of the solute and the solution are given as 75 g and 325 g, respectively. \[ \text{Mass percent (a)} = \frac{75 \text{ g}}{325 \text{ g}} \times 100 = 23.08\text{ \%} \]

- Calculate mass percent for part (b)

For part (b), the solute is KOH. The given masses are 2.0 g for the solute and 20.0 g for H₂O. First, calculate the total mass of the solution: \[ \text{Mass of solution (b)} = 2.0 \text{ g} + 20.0 \text{ g} = 22.0 \text{ g} \] Now, calculate the mass percent: \[ \text{Mass percent (b)} = \frac{2.0 \text{ g}}{22.0 \text{ g}} \times 100 = 9.09\text{ \%} \]

- Calculate mass percent for part (c)

For part (c), the solute is Na₂CO₃. The masses given are 48.5 g for the solute and 250.0 g for the solution. \[ \text{Mass percent (c)} = \frac{48.5 \text{ g}}{250.0 \text{ g}} \times 100 = 19.4\text{ \%} \]

Key concepts

mass percent

Mass percent is a way to express the concentration of a solution. It tells us how much of a solute is present compared to the entire solution.
To calculate the mass percent, we use the formula:
\[ \text{Mass percent} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 \]
Here, the mass of the solute is the amount of the substance dissolved in the solution, and the mass of the solution is the combined mass of the solute and the solvent.

solute

A solute is the substance that gets dissolved in a solvent to form a solution.
In the exercises given, \(\text{NaOH}, \text{KOH},\) and \(\text{Na}_2\text{CO}_3\) are solutes.
Simply put, the solute is what you have in a smaller amount in a solution.

solution composition

The composition of a solution defines its properties. When we look at a solution's composition, we're interested in:

• The solute: What is getting dissolved.
• The solvent: The substance in which the solute is dissolved.
• The total mass: The combined mass of both the solute and the solvent.

For example, in part (b), the solute is \(2.0 \text{ g} \text{ of KOH}\) and the solvent is \(20.0 \text{ g} \text{ of water}\), making the total solution mass \(22.0 \text{ g}\).

NaOH

NaOH, or Sodium Hydroxide, is often used as a solute. It is a strong base and highly soluble in water.
In the given exercise, the solute \(\text{NaOH}\) weighs \(75 \text{ g}\) and the total solution weighs \(325 \text{ g} \text{ of NaOH solution} \), thus:
\[ \text{Mass percent} = \frac{75 \text{ g}}{325 \text{ g}} \times 100 = 23.08\text{ \%} \]
This indicates that \(23.08\text{ \%}\) of the total solution mass is from NaOH.

KOH

KOH, or Potassium Hydroxide, is another strong base used as a solute.
In the exercise, \(2.0 \text{ g}\) of KOH is dissolved in \(20.0 \text{ g}\) of water to make a solution.
First, we calculate the total mass:
\[ \text{Total mass} = 2.0 \text{ g} + 20.0 \text{ g} = 22.0 \text{ g} \]
Then, we find the mass percent:
\[ \text{Mass percent} = \frac{2.0 \text{ g}}{22.0 \text{ g}} \times 100 = 9.09\text{ \%} \]

Na₂CO₃

Na₂CO₃, or Sodium Carbonate, is a reasonably common compound used as a solute in the exercise.
You have \(48.5 \text{ g}\) of Na₂CO₃ in a \(250.0 \text{ g} \text{ solution}\).
The mass percent is:
\[ \text{Mass percent} = \frac{48.5 \text{ g}}{250.0 \text{ g}} \times 100 = 19.4\text{ \%} \]
This means that \(19.4\text{ \%}\) of the whole solution's mass comes from the Sodium Carbonate.