Question

Calculate the mass/volume percent \((\mathrm{m} / \mathrm{v})\) for the solute in each of the following solutions: a. \(75 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in \(250 \mathrm{~mL}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) solution b. \(39 \mathrm{~g}\) of sucrose in \(355 \mathrm{~mL}\) of a carbonated drink

Short answer

a. 30% \( \mathrm{Na}_{2} \mathrm{SO}_{4} \), b. 10.99% sucrose

Step-by-step solution

Understanding the formula for mass/volume percent

The mass/volume percent (m/v) is calculated using the formula: \[ \text{Mass/Volume percent} = \left( \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \right) \times 100 \]

Substitute the given values for solution (a)

For the solution with 75 g of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in 250 mL of solution, substitute the values into the formula: \[ \text{Mass/Volume percent} = \left( \frac{75 \text{ g}}{250 \text{ mL}} \right) \times 100 \]

Calculate the mass/volume percent for solution (a)

\[ \text{Mass/Volume percent} = \left( \frac{75}{250} \right) \times 100 = 0.3 \times 100 = 30\% \]

Substitute the given values for solution (b)

For the solution with 39 g of sucrose in 355 mL of a carbonated drink, substitute the values into the formula: \[ \text{Mass/Volume percent} = \left( \frac{39 \text{ g}}{355 \text{ mL}} \right) \times 100 \]

Calculate the mass/volume percent for solution (b)

\[ \text{Mass/Volume percent} = \left( \frac{39}{355} \right) \times 100 \approx 0.10986 \times 100 \approx 10.99\% \]

Key concepts

solution concentration

Solution concentration is an important concept in chemistry. It tells us how much solute is present in a given volume of solution. Concentrations can be expressed in different ways, such as molarity, molality, and mass/volume percent. Here, we focus on mass/volume percent, which is particularly useful in practical scenarios like mixing solutions for lab work or in industrial applications.
Understanding concentration helps predict how substances will react and ensures consistency in experiments and formulations. Accurate concentration calculations are crucial when preparing solutions for chemical reactions.

mass/volume percent formula

The mass/volume percent formula is used to determine the concentration of a solution in terms of the mass of the solute in grams (g) per 100 milliliters (mL) of solution. The formula is:
\[\text{Mass/Volume percent} = \left( \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \right) \times 100 \] This formula indicates how many grams of solute are present in every 100 mL of solution. For example, if you have 75 grams of sodium sulfate in 250 mL of solution, you would use the formula to calculate:
\[\text{Mass/Volume percent} = \left( \frac{75 \text{ g}}{250 \text{ mL}} \right) \times 100 = 30\% \] The same formula can be applied to different solutes and volumes, making it versatile and useful for various scientific and practical applications.

solute mass in solution

The solute mass is the amount of solute present in a solution, measured in grams (g). To find this, you'll need to have your solution's concentration and its volume. Here's how you can understand the role of the solute mass in the given problem:
In solution (a), we have 75 grams of sodium sulfate (\(\mathrm{Na}_{2} \mathrm{SO}_{4}\)) as the solute. In solution (b), there are 39 grams of sucrose as the solute. By using these amounts and the volume of the solutions, we can determine the mass/volume percent.
Knowing the mass of solute in your solution is essential for several reasons:

• It helps in standardizing solutions for experiments.
• It ensures that the desired concentration is achieved.
• It is necessary for accurately scaling up or down in a lab setting or industrial process.

When calculating, make sure to always use consistent units (grams for mass and milliliters for volume) to get accurate results.