Problem 121 - Chemistry: An Atoms-Focused Approach

Question

CO as a Fuel Is carbon dioxide a viable source of the fuel CO? Pure carbon dioxide \(\left(P_{\mathrm{CO}_{2}}=1 \text { atm }\right)\) decomposes at high temperatures. For the system $$ 2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) $$ the percentage of decomposition of \(\mathrm{CO}_{2}(g)\) changes with temperature as follows: $$\begin{array}{cc} \text { Temperature }(\mathrm{K}) & \text { Decomposition }(\%) \\ 1500 & 0.048 \\ \hline 2500 & 17.6 \\ \hline 3000 & 54.8 \\ \hline \end{array}$$ Is the reaction endothermic? Calculate the value of \(K_{\text {p at each temperature and discuss the results. Is the }}\) decomposition of \(\mathrm{CO}_{2}\) an antidote for global warming?

Step-by-Step Solution

Answer

Answer: The CO2 decomposition reaction is endothermic, and the equilibrium constant Kp increases with temperature, favoring the forward reaction. However, very high temperatures (around 3000 K) are necessary for significant CO2 reduction, and the reaction produces carbon monoxide, a toxic gas and pollutant. Due to these factors, the decomposition of CO2 in this manner is not a viable solution to counter global warming.

Step 1: Identify the reaction and the equilibrium constant (Kp)

The given reaction is: $$ 2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) $$ Our goal is to determine the equilibrium constant Kp (the ratio of partial pressures) at each given temperature.

Step 2: Calculate the moles of each component in the system

We start with 1 atm of pure CO2, and we can consider having 1 mol of CO2 initially for simplicity. We also assume that initially, there is no CO or O2. Let x be the number of moles of CO2 decomposed. So, after the decomposition, we'll have: - (1-x) moles of CO2 - 2x moles of CO - x moles of O2 We are given the percentage of decomposition at different temperatures, which allows us to determine the moles of CO2 decomposed (x) at each temperature.

Step 3: Calculate x for each temperature

Using the percentage of decomposition, we can calculate x at each temperature: - T = 1500 K: x = 0.00048 (1 mol) - T = 2500 K: x = 0.176 (1 mol) - T = 3000 K: x = 0.548 (1 mol) Now, we can calculate the moles of each component at each temperature.

Step 4: Calculate partial pressures and Kp for each temperature

We can find the partial pressures of each component using the ideal gas law: \(P=\frac{nRT}{V}\). Since the initial pressure of the system was 1 atm, we can assume the initial volume V is \(\frac{RT}{1}\). Now, we can find the partial pressures of each component at each temperature and use these to calculate Kp. At T = 1500 K: - \(P_{CO2}\) = \(\frac{(1-x)RT}{V}\) = \(\frac{(1-0.00048)RT}{RT}\) = 0.99952 atm - \(P_{CO}\) = \(\frac{2xRT}{V}\) = \(\frac{2(0.00048)RT}{RT}\) = 0.00096 atm - \(P_{O2}\) = \(\frac{xRT}{V}\) = \(\frac{0.00048RT}{RT}\) = 0.00048 atm Kp = \(\frac{P_{CO}^2 P_{O2}}{(P_{CO2})^2}\) = \(\frac{(0.00096)^2 (0.00048)}{(0.99952)^2}\) ≈ 2.22 × 10^(-10) At T = 2500 K: - \(P_{CO2}\) = 0.824 atm - \(P_{CO}\) = 0.352 atm - \(P_{O2}\) = 0.176 atm Kp ≈ 9.01 × 10^(-3) At T = 3000 K: - \(P_{CO2}\) = 0.452 atm - \(P_{CO}\) = 1.096 atm - \(P_{O2}\) = 0.548 atm Kp ≈ 3.26

Step 5: Analyze the results

From the Kp values, we can see that increasing the temperature results in a larger Kp, meaning more CO2 is being converted to CO and O2. This indicates that the reaction is endothermic, as higher temperatures favor the reaction's forward direction. However, on the consideration of CO2 decomposition being an antidote for global warming, while the decomposition reaction may seem promising due to the reduction in CO2 levels, it requires very high temperatures (around 3000 K) to be significant. Additionally, the formation of CO (carbon monoxide), a pollutant and toxic gas is a significant concern. So, the decomposition of CO2 in this manner is not a viable solution to counter global warming. In summary, the reaction is endothermic, and the calculated Kp values show the dependency of the reaction on temperature. However, the high temperatures required and the formation of carbon monoxide make this reaction unsuitable as a solution to global warming.

Key Concepts

Endothermic reactions

In thermodynamics, an endothermic reaction is a chemical reaction that absorbs energy from its surroundings. This happens because the reactants require more energy to break their bonds than what is released when the reaction forms its products. As a result, endothermic reactions often occur more readily at higher temperatures.

When analyzing the decomposition of carbon dioxide (\(2 \text{CO}_2(g) \rightleftharpoons 2 \text{CO}(g)+\text{O}_2(g)\)), we find this reaction is endothermic. The evidence is observed in the increasing percentage of decomposition as the temperature rises, indicating that heat actively facilitates the decomposition process.

• At 1500 K, only 0.048% of CO2 decomposes.
• At 2500 K, 17.6% decomposes.
• At 3000 K, the decomposition rises significantly to 54.8%.

Such temperature dependence highlights the endothermic nature of the reaction, where heat acts as a key driver for proceeding in the forward direction.

Equilibrium constant (Kp)

The equilibrium constant, denoted as \(K_p\), is a measure of the ratio of the products' partial pressures to the reactants' partial pressures at equilibrium. For gas-phase reactions, \(K_p\) is used to indicate which direction a reaction favors under certain conditions.

In the case of carbon dioxide decomposition, \(K_p\) is calculated at varying temperatures reflecting different extents of reaction completion. At higher temperatures, \(K_p\) values increase:

• At 1500 K, \(K_p \approx 2.22 \times 10^{-10}\)
• At 2500 K, \(K_p \approx 9.01 \times 10^{-3}\)
• And at 3000 K, \(K_p \approx 3.26\)

These \(K_p\) values indicate that as the temperature climbs, the reaction shifts towards producing more CO and O2. The greater values at higher temperatures highlight the forward reaction's growth, conforming to Le Chatelier's principle, which predicts the direction of shift to absorb excess heat in endothermic reactions.

Carbon dioxide decomposition

The decomposition of carbon dioxide (CO2) into carbon monoxide (CO) and oxygen (O2) is an intriguing chemical process, especially within the context of studying possible methods for reducing atmospheric CO2 levels. However, the practical feasibility of such decomposition is limited due to the high temperatures required to achieve significant decomposition.

In this exercise, we observe that noticeable decomposition occurs around 2500 K to 3000 K. At these high temperatures:

• The reaction is endothermic, requiring energy input to form CO and O2 from CO2.
• The production of CO, while reducing CO2, introduces another pollution concern.

Though theoretically possible, the harsh energy requirements and considerations surrounding CO production make this method unsustainable as a large-scale approach to tackle global warming. The significant heat input and potential environmental detriment call for alternative methods that more favorably balance efficiency and environmental impact.