Question

When a 2.118 -g sample of copper is heated in an atmosphere in which the amount of oxygen present is restricted, the sample gains \(0.2666 \mathrm{~g}\) of oxygen in forming a reddishbrown oxide. However, when \(2.118 \mathrm{~g}\) of copper is heated in a stream of pure oxygen, the sample gains \(0.5332 \mathrm{~g}\) of oxygen. Calculate the empirical formulas of the two oxides of copper.

Short answer

The empirical formulas of the two copper oxides are \(Cu_2O\) for the reddish-brown oxide formed when 2.118g of copper gains 0.2666g of oxygen, and \(CuO\) for the oxide formed when 2.118g of copper gains 0.5332g of oxygen in a stream of pure oxygen.

Step-by-step solution

Calculate the moles of Copper (Cu) and Oxygen (O) for both scenarios

In both cases, the amount of Copper remains the same: 2.118 g. To find the moles, we can use the formula: Moles = Mass (g) / Molar mass (g/mol) For copper, the molar mass is 63.546 g/mol. For the first scenario: Moles of copper = 2.118 g / 63.546 g/mol ≈ 0.0333 mol Moles of oxygen = 0.2666 g / 16.00 g/mol ≈ 0.0167 mol For the second scenario: Moles of copper = 2.118 g / 63.546 g/mol ≈ 0.0333 mol Moles of oxygen = 0.5332 g / 16.00 g/mol ≈ 0.0333 mol

Find the mole ratio for both scenarios

Divide the moles of each element by the smallest number of moles to find the mole ratio. First scenario: Mole ratio (Cu:O) = 0.0333 / 0.0167 : 0.0167 / 0.0167 Mole ratio (Cu:O) = 2 : 1 Second scenario: Mole ratio (Cu:O) = 0.0333 / 0.0333 : 0.0333 / 0.0333 Mole ratio (Cu:O) = 1 : 1

Write the empirical formulas for both scenarios

Now that we have the mole ratios, we can write the empirical formulas for both copper oxides. First scenario (reddish-brown oxide): Mole ratio (Cu:O) = 2 : 1 Empirical formula: \(Cu_2O\) Second scenario (heated in pure oxygen): Mole ratio (Cu:O) = 1 : 1 Empirical formula: \(CuO\) Hence, the empirical formulas of the copper oxides are \(Cu_2O\) for the reddish-brown oxide and \(CuO\) for the oxide formed when heated in pure oxygen.

Key concepts

Chemical Stoichiometry

Chemical stoichiometry is a core concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is based on the conservation of mass and the principle that elements combine in fixed ratios of whole numbers.

For instance, when we analyze the formation of copper oxides, we see that copper (Cu) and oxygen (O) combine in different ratios depending on the conditions, forming distinct compounds with unique empirical formulas. The process of determining these formulas involves several steps.
First, we must obtain the mass of each element involved in the reaction. Then, using our understanding of the mole concept and molar masses, we calculate the number of moles of each element. Lastly, we determine the simplest whole number ratio of moles of the elements involved, which gives us the empirical formula of the compound.

Mole Concept

The mole concept is fundamental in stoichiometry. It allows chemists to count particles by weighing them. One mole of any substance contains Avogadro's number of particles, which is roughly \(6.022 \times 10^{23}\) particles.
When studying copper oxides, we measured the mass of the reactants (copper and oxygen) and converted these masses to moles because stoichiometry requires us to work with the ratio of particles, not mass. The mole concept simplifies these calculations immensely. The steps provided in the solution use the formula \( \text{{Moles}} = \text{{Mass (g)}} / \text{{Molar mass (g/mol)}}\) to convert grams to moles, incorporating the known molar masses of copper and oxygen, to find the ratio of their moles in the chemical reaction.

Molar Mass

Molar mass, which is the mass of one mole of a substance, is expressed in grams per mole (g/mol) and is a critical component in stoichiometry calculations because it links the mass of a substance to its mole quantity.

For any stoichiometry problem, including the empirical formula determination of copper oxides, the molar mass serves as the conversion factor between the mass of a sample and the number of moles in that sample. Copper has a molar mass of 63.546 g/mol, and oxygen has a molar mass of 16.00 g/mol. Using these values, we can precisely convert the masses of copper and oxygen into moles, which then allows for the calculation of the mole ratios and ultimately, the determination of empirical formulas, \(Cu_2O\) and \(CuO\), as demonstrated in the problem solution.