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Chapter 14: Problem 57

A hard water sample contains \(0.0085 \%\) Ca by mass (in the form of \(\mathrm{Ca}^{2+}\) ions). How much water (in grams) contains \(1.2 \mathrm{~g}\) of Ca? (1.2 g of Ca is the recommended daily allowance of calcium for adults between 19 and 24 years old. \()\)

Short Answer

Expert verified
X = 1.2 g / 0.000085 = 14117.65 grams

Step by step solution

01

Convert Percentage to Decimal Form

Convert the given percentage of calcium in the water sample to decimal form by dividing by 100. For example, 0.0085% becomes 0.000085.
02

Set up the Proportion

Using the decimal form of the calcium percentage, set up a proportion to relate calcium mass to the total water mass. If 0.000085 parts of every 1 part of water is calcium, then 1.2 g of calcium corresponds to X g of water.
03

Solve for the Total Water Mass

Solve for X (the total water mass containing 1.2 g of calcium) by dividing the amount of calcium needed by the decimal form of the percentage of calcium. X = (1.2 g calcium) / 0.000085.
04

Calculate and Find the Answer

Perform the division to find the total grams of water needed. X = 1.2 g / 0.000085.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hard Water Chemistry
Hard water refers to water that has a high mineral content, usually calcium and magnesium ions. In daily life, this manifests as water that does not lather soap easily and leaves deposits on fixtures and pipes, known as limescale. From a chemistry standpoint, when you dissolve calcium compounds like calcium carbonate or calcium bicarbonate in water, they dissociate to release \(\mathrm{Ca^{2+}}\) ions. The concentration of these calcium ions in the water determines the 'hardness' of the water.

Understanding hard water is crucial when dealing with issues such as the scaling of pipes, the efficiency of soaps and detergents, and nutritional calculations for water consumption. For instance, if someone is looking to meet their daily calcium intake through water, knowledge of the calcium content in their hard water supply would be indispensable.
Converting Percentages to Decimal
When you come across a percentage, it's presenting a value as a fraction of 100. To convert this percentage into a decimal, which is necessary for a variety of arithmetic calculations, you simply divide the percentage by 100. This step diminishes the value by two decimal places to the left. For instance, a percentage like \(0.0085\%\) becomes \(0.000085\) when converted into a decimal.

This conversion is not just a simple math trick; it's foundational for calculations in chemistry, finance, statistics, and more. When you grasp this concept, you unlock the ability to work with ratios and proportions that are imperative for solving real-world problems, such as calculating how much calcium is in a given amount of water, which is a key factor for dieticians and health-conscious individuals.
Mass Proportion Calculation
The concept of mass proportion in chemistry is about relating the mass of one substance to the total mass of the mixture it's a part of. This is often used to figure out how much of a certain chemical is present in a solution or mixture.

In the context of the exercise, we relate the mass of calcium to the mass of water to find how much water you would need to consume to intake a certain amount of calcium. Once you've converted the percentage concentration of calcium to a decimal, you set up a simple proportion: if \(0.000085\) parts of water are calcium, then \(1.2\) grams of calcium would be found in a certain amount of water. Solving this proportion, you discover the total mass of water required to provide the daily recommended allowance of calcium.

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Most popular questions from this chapter

Household hydrogen peroxide is an aqueous solution containing \(3.0 \%\) hydrogen peroxide by mass. What is the molarity of this solution? (Assume a density of \(1.01 \mathrm{~g} / \mathrm{mL}\).)

Silver nitrate solutions are often used to plate silver onto other metals. What is the maximum amount of silver (in grams) that can be plated out of \(4.8 \mathrm{~L}\) of an \(\mathrm{AgNO}_{3}\) solution containing \(3.4 \%\) Ag by mass? Assume that the density of the solution is \(1.01 \mathrm{~g} / \mathrm{mL}\).

Lithium iodide has a lattice energy of \(-7.3 \times 10^{2} \mathrm{~kJ} / \mathrm{mol}\) and a heat of hydration of \(-793 \mathrm{~kJ} / \mathrm{mol}\). Find the heat of solution for lithium iodide and determine how much heat is evolved or absorbed when \(15.0 \mathrm{~g}\) of lithium iodide completely dissolves in water.

A solution contains \(50.0 \mathrm{~g}\) of heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right)\) and \(50.0 \mathrm{~g}\) of octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) at \(25^{\circ} \mathrm{C}\). The vapor pressures of pure heptane and pure octane at \(25^{\circ} \mathrm{C}\) are 45.8 torr and 10.9 torr, respectively. Assuming ideal behavior, answer the following: a. What is the vapor pressure of each of the solution components in the mixture? b. What is the total pressure above the solution? c. What is the composition of the vapor in mass percent? d. Why is the composition of the vapor different from the composition of the solution?

A solution containing \(27.55 \mathrm{mg}\) of an unknown protein per \(25.0 \mathrm{~mL}\) solution was found to have an osmotic pressure of 3.22 torr at \(25^{\circ} \mathrm{C} .\) What is the molar mass of the protein?
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