Problem 52 - Chemistry Matter and Change

Question

Calculate Calcium carbonate is the calcium source for many vitamin tablets. The recommended daily allowance of calcium is 1000 \(\mathrm{mg}\) of \(\mathrm{Ca}^{2}+\) ions. How many moles of \(\mathrm{Ca}^{2+}\) does 1000 \(\mathrm{mg}\) represent?

Step-by-Step Solution

Answer

1000 mg of calcium represents approximately 0.0249 moles of \( \mathrm{Ca}^{2+} \).

Step 1: Understand the Problem

We need to find the number of moles of \( \mathrm{Ca}^{2+} \) ions in 1000 mg of calcium. The problem provides the mass of calcium and requires conversion to moles.

Step 2: Know the Molar Mass of Calcium

The molar mass of calcium (Ca) is known to be approximately \( 40.08 \ \mathrm{g/mol} \). This will help in converting mass to moles.

Step 3: Convert Milligrams to Grams

First, we convert the given mass of calcium from milligrams to grams, because the molar mass is in grams per mole:\[1000 \ \mathrm{mg} = 1 \ \mathrm{g}\]

Step 4: Use the Formula for Moles

To calculate moles, use the formula:\[\text{moles} = \frac{\text{mass in grams}}{\text{molar mass}}\]Substitute the known values:\[\text{moles of } \mathrm{Ca}^{2+} = \frac{1 \ \mathrm{g}}{40.08 \ \mathrm{g/mol}} \]

Step 5: Perform the Calculation

Calculate the number of moles:\[\text{moles of } \mathrm{Ca}^{2+} \approx 0.0249 \text{ moles}\]

Key Concepts

Molar Mass

The molar mass is a fundamental concept in chemistry that relates to the mass of one mole of a substance, expressed in grams per mole (g/mol). It's essential for converting between mass and moles, especially in analytical and chemical calculations. To find the molar mass, you'd sum up the atomic masses of all atoms present in a compound. For an element like calcium (Ca), its atomic mass directly corresponds to its molar mass, approximately 40.08 g/mol. Knowing the molar mass allows us to translate a given mass into its equivalent number of moles using the formula:

• moles = \( \frac{\text{mass in grams}}{\text{molar mass}} \)

This formula is a bridge between the weight we measure on a balance and the more abstract idea of moles, which represent a set number of atoms or molecules. Whether you're working with calcium or any other chemical, the molar mass is your go-to tool for these conversions.

Calcium Carbonate

Calcium carbonate (CaCO extsubscript{3}) is a common compound found in nature in the form of minerals such as limestone or chalk. It's a primary source of calcium and often used in things like dietary supplements or antacids. When we talk about the calcium content in calcium carbonate, it's important to break down its structure. Calcium carbonate contains calcium ions (Ca extsuperscript{2+}), carbonate ions (CO extsubscript{3} extsuperscript{2-}), and has a molar mass of approximately 100.09 g/mol. In dietary situations, like those requiring calcium supplements, understanding the content of calcium in calcium carbonate is crucial. For example, the calcium proportion in CaCO extsubscript{3} is important to ascertain the actual intake of elemental calcium. In pure form, calcium constitutes about 40% of calcium carbonate's total mass. This conversion factor is key when you're calculating how much calcium you're ingesting through a supplement like this.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. This includes the calculation of moles, masses, and particles involved, based on balanced chemical equations. At its core, stoichiometry ensures that we respect the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction. In practical terms, this means that the mass of the reactants must equal the mass of the products. For example, when working with a compound such as calcium carbonate in a practical scenario like supplementation, stoichiometry helps calculate the number of moles of calcium ions (Ca extsuperscript{2+}) present. Using stoichiometric relationships, one can determine how much Ca extsuperscript{2+} is released per unit of calcium carbonate reacted or consumed. Moreover, exercises like calculating the moles of Ca extsuperscript{2+} ions in a given mass involve stoichiometry at the level of:

• Converting mass to moles using the molar mass.
• Relating the quantity of individual compound components (like ions) to the whole compound.

These calculations are fundamental not only in classroom exercises but also in practical applications like nutrition and medicine.