Question

Cacodyl, a compound containing arsenic, was reported in 1842 by the German chemist Robert Wilhelm Bunsen. It has an almost intolerable garlic-like odor. Its molar mass is \(210 \mathrm{g} / \mathrm{mol}\), and it is \(22.88 \%\) C, \(5.76 \%\) H, and \(71.36 \%\) As. Determine its empirical and molecular formulas.

Short answer

The empirical formula is \( \text{C}_2\text{H}_6\text{As} \) and the molecular formula is \( \text{C}_4\text{H}_{12}\text{As}_2 \).

Step-by-step solution

Convert Percentages to Mass

Assume you have 100 grams of cacodyl. This means you have: - 22.88 grams of Carbon (C) - 5.76 grams of Hydrogen (H) - 71.36 grams of Arsenic (As)

Convert Mass to Moles

Calculate the number of moles of each element using their atomic masses:- Moles of C = \( \frac{22.88 \text{ g}}{12.01 \text{ g/mol}} = 1.905 \text{ mol} \)- Moles of H = \( \frac{5.76 \text{ g}}{1.008 \text{ g/mol}} = 5.714 \text{ mol} \)- Moles of As = \( \frac{71.36 \text{ g}}{74.92 \text{ g/mol}} = 0.952 \text{ mol} \)

Determine Empirical Formula

Divide the number of moles of each element by the smallest number of moles, which is 0.952:- C: \( \frac{1.905}{0.952} = 2.00 \)- H: \( \frac{5.714}{0.952} = 6.00 \)- As: \( \frac{0.952}{0.952} = 1.00 \)The empirical formula is \( \text{C}_2\text{H}_6\text{As} \).

Determine Molecular Formula

Calculate the molar mass of the empirical formula \( \text{C}_2\text{H}_6\text{As} \):\( 2(12.01) + 6(1.008) + 1(74.92) = 104 \text{ g/mol} \).Determine the ratio of the molar mass of the compound to the empirical formula mass:\( \frac{210}{104} \approx 2 \).Multiply the subscripts in the empirical formula by 2 to obtain the molecular formula \( \text{C}_4\text{H}_{12}\text{As}_2 \).

Key concepts

Molar Mass Calculation

When dealing with chemical compounds, calculating the molar mass is a fundamental step in understanding the compound's properties. The molar mass refers to the mass of one mole of a substance, which is directly related to the atomic masses of its constituent elements. For cacodyl, which has a published molar mass of 210 g/mol, determining the molar mass helps establish its molecular and empirical formulas. The molar mass can be simply calculated by adding the atomic masses of all the atoms in the empirical formula.

To find the molar mass, you can follow these steps:

• Identify the elements in the compound and their respective quantities from the empirical formula.
• Use the periodic table to find the atomic mass of each element.
• Multiply the atomic mass of each element by its subscript in the formula.
• Add all these values together to get the molar mass in g/mol.

For instance, in the empirical formula \( \text{C}_2\text{H}_6\text{As} \), the molar mass is calculated as follows: \( 2(12.01) + 6(1.008) + 1(74.92) \). The result, 104 g/mol, needs to be compared to the given molar mass to determine if the molecular formula is the same or a multiple of the empirical formula.

Elemental Composition

Understanding the elemental composition of a compound is critical in finding out how many grams of each element is present in a sample of the compound. In the case of cacodyl, knowing that it contains 22.88% carbon, 5.76% hydrogen, and 71.36% arsenic allows us to proceed with stoichiometric calculations.

To convert the elemental composition from percentages to a mass basis, assume you have a 100 g sample of the compound. In this situation:

• The mass of Carbon (C) is 22.88 g.
• The mass of Hydrogen (H) is 5.76 g.
• The mass of Arsenic (As) is 71.36 g.

With these masses, you can continue to determine the number of moles of each element. This approach simplifies the process of moving from percentage composition directly to formulas. By knowing the masses of each element, we can use the atomic weights to find how these elements come together in the substance.

Chemical Formula Determination

Determining the chemical formula, both empirical and molecular, involves a systematic approach to understanding how atoms are arranged in a compound. The empirical formula represents the simplest whole-number ratio of atoms in a compound. For cacodyl, steps include converting mass to moles, simplifying mole ratios, and confirming the empirical formula.

Here's how you can arrive at these formulas:

• Calculate the moles of each element using the formula: \( \text{moles} = \frac{\text{mass}}{\text{atomic mass}} \).
• Divide the moles of each element by the smallest number of moles from your calculations to get a ratio.
• For cacodyl, the mole ratio yielded the empirical formula: \( \text{C}_2\text{H}_6\text{As} \).
• Next, calculate the empirical formula mass and compare it to the known molar mass of the compound. If different, determine the ratio and multiply to get the molecular formula.

For cacodyl, multiplying \( \text{C}_2\text{H}_6\text{As} \) by a factor of 2 (since \( \frac{210}{104} \approx 2 \)) gives us the molecular formula \( \text{C}_4\text{H}_{12}\text{As}_2 \), demonstrating how the atoms group in the actual molecule.