A hard water sample contains 0.0085% Ca by mass (in the form of Ca2+ ions). How much water (in grams) contains 1.2 g of Ca? (1.2 g of Ca is the recommended daily allowance of calcium for adults between 19 and 24 years old.)

Verified step by step guidance

Identify the percentage of calcium in the water sample, which is given as 0.0085% by mass.

Understand that this means there are 0.0085 grams of calcium in every 100 grams of water.

Set up a proportion to find out how many grams of water contain 1.2 grams of calcium. Use the relationship: (0.0085 g Ca / 100 g water) = (1.2 g Ca / x g water).

Solve the proportion for x, which represents the mass of water that contains 1.2 grams of calcium.

Rearrange the equation to solve for x: x = (1.2 g Ca * 100 g water) / 0.0085 g Ca.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mass Percentage

Mass percentage is a way of expressing the concentration of a component in a mixture. It is calculated by taking the mass of the component, dividing it by the total mass of the mixture, and multiplying by 100. In this question, the mass percentage of calcium in hard water is given as 0.0085%, which indicates that for every 100 grams of hard water, there are 0.0085 grams of calcium.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In this context, stoichiometry helps us determine how much water is needed to contain a specific mass of calcium. By using the mass percentage of calcium, we can set up a proportion to find the total mass of water required to achieve the desired amount of calcium.

Conversion of Units

Conversion of units is essential in chemistry to ensure that measurements are compatible and calculations yield accurate results. In this problem, we need to convert the mass of calcium (1.2 g) into the corresponding mass of hard water using the mass percentage. Understanding how to convert between grams of calcium and grams of water is crucial for solving the problem correctly.

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Conversion Factors

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