Question

Copper(II) oxide can be reduced to copper metal by heating in a stream of hydrogen gas: $$ \mathrm{CuO}(s)+\mathrm{H}_{2}(g) \stackrel{\text { heat }}{\longrightarrow} \mathrm{Cu}(s)+\mathrm{H}_{2} \mathrm{O}(g) $$ What volume of hydrogen at \(27.0^{\circ} \mathrm{C}\) and 722 torr would be required to react with \(85.0 \mathrm{~g}\) of \(\mathrm{CuO}\) ?

Short answer

It would be required a volume of approximately 26.83 L of hydrogen to react with 85.0 g of CuO at the conditions of 27.0 degrees Celsius and 722 torr.

Step-by-step solution

Molar Mass Calculation

Firstly, calculate the molar mass of CuO by adding the atomic masses of Copper (Cu, 63.55 g/mol) and Oxygen (O, 16.00 g/mol).\n\nTypically, atomic masses can be found in the periodic table. The molar mass of CuO = 63.55 g/mol + 16.00 g/mol = 79.55 g/mol.

Moles Calculation

Next, use the mass and molar mass of CuO to calculate the number of moles (n) of CuO using the formula: n = mass / molar mass.\n\nTherefore, n_CuO = 85.0g / 79.55 g/mol = 1.07 mol.

Stoichiometry Application

Apply stoichiometric relationships in the balanced chemical equation, which shows 1 mole of CuO reacting with 1 mole of H2 to form 1 mole of Cu and 1 mole of H2O.\n\nGiven the moles of CuO (1.07 mol), the moles of H2 required = 1.07 mol.

Ideal Gas Law Application

Next, apply the Ideal Gas Law (PV=nRT) to calculate the volume, V, of H2. Given the temperature T = 27.0 degrees Celsius = (27.0+273.15) K = 300.15 K, pressure P = 722 torr = (722/760) atm = 0.95 atm, gas constant R = 0.0821 L.atm/K.mol, and n_H2 = 1.07 mol.\n\nSo, V = nRT / P = (1.07 mol * 0.0821 L.atm/K.mol * 300.15 K) / 0.95 atm = 26.83 L.

Key concepts

Molar Mass Calculation

The molar mass calculation is a fundamental aspect of stoichiometry. It involves finding the mass of one mole of a substance. In this exercise involving copper(II) oxide (CuO), the molar mass is calculated using atomic masses from the periodic table. To find the molar mass of CuO, you add the atomic masses of copper (Cu) and oxygen (O):

• Copper (Cu) has an atomic mass of 63.55 g/mol.
• Oxygen (O) has an atomic mass of 16.00 g/mol.

Adding these values gives the molar mass of CuO as 63.55 g/mol + 16.00 g/mol = 79.55 g/mol. Understanding this step helps in converting mass to moles, which is crucial for further calculations in stoichiometry. Always remember: the periodic table is your best friend when performing molar mass calculations.

Ideal Gas Law

The Ideal Gas Law is a powerful tool for calculating the properties of gases. It is represented by the equation: \( PV = nRT \), where:

• \( P \) is pressure,
• \( V \) is volume,
• \( n \) is number of moles,
• \( R \) is the ideal gas constant (0.0821 L.atm/K.mol),
• \( T \) is temperature in Kelvin.

In this particular example, we need to find the volume of hydrogen gas. Given parameters are pressure at 722 torr (converted to 0.95 atm), temperature at 27°C (converted to 300.15 K), and \( n \) = 1.07 moles of hydrogen. Plugging these values into the equation, the volume \( V \) can be calculated as: \[ V = \frac{nRT}{P} = \frac{1.07 \times 0.0821 \times 300.15}{0.95} \approx 26.83 \text{ L} \] This equation is incredibly useful for predicting gas behavior under various conditions and for checking assumptions made during stoichiometry.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. Here, copper(II) oxide reacts with hydrogen to produce copper and water. The balanced equation is: \[ \mathrm{CuO}(s) + \mathrm{H}_2(g) \rightarrow \mathrm{Cu}(s) + \mathrm{H}_2\mathrm{O}(g) \] Balancing chemical equations is crucial, as it ensures that the same number of each type of atom appears on both sides of the equation, reflecting the law of conservation of mass. Understanding this reaction helps us apply stoichiometry to predict the amounts of products formed from given reactants. For this reaction:

• 1 mole of CuO reacts with 1 mole of H\(_2\).
• It produces 1 mole of Cu and 1 mole of H\(_2\)O.

This stoichiometric relationship allows you to determine the required amount of hydrogen to fully react with a given amount of CuO, ensuring that no excess hydrogen is used than necessary.