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?

Short answer

There are approximately 0.0249 moles of Ca²⁺ ions in 1000 mg of calcium, calculated by converting 1000 mg to 1 g and then dividing by the molar mass of calcium (40.08 g/mol).

Step-by-step solution

1. Convert mg to g

To convert 1000 mg of calcium to grams, divide by 1000, as there are 1000 mg in a gram: 1000 mg × (1 g / 1000 mg) = 1 g So, we have 1 g of Ca²⁺ ions.

2. Calculate moles using molar mass

Using the molar mass of calcium (40.08 g/mol), we can now calculate the number of moles: moles = (mass of calcium) / (molar mass of calcium) moles = (1 g) / (40.08 g/mol)

3. Find the number of moles

Now we can find the number of moles by dividing 1 g by 40.08 g/mol: moles = 1 g / 40.08 g/mol ≈ 0.0249 mol There are approximately 0.0249 moles of Ca²⁺ ions in 1000 mg of calcium.

Key concepts

Calcium Carbonate

Calcium carbonate is a chemical compound commonly found in rocks and is the main component of pearls, marine organisms, and even eggshells. This compound is widely used in the production of materials like cement and also serves as the foundational calcium source in dietary supplements. For those aiming to boost their calcium intake, especially through supplements, calcium carbonate is a popular choice.

In vitamin tablets, calcium carbonate plays a crucial role due to its high calcium content. When incorporated into diets, it helps maintain healthy bones and teeth. Understanding how calcium carbonate contributes to our calcium intake is essential in calculating the exact amount of calcium derived from supplements.

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It is crucial in converting between grams and moles and plays a central role in stoichiometry. The molar mass is usually expressed in grams per mole (g/mol), and you can find it on the periodic table.

For calcium, the molar mass is 40.08 g/mol. This number is the mass of one mole of calcium atoms. Knowing this value is key when calculating moles of calcium in chemical reactions or dietary formulations. In our scenario, it allows us to convert the mass of calcium to the number of moles to understand how much calcium ion is present.

Moles of Calcium

A mole is a unit used to represent a specific quantity of a substance, allowing chemists to count particles like atoms and ions in bulk terms. One mole of any substance contains Avogadro's number of entities, around 6.022 x 10²³ particles.

In this exercise, the focus is on moles of calcium ions ( Ca^{2+}) derived from calcium carbonate. When calculating the moles of calcium, the molar mass helps us determine exactly how many moles are present in a given mass. For example, 1 gram of calcium divided by its molar mass of 40.08 g/mol gives approximately 0.0249 moles. This simplifies understanding the actual number of calcium ions provided in a given amount.

Conversion of Units

Conversion of units is a vital skill in scientific calculations. It involves changing the measurement of a quantity into different units without altering its value. In chemistry, achieving accuracy often necessitates converting between units, such as milligrams to grams, to match standard molar calculations.

In the exercise, converting 1000 mg of calcium to grams by dividing by 1000 (since 1 g = 1000 mg) was necessary. Once in grams, the calculation was facilitated by the molar mass to determine the moles of calcium present. Mastering unit conversions like this ensures precision in calculations and prevents errors, particularly in complex chemical equations.