Question

Mercurous chloride is a fungicide. If the molar mass is \(470 \mathrm{~g} / \mathrm{mol}\) and the percent composition is \(85.0 \% \mathrm{Hg}\) and \(15.0 \% \mathrm{Cl}\), what is the molecular formula of mercurous chloride?

Short answer

The molecular formula of mercurous chloride is Hg2Cl2.

Step-by-step solution

Determine the Mass Contribution of Each Element

Given that the molar mass is 470 g/mol, start by calculating the mass of each element in the molecular formula based on the percent composition. Mercury (Hg) accounts for 85.0% of the mass, and Chlorine (Cl) accounts for 15.0% of the mass. Therefore, the mass of Hg is \( 470 \, \text{g/mol} \times 0.85 = 399.5 \, \text{g/mol} \) and the mass of Cl is \( 470 \, \text{g/mol} \times 0.15 = 70.5 \, \text{g/mol} \).

Calculate the Moles of Each Element

To find the number of moles, divide the mass of each element by its atomic mass. The atomic mass of Hg is approximately 200.59 g/mol and that of Cl is 35.45 g/mol. For Hg, the moles are \( \frac{399.5 \, \text{g/mol}}{200.59 \, \text{g/mol}} \approx 1.99 \) moles. For Cl, the moles are \( \frac{70.5 \, \text{g/mol}}{35.45 \, \text{g/mol}} \approx 1.99 \) moles.

Establish the Mole Ratio

The mole ratio between Hg and Cl is 1.99:1.99, which simplifies to 1:1. This implies there is one mercury atom for every chlorine atom in the molecular formula.

Determine the Molecular Formula

Since the simplest whole number ratio of moles is 1:1 for Hg and Cl, the empirical formula is HgCl. The molar mass confirms that this is also the molecular formula because the empirical molar mass of HgCl (which is 200.59 + 35.45 = 236.04 g/mol) would need to be multiplied to get to 470 g/mol, meaning two empirical units are needed, thus Hg2Cl2.

Key concepts

Molar Mass

Understanding molar mass is vital for tackling many chemistry problems. Molar mass is essentially the mass of one mole of a substance, typically measured in grams per mole (g/mol). It acts like a bridge, connecting the mass of substances with the number of particles or atoms they contain.

To calculate the molar mass of a compound, you simply add up the atomic masses of all the atoms in a molecule. You can find these atomic masses on the periodic table, usually located beneath the element symbol.

For instance, in our exercise, mercurous chloride (HgCl) has a molar mass of 470 g/mol. This molar mass represents the mass of both mercury (Hg) and chlorine (Cl) in every mole of the substance. Knowing this value helps us figure out how many moles of each element are in the compound based on their percent composition.

Percent Composition

Percent composition shows what percentage of a compound's mass comes from each of its elements. Calculating percent composition can tell you a lot about the formula of a compound, as it shows the ratio of the different elements by mass.

Here's how you can calculate it: Divide the total mass of each element in the compound by the compound's total molar mass, and then multiply by 100 to get a percentage. You repeat this for each element present in the compound.

In our example, mercurous chloride is 85% mercury and 15% chlorine. This means that if you have 470 grams of the compound, 85% of it by mass is mercury, equating to 399.5 grams, and the remaining 15% is chlorine, equating to 70.5 grams. This percent composition helps us determine the relative number of moles of each element in the compound.

Molecular Formula

The molecular formula is the key piece of information that tells us the exact number of each type of atom in a molecule. It provides a detailed map of the molecule's composition and differentiates it from compounds with the same empirical formula.

Determining a molecular formula requires knowledge of the molar mass and the percent composition. You start from the empirical formula and, using percent composition, derive the individual mass contributions of each element. With these figures, you can calculate how many atoms of each element are present by converting mass into moles.

In the case of mercurous chloride, the molecular formula Hg₂Cl₂ was determined by knowing that both mercury and chlorine show a 1:1 mole ratio in the empirical formula HgCl and that the total molar mass indicates that two units of the empirical formula pair together to form the actual Hg₂Cl₂ compound.

Empirical Formula

The empirical formula provides the simplest ratio of the elements in a compound rather than the exact number found in the molecular formula. It's essentially the 'simplified' version of a compound's formula, reducing element quantities to their smallest whole numbers.

To find an empirical formula, you calculate the moles of each element in your compound using percent composition data and then establish the simplest whole number ratio. This ratio reflects the most basic structural skeleton of the compound.

In our exercise, the empirical formula HgCl was derived because the mole ratio between mercury and chlorine is 1.99:1.99, simplifying directly to 1:1. While the empirical formula provides a basic picture, it still needs to be checked against the molar mass calculation to decide if it's also the molecular formula. In this case, it turned out that duplicating the empirical unit HgCl perfectly matches the known molar mass, leading to the final molecular formula Hg₂Cl₂.