Question

A given sample of pure compound contains \(9.81 \mathrm{gm}\) of \(\mathrm{Zn}, 1.8 \times 10^{23}\) atoms of chromium and \(0.60\) mole of oxygen atoms. What is the simplest formula ? (a) \(\mathrm{ZnCr}_{2} \mathrm{O}_{7}\) (b) \(\mathrm{ZnCr}_{2} \mathrm{O}_{4}\) (c) \(\mathrm{ZnCrO}_{4}\) (d) \(\mathrm{ZnCrO}_{6}\)

Short answer

The simplest formula of the compound is (b) \(\mathrm{ZnCr}_{2} \mathrm{O}_{4}\).

Step-by-step solution

Determine the moles of Zinc (Zn)

Calculate moles of Zinc (Zn) by dividing the mass of Zinc by its molar mass. The molar mass of Zinc is approximately 65.38 gm/mol. So number of moles of Zinc (Zn) = mass of Zn / molar mass of Zn = 9.81 gm / 65.38 gm/mol.

Determine the moles of Chromium (Cr)

Calculate the moles of Chromium by using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol. Number of moles of Chromium (Cr) = number of atoms of Cr / Avogadro's number = \(1.8 \times 10^{23}\) atoms / \(6.022 \times 10^{23}\) atoms/mol.

Determine the moles of Oxygen (O)

The number of moles of Oxygen is given directly in the problem as 0.60 mol.

Calculate molar ratios

Determine the ratio of moles of Zn, Cr, and O to each other by dividing each by the smallest number of moles obtained from the previous steps.

Find the simplest whole number ratio

If the molar ratios obtained are not whole numbers, multiply them by the smallest number that will give whole numbers to obtain the empirical formula.

Determine simplest formula

Write the empirical formula using the whole number ratios for each element.

Key concepts

Chemical Formula Calculation

Chemical formula calculation is a fundamental skill in chemistry that involves finding the simplest ratio of elements in a compound. This ratio is represented by the empirical formula, which provides the smallest whole number ratio of the types of atoms in a substance.

When calculating an empirical formula, start by determining the number of moles of each element in a sample. This can involve dividing the mass of each element by its atomic weight to obtain the moles. In the problem provided, the mass of Zinc (Zn) is given, from which moles can be calculated. Once you have the moles for each element, you compare them by dividing by the smallest value to obtain the molar ratio. If these ratios are not whole numbers, they may be multiplied by a common factor to achieve whole numbers, as often seen in empirical formula calculations.

The correct empirical formula is a critical foundation for understanding various chemical properties and reactions. It highlights the proportional relationships and stoichiometry within the compound, providing insights into its composition.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships, or ratios, of reactants and products in chemical reactions. It is based on the law of conservation of mass and the concept that elements combine in fixed ratios.

In the given exercise, stoichiometry comes into play when determining the ratio of each element in the compound. You need to compare the amount of each element in moles and balance them to find the most reduced ratio, which in this case is the empirical formula of the compound. It's much like a recipe; stoichiometry tells you how much of each ingredient you need to combine to create a specific product.

Understanding stoichiometry is not only crucial for finding empirical formulas but also for predicting the amounts of products formed and reactants needed in chemical reactions, which is invaluable in both laboratory and industrial chemical processes.

Avogadro's Number

Avogadro's number is a key constant in chemistry, representing the number of particles, often atoms or molecules, in one mole of substance. Its value is approximately \(6.022 \times 10^{23}\). This number enables chemists to count particles by weighing, as one mole of any element contains the same number of atoms, regardless of what element it is.

In the context of our exercise, Avogadro's number is used to convert the number of chromium atoms into moles. This allows for all elements in the compound to be compared on the same scale – moles – enabling the determination of the empirical formula. By knowing how to use Avogadro's number in calculations, students can bridge the gap between the microscopic particles that make up substances and the macroscopic amounts measured in labs.