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Chapter 14: Problem 11

The oxidation of copper(I) oxide, \(\mathrm{Cu}_{2} \mathrm{O}(s)\), to copper(II) oxide, \(\mathrm{CuO}(s)\), is an exothermic process, $$ \begin{aligned} 2 \mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{O}_{2}(g) \rightarrow 4 \mathrm{CuO}(s) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-292.0 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \end{aligned} $$ Calculate the energy released as heat when \(25.0\) grams of \(\mathrm{Cu}_{2} \mathrm{O}(s)\) undergo oxidation at constant pressure.

Short Answer

Expert verified
Approximately \(-25.5\, \mathrm{kJ}\) of energy is released.

Step by step solution

01

Determine the Molar Mass of Cu2O

We need to calculate the molar mass of copper(I) oxide, \(\mathrm{Cu}_{2}\mathrm{O}\). Copper has an atomic mass of approximately \(63.55\, \mathrm{g/mol}\), and oxygen has an atomic mass of \(16.00\, \mathrm{g/mol}\). Since \(\mathrm{Cu}_{2}\mathrm{O}\) has two copper atoms and one oxygen atom, the molar mass is calculated as follows: \((2 \times 63.55) + 16.00 = 143.1\, \mathrm{g/mol}\).
02

Calculate the Moles of Cu2O

To find the number of moles of \(\mathrm{Cu}_{2}\mathrm{O}\) in \(25.0\, \mathrm{grams}\), divide the mass by the molar mass: \(\text{moles of \(\mathrm{Cu}_{2}\mathrm{O}\)} = \frac{25.0\, \mathrm{g}}{143.1\, \mathrm{g/mol}} \approx 0.1747\, \mathrm{mol}\).
03

Relationship Between Moles of Cu2O and Reaction

The given balanced chemical equation shows that \(2\, \mathrm{mol}\) of \(\mathrm{Cu}_{2}\mathrm{O}\) produces energy. Therefore, the heat released per mole of \(\mathrm{Cu}_{2}\mathrm{O}\) is \(\frac{-292.0\, \mathrm{kJ}}{2}\, = -146.0\, \mathrm{kJ/mol}\).
04

Calculate the Energy Released

Multiply the number of moles of \(\mathrm{Cu}_{2}\mathrm{O}\) by the energy released per mole to find the total energy: \(-146.0\, \mathrm{kJ/mol} \times 0.1747\, \mathrm{mol} \approx -25.5\, \mathrm{kJ}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Oxidation Process
In chemistry, an oxidation process is a reaction where a substance loses electrons. It's one of the half-reactions in redox processes, the other being reduction, where a substance gains electrons. When we talk about copper in
  • Copper(I) oxide, Cu2O, is the starting material in our exercise, which undergoes oxidation to form
  • Copper(II) oxide, CuO.
This oxidation involves an increase in the oxidation state of copper from +1 in Cu2O to +2 in CuO. This transformation requires the introduction of oxygen, which takes electrons away from copper, thereby oxidizing it. In practical terms, what happens is that oxygen, from its diatomic form, combines with copper(I) oxide to produce copper(II) oxide, and this process emits heat energy, making it exothermic.

