Problem 89 - Chemistry The Central Science In Si Units

Question

Calcium is an essential nutrient in our body. It is important for bone health. Four common calcium-containing supplements are calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\), calcium citrate \(\left(\mathrm{Ca}_{3} \mathrm{C}_{12} \mathrm{H}_{10} \mathrm{O}_{14}\right)\), calcium gluconate \(\left(\mathrm{CaC}_{12} \mathrm{H}_{22} \mathrm{O}_{14}\right),\) and calcium lactate \(\left(\mathrm{CaC}_{6} \mathrm{H}_{10} \mathrm{O}_{6}\right)\). Rank these calcium supplements in terms of the mass percentage of calcium they contain.

Step-by-Step Solution

Answer

Calcium carbonate > Calcium citrate > Calcium lactate > Calcium gluconate.

Step 1: Understand the Problem

The task is to determine the mass percentage of calcium in each of the four supplements: calcium carbonate, calcium citrate, calcium gluconate, and calcium lactate. Mass percentage is the ratio of the mass of calcium to the total mass of the compound, expressed as a percentage.

Step 2: Calculate Molar Mass of Each Compound

First, find the molar mass of each compound by adding the molar masses of all atoms in the formula: - Calcium carbonate (\( \text{CaCO}_3 \)): \( 40.08 + 12.01 + 3 \times 16.00 = 100.09 \, \text{g/mol} \)- Calcium citrate (\( \text{Ca}_3\text{C}_{12}\text{H}_{10}\text{O}_{14} \)): \( 3 \times 40.08 + 12 \times 12.01 + 10 \times 1.01 + 14 \times 16.00 = 498.46 \, \text{g/mol} \)- Calcium gluconate (\( \text{CaC}_{12}\text{H}_{22}\text{O}_{14} \)): \( 40.08 + 12 \times 12.01 + 22 \times 1.01 + 14 \times 16.00 = 430.39 \, \text{g/mol} \)- Calcium lactate (\( \text{CaC}_6\text{H}_{10}\text{O}_6 \)): \( 40.08 + 6 \times 12.01 + 10 \times 1.01 + 6 \times 16.00 = 218.14 \, \text{g/mol} \).

Step 3: Determine Mass of Calcium in Each Compound

For each compound, find the total mass of calcium present:- Calcium carbonate: 1 calcium atom, mass \( = 40.08 \, \text{g/mol} \)- Calcium citrate: 3 calcium atoms, mass \( = 3 \times 40.08 = 120.24 \, \text{g/mol} \)- Calcium gluconate: 1 calcium atom, mass \( = 40.08 \, \text{g/mol} \)- Calcium lactate: 1 calcium atom, mass \( = 40.08 \, \text{g/mol} \).

Step 4: Calculate Mass Percentage

Use the formula for mass percentage: \[ \text{Mass percentage of calcium} = \frac{\text{Mass of calcium in compound}}{\text{Total molar mass of compound}} \times 100\%\]Calculate for each:- Calcium carbonate: \( \frac{40.08}{100.09} \times 100 \% = 40.05\% \)- Calcium citrate: \( \frac{120.24}{498.46} \times 100\% = 24.13\% \)- Calcium gluconate: \( \frac{40.08}{430.39} \times 100\% = 9.31\% \)- Calcium lactate: \( \frac{40.08}{218.14} \times 100\% = 18.38\% \).

Step 5: Rank the Supplements

Based on the calculated mass percentages of calcium, rank the supplements from highest to lowest: 1. Calcium carbonate: 40.05% 2. Calcium citrate: 24.13% 3. Calcium lactate: 18.38% 4. Calcium gluconate: 9.31%.

Key Concepts

Mass Percentage

When we talk about mass percentage in chemistry, we are referring to a way of describing the concentration of a particular element within a compound. For calcium supplements, this is incredibly useful. The mass percentage is determined by taking the mass of the desired element, in this case, calcium, and dividing it by the total molar mass of the compound. Then we multiply by 100 to turn this ratio into a percentage.

The formula is given by: \[ \text{Mass percentage} = \frac{\text{mass of element in 1 mole of compound}}{\text{total molar mass of compound}} \times 100\% \]This tells you what fraction of the total weight of the supplement comes from the calcium itself. It's handy for comparing the efficiency of different calcium supplements.

Calcium Carbonate

One of the most commonly used calcium supplements is calcium carbonate (\( \text{CaCO}_3 \)). It's popular because it contains a high mass percentage of calcium, making it efficient for bone health maintenance.

To calculate this, we first need to find its molar mass by adding the atomic masses of calcium, carbon, and oxygen present in the compound. According to the formula:- Calcium: 40.08 g/mol
- Carbon: 12.01 g/mol
- Oxygen: 3 x 16.00 g/mol (since there are three oxygen atoms)

Adding these, we find that the molar mass of calcium carbonate is 100.09 g/mol. Given that only 40.08 g/mol of this entire mass is calcium, we compute the mass percentage as follows:\[ \frac{40.08}{100.09} \times 100\% = 40.05\% \]This high percentage means more calcium intake per dose, which is often why people choose calcium carbonate supplements.

Molar Mass

Understanding molar mass is fundamental when dealing with chemical compositions and nutritional analysis like the one we're exploring here. Molar mass is the weight of one mole of a given substance and is represented in g/mol. It's calculated by summing up the atomic masses of each atom in the molecule.

For example, in calcium citrate (\( \text{Ca}_3\text{C}_{12}\text{H}_{10}\text{O}_{14} \)), we calculate:- Calcium: 3 x 40.08 g/mol
- Carbon: 12 x 12.01 g/mol
- Hydrogen: 10 x 1.01 g/mol
- Oxygen: 14 x 16.00 g/mol

These add up to a molar mass of 498.46 g/mol. Knowing this helps us find the mass percentage of calcium, which informs us how effective it is as a supplement when compared to others.

Nutrient Analysis

Nutrient analysis is critical in determining the nutritional value of dietary supplements. This includes evaluating the mass percentage of essential nutrients like calcium in supplements such as calcium gluconate or calcium lactate.

Calcium is vital for maintaining healthy bones and other functions in our bodies. Through nutrient analysis, we can determine how supplements stack up against each other in delivering calcium. For instance, calcium gluconate has a lower mass percentage of calcium at 9.31% compared to 40.05% in calcium carbonate. This analysis guides consumers to make an informed choice depending on their dietary needs.

So, when choosing a supplement, understanding the nutrient content, as revealed by analyses like mass percentage, is essential for ensuring adequate calcium intake.