Problem 91 - Chemistry The Science in Context

Question

How can the standard enthalpy of formation of \(\mathrm{CO}(g)\) be calculated from the standard enthalpy of formation \(\Delta H_{f}^{\circ}\) of \(\mathrm{CO}_{2}(g)\) and the standard enthalpy of combustion \(\Delta H_{\mathrm{comb}}^{\circ}\) of \(\mathrm{CO}(g) ?\)

Step-by-Step Solution

Answer

Question: Calculate the standard enthalpy of formation of CO(g) using the standard enthalpy of formation ΔHf° of CO2(g) and the standard enthalpy of combustion ΔHcomb° of CO(g). Answer: The standard enthalpy of formation of CO(g) can be calculated using the equation: ΔHf1° = ΔHf2° - ΔHcomb° + CO2(g) - CO(g), where ΔHf1° is the standard enthalpy of formation of CO(g), ΔHf2° is the standard enthalpy of formation of CO2(g), and ΔHcomb° is the standard enthalpy of combustion of CO(g).

Step 1: Write the combustion equation for \(\mathrm{CO}(g)\)

The complete combustion of \(\mathrm{CO}(g)\) in the presence of Oxygen (\(\mathrm{O}_{2}\)) each mole of carbon monoxide will produce one mole carbon dioxide and release the standard enthalpy of combustion: \(\mathrm{CO}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) \ \ \ \Delta H_{\mathrm{comb}}^{\circ}\)

Step 2: Write the enthalpy of formation equations for \(\mathrm{CO}(g)\) and \(\mathrm{CO}_{2}(g)\)

The standard enthalpy of formation equations for \(\mathrm{CO}(g)\) and \(\mathrm{CO}_{2}(g)\) are given below: \(\mathrm{C}(s) + \frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}(g) \ \ \ \Delta H_{f1}^{\circ}\) \(\mathrm{C}(s) + \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) \ \ \ \Delta H_{f2}^{\circ}\)

Step 3: Manipulate the equations to isolate the \(\mathrm{CO}(g)\) formation equation

Subtract equation 1 from equation 2, in which the standard enthalpy of combustion \(\Delta H_{\mathrm{comb}}^{\circ}\) will be cancelled out: \((\Delta H_{f2}^{\circ} - \Delta H_{\mathrm{comb}}^{\circ}) - \Delta H_{f1}^{\circ} = \mathrm{CO}_{2}(g) - \mathrm{CO}(g)\) Now solve for the standard enthalpy of formation of \(\mathrm{CO}(g)\), \(\Delta H_{f1}^{\circ}\): \(\Delta H_{f1}^{\circ} = \Delta H_{f2}^{\circ} - \Delta H_{\mathrm{comb}}^{\circ} + \mathrm{CO}_{2}(g) - \mathrm{CO}(g)\)

Step 4: Substitute the given values and calculate the standard enthalpy of formation for \(\mathrm{CO}(g)\)

We need to plug in the given values for the standard enthalpy of formation of \(\mathrm{CO}_{2}(g)\) and the standard enthalpy of combustion of \(\mathrm{CO}(g)\) into the equation from Step 3. \(\Delta H_{f1}^{\circ} = \Delta H_{f2}^{\circ} - \Delta H_{\mathrm{comb}}^{\circ}\) The standard enthalpy of formation of \(\mathrm{CO}(g)\) is calculated, and this is the final answer.

Key Concepts

Combustion Reaction

In simple terms, a combustion reaction is a chemical process where a compound reacts with oxygen to produce heat, light, and other compounds. This reaction is most commonly observed in burning processes where fuel is oxidized. For carbon monoxide (\( \mathrm{CO}(g) \)), the combustion reaction involves oxygen (\( \mathrm{O}_2(g) \)) and results in carbon dioxide (\( \mathrm{CO}_2(g) \)). This can be represented by the simple equation:

• 
  \[ \mathrm{CO}(g) + \frac{1}{2} \mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) \]
  

This reaction type is categorized as exothermic, meaning it releases energy in the form of heat. Such reactions are integral to everyday applications, such as energy production in car engines and power stations. Understanding combustion reactions helps in calculating energy efficiency and impact on the environment.

Enthalpy Change

Enthalpy change (\( \Delta H \)) refers to the heat change at constant pressure that accompanies a chemical reaction. It's a crucial concept for understanding heat transfer in reactions, especially when dealing with reactions like combustion. The enthalpy change can tell us if a reaction is endothermic (absorbs heat) or exothermic (releases heat).
In the case of carbon monoxide (\( \mathrm{CO}(g) \)), the enthalpy change during combustion can be calculated by comparing the enthalpies of formation of reactants and products. The formula used is:

• 
  \[ \Delta H = \Delta H_{f2}^{\circ} - \Delta H_{\mathrm{comb}}^{\circ} \]
  

Here, the symbols correspond to the standard enthalpy of formation of carbon dioxide and the standard enthalpy of combustion of carbon monoxide. By measuring this change, scientists can determine essential properties such as the efficiency of combustion reactions or potential energy output.

Carbon Monoxide

Carbon monoxide (\( \mathrm{CO}(g) \)) is a colorless, odorless gas produced by the burning of fuel not fully oxidized due to insufficient oxygen. It is known for its toxic properties but also for playing a role in certain chemical processes like combustion. Analyzing its properties through enthalpy changes helps to understand its formation and energy transformation.
The standard enthalpy of formation for carbon monoxide involves a transformation from solid carbon and gaseous oxygen. Knowing this value allows chemists to calculate energy changes in reactions where carbon monoxide is involved. It also highlights safety and environmental concerns since CO emissions can be harmful to health. Therefore, controlling the production and reaction of carbon monoxide is vital in both industrial applications and environmental conservation.