Question

A pulverized rock sample believed to be pure calcium carbonate, \(\mathrm{CaCO}_{3}\), is subjected to chemical analysis and found to contain \(51.3 \% \mathrm{Ca}, 7.7 \% \mathrm{C}\), and \(41.0 \% \mathrm{O}\) by mass. Why can't this rock sample be pure \(\mathrm{CaCO}_{3} ?\)

Short answer

The mass percentages of the elements do not match those of pure \(\mathrm{CaCO}_{3}\), indicating the sample is not pure.

Step-by-step solution

Determine the Molar Mass of CaCO3

First, let's find the molar mass of calcium carbonate (\(\mathrm{CaCO}_{3}\)). For this, we add the atomic masses of calcium (\(\mathrm{Ca}\) = 40.08 g/mol), carbon (\(\mathrm{C}\) = 12.01 g/mol), and three oxygen atoms (\(\mathrm{O}\) = 16.00 g/mol each). \\[\text{Molar mass of } \mathrm{CaCO}_{3} = 40.08 + 12.01 + 3 \times 16.00 = 100.09 \text{ g/mol}\]

Calculate Theoretical Mass Percentages

Now, calculate the theoretical mass percentages of each element in pure \(\mathrm{CaCO}_{3}\). This is done using the formula for percent by mass: \(\frac{\text{mass of element in 1 mol}}{\text{molar mass of the compound}} \times 100\). \For calcium: \[\frac{40.08}{100.09} \times 100 \approx 40.04\%\] \For carbon: \[\frac{12.01}{100.09} \times 100 \approx 12.00\%\] \For oxygen: \[\frac{48.00}{100.09} \times 100 \approx 47.96\%\]

Compare Given and Theoretical Percentages

Compare the given mass percentages in the sample with the theoretical percentages calculated in Step 2. \ - Given: \(51.3\% \mathrm{Ca}, 7.7\% \mathrm{C}, 41.0\% \mathrm{O}\) \ - Theoretical for \(\mathrm{CaCO}_{3}\): \(40.04\% \mathrm{Ca}, 12.00\% \mathrm{C}, 47.96\% \mathrm{O}\)

Analyze the Differences in Percentages

Notice the discrepancies: the given percentage for calcium is higher than theoretical, whereas percentages for carbon and oxygen are lower than theoretical. \ - Increased \(\mathrm{Ca}\) suggests more calcium or a different compound present. \ - Lower \(\mathrm{C}\) and \(\mathrm{O}\) suggest a less carbon and less oxygen than expected for pure \(\mathrm{CaCO}_{3}\).

Key concepts

Molar Mass Calculation

In chemistry, calculating the molar mass of a compound is a fundamental skill that aids in determining several other chemical characteristics of the substance. Let's focus on the molar mass calculation for calcium carbonate, often denoted as \(\text{CaCO}_{3}\). To calculate its molar mass, we sum up the atomic masses of each atom in the compound:

• Atomic mass of Calcium (\(\text{Ca}\)) is 40.08 g/mol.
• Atomic mass of Carbon (\(\text{C}\)) is 12.01 g/mol.
• Atomic mass of Oxygen (\(\text{O}\)) is 16.00 g/mol. Since there are three oxygen atoms, we multiply this by 3.

Overall, the molar mass of \(\text{CaCO}_{3}\) is computed as:
\[ \text{Molar mass of } \text{CaCO}_{3} = 40.08 + 12.01 + 3 \times 16.00 = 100.09 \text{ g/mol} \] Understanding the correct calculation of the molar mass is important for further analyses, such as determining the percent composition of the elements in the compound.

Chemical Composition Analysis

Chemical composition analysis helps to identify the proportion of different elements within a compound. This involves calculating the mass percent of each element in metal complexes, crystalline solids or any other compounds being analyzed.
In this case, we focus on calcium carbonate, \(\text{CaCO}_{3}\). For a compound to reflect its true chemical formula, its elements should be present in their empirical ratio. This is checked by calculating the percent composition using the formula:

• Mass percent of an element = \(\dfrac{\text{mass of element in 1 mol}}{\text{molar mass of the compound}} \times 100\)

When calculated for calcium carbonate, the theoretical compositions are:

• For calcium: \(\dfrac{40.08}{100.09} \times 100 \approx 40.04\%\)
• For carbon: \(\dfrac{12.01}{100.09} \times 100 \approx 12.00\%\)
• For oxygen: \(\dfrac{48.00}{100.09} \times 100 \approx 47.96\%\)

These theoretical values provide a benchmark to compare against experimental or given compositions.

Percent Composition in Chemistry

In chemistry, percent composition by mass is a critical concept used to describe the percentage by mass of each element in a compound. It not only confirms the purity of a substance but can identify discrepancies if the measurements do not match theoretical values.
For example, if a sample is believed to be pure \(\text{CaCO}_3\), its calculated theoretical percent compositions should match closely with the measured data. However, let's say the analysis yielded 51.3% calcium, 7.7% carbon, and 41.0% oxygen by mass from the sample. There are clear differences from the theoretical values:

• The actual value for calcium (51.3%) greatly exceeds the theoretical (40.04%).
• Carbon and oxygen are lower at 7.7% and 41.0%, compared to theoretical values of 12.00% and 47.96%, respectively.

Such discrepancies imply that the sample contains impurities or additional compounds not accounted for in pure calcium carbonate. This analysis is crucial in quality control, material verification, and when determining the potential presence of other chemical species.