Question

A solution is \(0.1 \%\) by mass calcium chloride. Therefore, \(100 . \mathrm{g}\) of the solution contains _____ g of calcium chloride.

Short answer

100 grams of the solution contains \(0.1 \ \mathrm{grams}\) of calcium chloride.

Step-by-step solution

Understand the percentage by mass

Percentage by mass refers to the mass of the solute (calcium chloride in this case) divided by the mass of the solution (solute + solvent), multiplied by 100. In this exercise, we are given a solution that is 0.1% by mass calcium chloride. Thus, for 0.1% of the total mass of the solution, we have calcium chloride.

Apply the percentage to the mass of the solution

Since we are asked to find the mass of calcium chloride in 100 grams of the solution, we can simply apply the given percentage (0.1%) to this total mass: \[0.1 \% \times 100 \ \mathrm{grams} \]

Calculate the mass of calcium chloride in the given amount of solution

Now, we can perform the calculation: \[0.1 \% \times 100 \ \mathrm{grams} = \frac{0.1}{100} \times 100 \ \mathrm{grams} = 0.1 \ \mathrm{grams} \] Thus, 100 grams of the solution contains 0.1 grams of calcium chloride.

Key concepts

Concentration of Solutions

Understanding the concentration of solutions is essential in chemistry, as it quantifies how much solute is present in a certain amount of solvent. In the context of our problem, the concentration is given as a percentage by mass, which indicates that for every 100 parts by mass of the solution, a certain part is the solute. For example, a solution that is 0.1% by mass calcium chloride means that out of 100 grams of this solution, 0.1 grams is calcium chloride and the rest is the solvent.

To find the mass of calcium chloride in any given mass of solution, we use the percentage by mass in a straightforward calculation. This allows us to accurately measure out chemicals for reactions and to make solutions of desired concentrations. In laboratory and industrial settings, being able to calculate and prepare solutions with specific concentrations is crucial for the success of chemical processes and experiments.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. The term comes from the Greek words 'stoicheion' (element) and 'metron' (measure). In stoichiometry, we use balanced chemical equations to relate the masses of reactants and products.

Applying stoichiometry to our problem enables us to understand how the mass of calcium chloride relates to the mass of the entire solution. It is a fundamental tool that chemists use to make predictions about the outcomes of chemical reactions, such as how much product can be formed from a certain amount of reactants or how much of one reactant is needed to fully react with another. These calculations involve molar masses, the mole concept, and the law of conservation of mass, ensuring matter is neither created nor destroyed during a chemical reaction.

Solutes and Solvents

In a solution, the substance that is dissolved is called the solute, while the substance that does the dissolving is the solvent. Water is a common solvent and is often referred to as the 'universal solvent' due to its ability to dissolve many different substances.

In our textbook exercise, calcium chloride is the solute, and it is dispersed uniformly throughout the solvent creating a homogenous mixture. The solute-solvent interaction is important for various processes, such as forming electrolyte solutions that conduct electricity. Solutions can be solid, liquid, or gas; examples include alloys, saline water, and air, respectively. Understanding the nature of solutes and solvents helps in predicting solubility, preparing solutions of desired concentration, and facilitates discussions regarding various chemical properties like boiling point elevation and freezing point depression.