Question

A 1.500 -g sample of a mixture containing only \(\mathrm{Cu}_{2} \mathrm{O}\) and CuO was treated with hydrogen to produce 1.252 \(\mathrm{g}\) of pure cupper metal. Calculate the mass percent of \(\mathrm{Cu}_{2} \mathrm{O}\) in the original mixture.

Short answer

The mass percent of Cu2O in the original 1.500 g mixture of Cu2O and CuO is approximately 77.3%.

Step-by-step solution

Calculate moles of produced copper

To determine the moles of copper produced, we can use the equation: moles of copper = mass of copper / molar mass of copper The atomic mass of copper is 63.54 g/mol. Thus, we can calculate the moles of copper produced as follows: moles of copper = 1.252 g / (63.54 g/mol) = 0.0197 mol Now, we have found the moles of produced copper, which is 0.0197 mol.

Calculate moles of Cu2O and CuO in the original mixture

Since the produced copper comes from both the Cu2O and CuO in the original mixture and the mixture contains only these two compounds, their moles can be determined as follows: From Cu2O: moles of Cu = 2 × moles of Cu2O moles of Cu2O = (moles of Cu) / 2 From CuO: moles of Cu = moles of CuO Let x be the moles of Cu2O and y be the moles of CuO. Then, we can write an equation based on the moles of copper produced: 0.0197 = (x / 2) + y (1)

Calculate the mass of the original Cu2O and CuO

To calculate the mass of the original Cu2O and CuO, we can use the following equations: mass of Cu2O = moles of Cu2O × molar mass of Cu2O mass of CuO = moles of CuO × molar mass of CuO The molar mass of Cu2O is (2 * 63.54) + 16 = 143.08 g/mol, and the molar mass of CuO is 63.54 + 16 = 79.54 g/mol. Since the total mass of the original mixture is given to be 1.500 g, we can write the second equation based on the mass: 143.08x + 79.54y = 1.500 (2)

Solve the system of equations for x and y

Now, we solve the system of equations (1) and (2) to find the moles of Cu2O and CuO in the original mixture. Multiply equation (1), with a factor two: 0.0394 = x + 2y (1b) Express y from equation (1b): y = (0.0394 - x) / 2 Now substitute this expression of y into equation (2) and solve for x: 143.08x + 79.54(0.0394 - x) = 1.500 x ≈ 0.00811 Now, substitute the value of x back into the equation for y: y = (0.0394 - 0.00811) / 2 y ≈ 0.0157 We found that the moles of Cu2O and CuO in the original mixture are approximately 0.00811 mol and 0.0157 mol, respectively.

Calculate the mass percent of Cu2O in the original mixture

Now, we can calculate the mass percent of Cu2O in the original mixture using the following equation: mass percent of Cu2O = (mass of Cu2O / total mass of the original mixture) × 100% First, calculate the mass of Cu2O: mass of Cu2O = 0.00811 mol × 143.08 g/mol = 1.159 g Now, calculate the mass percent of Cu2O: mass percent of Cu2O = (1.159 g / 1.500 g) × 100% ≈ 77.3% The mass percent of Cu2O in the original mixture is approximately 77.3%.

Key concepts

Chemical Reactions

Chemical reactions are the processes in which substances are transformed into new substances. In our example, a mix containing two copper oxides, namely, \(\mathrm{Cu}_{2}\mathrm{O}\) (cuprous oxide) and \(\mathrm{CuO}\) (cupric oxide), undergoes a transformation. This transformation is aided by hydrogen, which reduces the copper oxides into pure copper metal and water. Such reactions, which involve the transfer of electrons leading to changes in oxidation states, are known as redox reactions.

In the case of copper oxides:

• Cuprous oxide, \(\mathrm{Cu}_{2}\mathrm{O}\), comprises two copper atoms and one oxygen atom.
• Cupric oxide, \(\mathrm{CuO}\), contains one copper atom and one oxygen atom.

During the reaction, the reduction process converts these compounds into metallic copper, clearly illustrating the principles of stoichiometry, the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction.

Mass Percent

Mass percent is a way of expressing a concentration of a component in a mixture. It helps us understand what portion of a mixture or compound a particular component constitutes. Calculating the mass percent involves dividing the mass of the component by the total mass of the mixture, and then multiplying by 100 to convert the result into a percentage format.

The formula is expressed as:\[\text{Mass percent} = \left(\frac{\text{mass of component}}{\text{total mass of mixture}}\right) \times 100\%\]In our exercise, we found that the mass percent of \(\mathrm{Cu}_{2}\mathrm{O}\) in the mixture is approximately 77.3%. Mass percent can be a useful measure in both laboratories and industries, helping to establish ingredient proportions in chemical processes or products.

Copper Oxides

Copper oxides are compounds composed of copper and oxygen. The two most common copper oxides are cuprous oxide \(\mathrm{Cu}_{2}\mathrm{O}\), and cupric oxide \(\mathrm{CuO}\). These compounds differ in chemical structure and properties due to the number of copper and oxygen atoms in each molecule.

• Cuprous Oxide (\(\mathrm{Cu}_{2}\mathrm{O}\)): This compound consists of two copper atoms for every one oxygen atom, giving it a 1:2 stoichiometry. It typically appears as a red or brown solid.
• Cupric Oxide (\(\mathrm{CuO}\)): It contains one copper atom per one oxygen atom, making its stoichiometry 1:1. It often appears as a black solid.

Copper oxides are used in various applications such as pigments, catalysts, and in semiconductor devices. They share similar traits but vary in oxidation states, which impacts their solubility, color, and reactivity.

Molar Mass Calculation

Calculating the molar mass of a compound involves summing the atomic masses of each constituent element multiplied by their respective number in the compound. Molar mass, expressed in grams per mole (g/mol), provides the link between the number of moles of a substance and its mass.

For example, consider the molar mass of \(\mathrm{Cu}_{2}\mathrm{O}\) and \(\mathrm{CuO}\):

• For \(\mathrm{Cu}_{2}\mathrm{O}\), calculate as follows: \[\text{Molar mass of } \mathrm{Cu}_{2}\mathrm{O} = (2 \times 63.54\,\text{g/mol}) + 16\,\text{g/mol} = 143.08\,\text{g/mol}\]
• For \(\mathrm{CuO}\), calculate as follows: \[\text{Molar mass of } \mathrm{CuO} = 63.54\,\text{g/mol} + 16\,\text{g/mol} = 79.54\,\text{g/mol}\]

Understanding molar mass is crucial for converting between grams and moles and for accurately reacting and working with chemical compounds in experimental settings.