Question

Calculate the amount of solution ( \(\mathrm{g}\) or \(\mathrm{mL}\) ) that contains each of the following amounts of solute: a. \(7.50 \mathrm{~g}\) of \(\mathrm{NaCl}\) from a \(2.0 \%(\mathrm{~m} / \mathrm{m}) \mathrm{NaCl}\) solution b. \(4.0 \mathrm{~g}\) of \(\mathrm{NaF}\) from a \(25 \%(\mathrm{~m} / \mathrm{v}) \mathrm{NaF}\) solution c. \(20.0 \mathrm{~g}\) of \(\mathrm{KBr}\) from an \(8.0 \%(\mathrm{~m} / \mathrm{m}) \mathrm{KBr}\) solution

Short answer

a) 375 g b) 16 mL c) 250 g

Step-by-step solution

Understand the formula for mass/mass percentage

The mass/mass percentage concentration formula is given by: \[ \text{Mass percentage} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 \ \text{For example, } 2.0\text{ % (m/m) } \text{NaCl}\] This means that 2 grams of NaCl are present in every 100 grams of solution.

Calculate the total mass of the solution for (a)

Given: \[7.50 \text{ g NaCl in a } 2.0\text{ % (m/m) } \text{NaCl solution} \] Rearrange the formula to solve for the mass of the solution: \[ \text{Mass of solution} = \frac{\text{mass of solute}}{\text{percentage}} \times 100 \ = \frac{7.50\text{ g}}{2.0} \times 100 \ = 375 \text{ g} \]

Understand the formula for mass/volume percentage

The mass/volume percentage concentration formula is given by: \[ \text{Mass/volume percentage} = \frac{\text{mass of solute}}{\text{volume of solution}} \times 100 \ \text{For example, } 25\text{ % (m/v) } \text{NaF}\] This means that 25 grams of NaF are present in every 100 mL of solution.

Calculate the solution volume for (b)

Given: \[4.0 \text{ g NaF in a } 25\text{ % (m/v) } \text{NaF solution} \] Rearrange the formula to solve for the volume of the solution: \[ \text{Volume of solution} = \frac{\text{mass of solute}}{\text{percentage}} \times 100 \ = \frac{4.0\text{ g}}{25} \times 100 \ = 16 \text{ mL} \]

Calculate the total mass of the solution for (c)

Given: \[20.0 \text{ g KBr in an } 8.0\text{ % (m/m) } \text{KBr solution} \] Rearrange the formula to solve for the mass of the solution: \[ \text{Mass of solution} = \frac{\text{mass of solute}}{\text{percentage}} \times 100 \ = \frac{20.0\text{ g}}{8.0} \times 100 \ = 250 \text{ g} \]

Key concepts

mass/mass percentage

Mass/mass percentage is an important concept in solution chemistry.
It tells us the concentration of a solute in a solution, expressed as a percentage of the total mass.
The formula for mass/mass percentage is given by:
\[ \text{Mass percentage} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 \]

For example, if we have a 2.0% (m/m) NaCl solution, it means there are 2 grams of NaCl in every 100 grams of the solution. Understanding this concept helps to calculate the amount of solute or the total mass of the solution.

Let's see it in practice: Given 7.50 grams of NaCl in a 2.0% (m/m) NaCl solution, the mass of the solution is calculated as:
\[ \text{Mass of solution} = \frac{\text{mass of solute}}{\text{percentage}} \times 100 \text{Mass of solution} = \frac{7.50 \text{ g}}{2.0} \times 100 \text{Mass of solution} = 375 \text{ g} \]

So, we need 375 grams of the NaCl solution to get 7.50 grams of NaCl.

mass/volume percentage

Mass/volume percentage is another way to express solution concentration.
In this method, the mass of the solute is compared with the volume of the solution rather than its mass.

The formula for mass/volume percentage is:
\[ \text{Mass/volume percentage} = \frac{\text{mass of solute}}{\text{volume of solution}} \times 100 \]

For instance, if we have a 25% (m/v) NaF solution, it means there are 25 grams of NaF in every 100 mL of solution.

To see how it works: Given 4.0 grams of NaF in a 25% (m/v) NaF solution, the volume of the solution is calculated by rearranging the formula:
\[ \text{Volume of solution} = \frac{\text{mass of solute}}{\text{percentage}} \times 100 \text{Volume of solution} = \frac{4.0 \text{ g}}{25} \times 100 \text{Volume of solution} = 16 \text{ mL} \]

Therefore, we need 16 mL of the NaF solution to get 4.0 grams of NaF.

solution concentration formulas

Solution concentration formulas help us to determine the strength of a solution.
They quantify how much solute is present in a given amount of solution.

Two common concentration formulas are:

• Mass/volume percentage
• Mass/mass percentage

Each formula serves a different purpose and is used based on whether the problem provides mass or volume.

For example:
- Mass/mass percentage is used when both solute and solution are measured by mass. \[ \text{Mass percentage} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 \]
- Mass/volume percentage is employed when the solute is given in mass and the solution in volume. \[ \text{Mass/volume percentage} = \frac{\text{mass of solute}}{\text{volume of solution}} \times 100 \]

Understanding how and when to use these formulas can make solving concentration problems less confusing.

solute and solution calculations

Solute and solution calculations are essential for determining the exact amounts of solute and solution required.

To master these calculations, always follow these steps:

• Identify the given quantities (mass of solute, percentage concentration).
• Determine the type of concentration (mass/mass or mass/volume).
• Use the corresponding formula to solve for the unknown quantity.

For instance, with mass/mass percentage:
Given 20.0 grams of KBr in an 8.0% (m/m) KBr solution, we find the mass of the solution as:
\[ \text{Mass of solution} = \frac{\text{mass of solute}}{\text{percentage}} \times 100 \text{Mass of solution} = \frac{20.0 \text{ g}}{8.0} \times 100 \text{Mass of solution} = 250 \text{ g} \]

By understanding solute and solution calculations, you can effectively tackle chemistry problems involving various concentrations.