Question

A solution is to be prepared that will be \(4.50 \%\) by mass calcium chloride. To prepare 175 g of the solution, what mass of calcium chloride will be needed?

Short answer

To prepare a 175 g solution with a 4.50% by mass concentration of calcium chloride, we need 7.88 g of calcium chloride.

Step-by-step solution

Write down the given information

We are given the following information: - Mass percent of calcium chloride = 4.50% - Total mass of the solution = 175 g - Mass of calcium chloride = ?

Convert mass percent to decimal

In order to solve for the mass of calcium chloride in the solution, we first need to convert the mass percent into decimal form. To do this, divide the mass percent by 100: Mass percent as decimal: \(\frac{4.50}{100} = 0.045\)

Rearrange the mass percent formula to solve for the mass of calcium chloride

Now, we will rearrange the mass percent formula and solve for the mass of calcium chloride: Mass of calcium chloride = \(\frac{Mass\,Percent \times Total\,Mass\,of\,Solution}{100} \) Since we have already converted the mass percent to decimal, we can use the decimal value directly: Mass of calcium chloride = 0.045 * Total mass of the solution

Plug in the given values and solve for the mass of calcium chloride

Now, we will plug in the given values into the formula: Mass of calcium chloride = 0.045 * 175 g Mass of calcium chloride = 7.875 g

Round the result and write the final answer

Finally, round the result to an appropriate number of decimal places (in this case, two decimal places) and write the final answer: Mass of calcium chloride needed = 7.88 g So, to prepare a 175 g solution with a 4.50% by mass concentration of calcium chloride, we need 7.88 g of calcium chloride.

Key concepts

Calcium Chloride Solution

Calcium chloride is a chemical compound composed of calcium and chlorine. This compound is commonly used in solutions for various applications, such as de-icing roads, controlling dust, and even in some food processing activities.
To make a calcium chloride solution, a specific amount of the solid calcium chloride is mixed with water. In this exercise, the task is to prepare a solution where the final mixture contains 4.50% calcium chloride by mass. This means that in every 100 grams of the solution, 4.50 grams are calcium chloride, and the rest is typically water and other components.
Such solutions are formulated to achieve certain properties, like freezing point depression or concrete acceleration, so getting the correct mass of calcium chloride is key for effectiveness.

Mass Percent to Decimal Conversion

Mass percent represents the concentration of a component in a mixture or solution. It is calculated as the mass of the solute divided by the total mass of the solution, similar to the idea of a percentage in everyday math.
Converting a mass percent to a decimal is useful because it simplifies calculations. To convert the mass percent, simply divide by 100. This transforms the percentage into a decimal usable in mathematical operations.
For instance, a mass percent of 4.50% is converted by dividing 4.50 by 100, resulting in 0.045. Using decimals streamlines the process of finding out how much of a particular substance is needed to achieve a desired solution concentration. By setting up calculations using the decimal equivalent, you can easily determine the amount of solute needed.

Mass of Solute in Solution

To find out how much solute is in a solution, you can use the rearranged form of the mass percent equation. This helps in determining the precise mass of the solute, such as calcium chloride, required per certain amount of the entire solution.
The formula is straightforward: \[ \text{Mass of solute} = \text{Decimal mass percent} \times \text{Total mass of solution} \]
In the given problem, it translates to multiplying 0.045 (decimal form of 4.50%) with 175 grams, the total mass of the desired solution. This computation gives 7.875 grams as the calculated mass of calcium chloride required.
It's important always to round appropriately. In this case, rounding 7.875 to two decimal places results in 7.88 grams. This ensures that the solution is prepared correctly and meets the required specifications.