Question

The percent by mass of calcium chloride in a solution is found to be 2.65%. If 50.0 g of calcium chloride is used, what is the mass of the solution?

Short answer

The mass of the solution containing 50.0 g of calcium chloride with a mass percentage of 2.65% is approximately 1887.23 g.

Step-by-step solution

Write the given information and formula

We are given the following information: - Percent by mass of calcium chloride: 2.65% - Mass of calcium chloride: 50.0 g The formula for mass percentage is: Mass percentage = (Mass of solute / Mass of solution) × 100 In this case, the mass percentage is already given, and we want to find the mass of the solution. Let's rearrange the formula to solve for the mass of the solution.

Rearrange the formula to solve for the mass of the solution

We need to find the mass of the solution, represented by "Mass of solution" in the formula. So, we can rearrange the formula as follows: Mass of solution = (Mass of solute / Mass percentage) × 100 Now we can plug in the given values for the mass of solute (calcium chloride) and mass percentage to find the mass of the solution.

Plug in the given values and solve for the mass of the solution

Now, let's plug in the given values into the rearranged formula: Mass of solution = (50.0 g / 2.65%) × 100 First, we need to convert 2.65% to decimal form by dividing by 100: 2.65% = 2.65/100 = 0.0265 Now, we can substitute the decimal value back into the formula: Mass of solution = (50.0 g / 0.0265) × 100 Now, let's perform the calculations: Mass of solution = (50.0 g / 0.0265) × 100 ≈ 1887.23 g

Write the final answer

The mass of the solution containing 50.0 g of calcium chloride with a mass percentage of 2.65% is approximately 1887.23 g.

Key concepts

Solution Concentration

Understanding solution concentration is essential when working with chemical solutions. It represents how much solute is dissolved in a given amount of solvent. There are several ways to quantify this, one of which is mass percent. In our exercise, the mass percent tells us the amount of calcium chloride in relation to the total mass of the solution. This is particularly useful when preparing a solution with a specific concentration needed to conduct an experiment or in industrial processes.
To further enhance learning, we could consider visual aids such as diagrams that depict the dissolution process, or interactive simulations that allow students to adjust concentrations and see the outcomes. Such tools can make this often abstract concept more tangible and easier to comprehend.

Stoichiometry

Stoichiometry is at the heart of chemistry, concerned with the quantitative relationships between reactants and products in a chemical reaction. It helps us predict the amounts of substances consumed and products formed in a given reaction. In our textbook problem, while stoichiometry isn't directly used, the principles behind it—like the conservation of mass—are inherent in understanding mass percent and solution composition.
For educational improvement, linking stoichiometry to real-life examples, such as cooking recipes, could be valuable. By equating the concept of reactants to ingredients and products to the final dish, students can create mental bridges that simplify the understanding of stoichiometric calculations.

Percent Composition

Percent composition is the calculation that shows the proportionate amounts of each element in a compound or each component in a mixture. As seen in the original exercise, it's expressed as a percentage. This concept is widely used in formulation, pharmacology, and material science to control the properties of the final product.
To give students a better grasp of percent composition, including its practicality in everyday items can be beneficial. For example, by analyzing the percent composition of macronutrients on food labels, students can relate classroom knowledge to their daily lives, demonstrating the practicality of chemistry outside the lab.