Understanding the oxidation process, especially in a reaction involving elements like copper, helps see how changes in oxidation states correspond to the gain or loss of electrons, and thus the transformation of substances.
Enthalpy Change
Enthalpy change, represented as \( \Delta H \), signifies the total heat content of a system. When we say a reaction is exothermic, like the oxidation of copper(I) oxide to copper(II) oxide discussed in the exercise, it means the reaction releases energy to its surroundings, usually in the form of heat. \The given reaction has an enthalpy change of \(-292.0 \ \mathrm{kJ/mol}\). This negative sign indicates energy release, and each mole of reaction leads to this specific amount of energy being emitted as heat. In our step-by-step solution:
  • The structural equation shows that two moles of Cu2O and one mole of O2 produce four moles of CuO, emitting 292.0 kJ.
  • To calculate energy for specific mass, we derive from energy per mole of Cu2O.
The understanding of enthalpy change is crucial for predicting how much energy will be involved, which is especially significant in practical applications where thermal energy management is a concern.
Molar Mass Calculation
Molar mass is a measure of the mass of one mole of a chemical substance. It is expressed in units of grams per mole (g/mol). In our specific exercise scenario, calculating the molar mass of copper(I) oxide, Cu2O, is a crucial first step to determine the moles present in a given mass.To calculate the molar mass of Cu2O:
  • Take the atomic mass of copper, approximately 63.55 g/mol.
  • Since there are two copper atoms per Cu2O molecule, multiply by 2: \( 2 \times 63.55 = 127.1 \ \mathrm{g/mol} \).
  • Consider the atomic mass of oxygen, which is 16.00 g/mol, and add it to the contribution of copper: \( 127.1 + 16.00 = 143.1 \ \mathrm{g/mol} \).
With the calculated molar mass, converting a mass in grams to moles is straightforward using the expression:\[\text{moles} = \frac{\text{given mass (g)}}{\text{molar mass (g/mol)}}\]This conversion is essential for quantitatively relating the mass of a substance to the amount of heat released in its corresponding exothermic reaction, thereby linking it directly to enthalpy change.

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Most popular questions from this chapter

When a solution of hydrochloric acid, HCl \((a q)\), is neutralized by a solution of sodium hydroxide, \(\mathrm{NaOH}(a q)\), the standard molar enthalpy of reaction is \(-55.7 \mathrm{~kJ}\) per mole of each of the reactants. Calculate the energy in the form of heat released when \(100.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}(a q)\) is neutralized by \(100.0\) \(\mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}(a q)\). If the reaction is performed inside an insulated Dewar flask at constant pressure, what will the temperature change of the solution be? Assume no energy is transferred to the surroundings as heat and that the heat capacity and density of the mixture is the same as that of pure water.

Fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)\), is a sugar found in fruits and a source of energy for the body. The combustion of fructose takes place according to the equation $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ When \(5.00\) grams of fructose are burned in excess oxygen in a bomb calorimeter with a heat capacity of \(29.7 \mathrm{~kJ} \cdot \mathrm{K}^{-1}\), the temperature of the calorimeter increases by \(2.635 \mathrm{~K}\). Calculate the standard enthalpy of combustion per gram and per mole of fructose. Assume that \(\Delta H_{\mathrm{rxn}} \approx \Delta U_{\mathrm{rxn}} .\)

Use the values of \(\Delta H_{\mathrm{rxn}}^{\circ}\) given for the equations $$ \begin{aligned} \mathrm{Cu}(s)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CuCl}_{2}(s) & \\ \Delta H_{\mathrm{rxn}}^{\circ} &=-220.1 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \\\ 2 \mathrm{Cu}(s)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{CuCl}(s) & \\ \Delta H_{\mathrm{rxn}}^{\circ} &=-137.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \end{aligned} $$ to calculate the value of \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the equation $$ \mathrm{CuCl}_{2}(s)+\mathrm{Cu}(s) \rightarrow 2 \mathrm{CuCl}(s) $$

Calculate the work done in joules when a mechanical compressor exerting a constant pressure of \(350.0\) kPa compresses an air sample from a volume of \(500.0 \mathrm{~cm}^{3}\) to a volume of \(250.0 \mathrm{~cm}^{3}\).

The French chemists Pierre L. Dulong and Alexis T. Petit noted in 1819 that the molar heat capacity of many solids at ordinary temperatures is proportional to the number of atoms per formula unit of the solid. They quantified their observations in what is known as Dulong and Petit's rule that says that the molar heat capacity of a solid can be expressed as $$ C_{\mathrm{p}} \approx N \times 25 \mathrm{~J} \cdot \mathrm{K}^{-1} \cdot \mathrm{mol}^{-1} $$ where \(N\) is the number of atoms per formula unit. The observed heat capacity per gram of a compound containing thallium and chlorine is \(0.208 \mathrm{~J} \cdot \mathrm{K}^{-1} \cdot \mathrm{g}^{-1}\). Use Dulong and Petit's rule to determine the formula of the compound.
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