Question

A solution contains \(7.5 \%\) by mass \(\mathrm{NaCl}\) and \(2.5 \%\) by mass \(\mathrm{KBr}\). What mass of each solute is contained in \(125 \mathrm{~g}\) of the solution?

Short answer

In a 125 g solution containing 7.5% by mass NaCl and 2.5% by mass KBr, there are 9.375 g of NaCl and 3.125 g of KBr.

Step-by-step solution

Understand the concept of percent by mass

Percent by mass is defined as the ratio of the mass of the solute to the mass of the solution, multiplied by 100. Mathematically, it can be expressed as: Percent by mass = \(\frac{mass\ of\ solute}{mass\ of\ solution}\) × 100 We will use this formula to find the mass of each solute in the given mass of the solution.

Calculate the mass of NaCl

We are given that NaCl is 7.5% by mass in the solution. Using the formula for percent by mass, we can write: 7.5 = \(\frac{mass\ of\ NaCl}{125}\) × 100 Now, we will solve for the mass of NaCl: mass of NaCl = \(\frac{7.5 × 125}{100}\) mass of NaCl = 9.375 g So, 9.375 g of NaCl is contained in 125 g of the solution.

Calculate the mass of KBr

Similarly, we are given that KBr is 2.5% by mass in the solution. Using the formula for percent by mass, we can write: 2.5 = \(\frac{mass\ of\ KBr}{125}\) × 100 Now, we will solve for the mass of KBr: mass of KBr = \(\frac{2.5 × 125}{100}\) mass of KBr = 3.125 g So, 3.125 g of KBr is contained in 125 g of the solution. In conclusion, in 125 g of the given solution, there are 9.375 g of NaCl and 3.125 g of KBr.

Key concepts

Understanding Mass of Solute

The mass of solute refers to the actual amount, in grams, of a substance that is dissolved in a solution. In any given solution, the solute is the component that is present in a smaller amount compared to the solvent. To determine the mass of the solute, you can use the information provided, such as percent by mass and the total mass of the solution.

In our exercise, we need to find out how much NaCl and KBr are in a solution that weighs 125 grams. We use the percent by mass formula, which establishes the relationship between the mass of solute and the mass of solution. By understanding this relationship, we can solve for the solute mass using the given percentage of each solute in the solution.

More directly, we use this formula:

• First, change the percentage value to a decimal (e.g., 7.5% becomes 0.075).
• Multiply the decimal with the total mass of the solution (for NaCl, that would be 0.075 × 125 g).
• This calculation will give you the mass of the solute in grams.

In our example, NaCl has a mass of 9.375 grams and KBr has 3.125 grams.

Determining Mass of Solution

The mass of a solution is the total weight or mass of the solution, which includes both the solute and the solvent. In cases where the composition of the solution is known in terms of percentages by mass, the given total mass of the solution allows us to calculate how much of each solute is present.

To solve problems involving the mass of the solution, remember the following steps:

• First, determine the total mass of the solution, which serves as the base for calculating the individual masses of solutes based on their respective percentages.
• Use the given total mass to apply the percent by mass formula, enabling us to extract the masses of specific solutes contained within the solution.

In the problem being discussed, the total mass of the solution is 125 grams. This mass of 125 grams includes the mass of NaCl, KBr, and the solvent itself. Knowing the total mass helps in understanding how solutes are distributed based on their percent by mass.

Calculating Solution Concentration

Solution concentration is a measure of how much solute is present compared to the overall solution, often expressed as a percentage by mass or volume. It's a way to specify the strength or purity of a solution.


In the context of percent by mass, the concentration is calculated using the formula:

• We use the formula: \(\text{Percent by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\).
• This tells us what fraction of the total solution's mass consists of the solute.
• For practical applications, changing this percentage to a decimal helps to find the exact mass of each solute in the solution.

This concentration is important for understanding the mix of substances in a physical context. When you know the percent by mass, it becomes easy to calculate precise amounts of solutes, which is very helpful in scientific and industrial applications, or even in daily life situations such as preparing recipes or chemical baths.