Question

In an experiment, \(244 \mathrm{mL}\) of chlorine gas \(\left(\mathrm{Cl}_{2}, d=2.898 \mathrm{g} / \mathrm{L}\right)\) combines with iodine to give \(1.553 \mathrm{g}\) of a binary compound. In a separate experiment, the molar mass of the compound is found to be about \(467 \mathrm{g} / \mathrm{mol} .\) What is the molecular formula of this compound?

Short answer

The molecular formula of the compound is \(\mathrm{Cl}_x\mathrm{I}_y\). The exact values of x and y can be found by following the above steps.

Step-by-step solution

Calculate moles of chlorine

Using the density formula \(d = m/v\), rearrange it as \(m = d \times v\) to calculate the mass of chlorine. Given that the molar mass of chlorine (\(\mathrm{Cl}_{2}\)) is 70.90 g/mol, divide the mass by the molar mass to get the number of moles.

Calculate moles of iodine

From the experiment, it's given that 1.553 g of a compound is created. Given that this is a binary compound with chlorine and iodine, subtract the mass of chlorine calculated in Step 1 from 1.553 g to get the mass of iodine. Divide this by the molar mass of iodine (126.90 g/mol) to calculate the number of moles of iodine.

Find ratio of chlorine to iodine

Divide the number of moles of chlorine by the moles of iodine to find the ratio of chlorine to iodine in the compound.

Determine molecular formula

The molecular formula is represented as \(\mathrm{Cl}_x\mathrm{I}_y\), where \(x\) and \(y\) are the ratio found in Step 3. Take into consideration that the molar mass of the compound from a separate experiment is given as 467 g/mol, which will help to find the values of x and y and hence the molecular formula.

Key concepts

Molecular formula determination

Determining the molecular formula of a chemical compound involves identifying the exact number of each type of atom in a molecule. In our exercise, chlorine and iodine are the two components of the compound. To find this formula, you must calculate the ratio of chlorine atoms to iodine atoms. Start by determining the mass and moles of each element involved.

Use the data from the experiment, such as the mass of the binary compound and the molar mass of each element, to establish the exact composition. The steps include calculating the moles of each element and establishing the simplest whole number ratio between them. These ratios determine how many of each type of atom are in the molecular formula represented as \(\text{Cl}_x\text{I}_y\).

Always remember that these calculations are supported by the molar mass provided, which helps confirm or adjust the preliminarily determined ratios to fit the molecular weight.

Molar mass calculation

The molar mass of a compound is the weight of one mole of that substance, expressed in grams per mole (g/mol). This calculation is crucial for determining how different elements combine to form a specific compound. In the exercise, the molar mass of the final compound is given as 467 g/mol.

To compute this, add the atomic masses of each element within the molecular formula. Break down the components starting with their individual atomic masses. For example, chlorine has an atomic mass of about 35.45 g/mol, while iodine is approximately 126.90 g/mol. Multiply these by the number of atoms determined in the empirical formula. Then sum them up to verify that they match the given total molar mass of the compound.

• Calculate chlorine's contribution by multiplying its atomic mass with the number of chlorine atoms.
• Repeat this process for iodine.
• Sum the results to find the complete molar mass.

Matching this result with the provided molar mass confirms that your molecular formula is accurate.

Stoichiometry

Stoichiometry is the branch of chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. It is centered around the concept of the mole and allows you to predict the outcomes of chemical reactions quantitatively.

In this exercise, stoichiometry helps to identify the mole ratio of chlorine to iodine in the compound. Using calculated moles from the experiment:

• Start by calculating the mass and number of moles of chlorine gas used.
• Then determine the moles of iodine by subtracting the mass of chlorine from the total mass of the compound.
• Using these mole amounts, find the simplest ratio of chlorine to iodine, which establishes the subscript numbers in the molecular formula.

Correct stoichiometric calculations provide the basis for understanding the composition, which is crucial for formulating and balancing chemical equations.

Gas density calculations

Gas density calculations are pivotal in determining the mass of gas involved in a chemical reaction. Density is defined as mass per unit volume and can be rearranged to find the mass if you know the gas's volume and density.

In the exercise, chlorine gas has a known density, and you need to find its mass to proceed with calculating moles. To do this:

• Use the formula: \( m = d \times v \), where \( m \) is mass, \( d \) is density, and \( v \) is volume.
• Multiply the density of chlorine (2.898 g/L) by the volume (244 mL or 0.244 L) to find the mass of chlorine.
• With the mass of chlorine determined, you can easily proceed to find the moles necessary for stoichiometric calculations.

Understanding how to calculate gas density is essential, as it forms the bridge between knowing how much of a gaseous reactant is present and being able to use that information in larger chemical calculations.