Problem 156 - A Complete Resource Book in Chemistry for JEE Main

Question

The enthalpies of combustion of carbon and carbon monoxide are \(-393.5\) and \(-283 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The enthalpy of formation of carbon monoxide per mole is (a) \(-676.5 \mathrm{~kJ}\) (b) \(-110.5 \mathrm{~kJ}\) (c) \(110.5 \mathrm{~kJ}\) (d) \(676.5 \mathrm{~kJ}\)

Step-by-Step Solution

Answer

The enthalpy of formation of carbon monoxide is \(-110.5 \text{ kJ/mol} \) (option b).

Step 1: Write Combustion Reactions

Write the balanced chemical equations for the combustion reactions given: \( \text{C(s) + O}_2\text{(g) } \rightarrow \text{CO}_2\text{(g)} \) with enthalpy \( \Delta H = -393.5 \text{ kJ/mol} \) and \( \text{2CO(g) + O}_2\text{(g) } \rightarrow \text{2CO}_2\text{(g)} \) with enthalpy \( \Delta H = -283 \times 2 = -566 \text{ kJ} \).

Step 2: Apply Hess's Law

Use Hess's Law to derive the reaction for the formation of carbon monoxide: \( \text{C(s) +}\ \frac{1}{2} \text{O}_2\text{(g)} \rightarrow \text{CO(g)} \). According to Hess's law, the enthalpy change for this reaction \(( \text{CO formation} )\) can be derived from the combustion reactions given.

Step 3: Calculate Enthalpy of CO Formation

The enthalpy of formation of \( \text{CO} \) is calculated using the equation: \( \Delta H_f^\circ(\text{CO}) = \Delta H_c^\circ(\text{C}) - \frac{1}{2}\Delta H_c^\circ(\text{CO}) = -393.5 - \frac{1}{2}(-566) \). Substituting the given values, \( -393.5 + 283 = -110.5 \text{ kJ/mol} \).

Step 4: Compare to Options

Compare the calculated enthalpy of formation to the given choices. The calculated value is \(-110.5 \text{ kJ/mol} \), which corresponds to option (b).

Key Concepts

Hess's Law

Hess's Law is a fundamental principle in chemistry that reflects the conservation of energy. According to this law, the total enthalpy change of a chemical reaction is the same, no matter how many steps or the path taken to complete the reaction. This is incredibly useful for determining enthalpy changes of reactions that are difficult to measure directly.

When applying Hess's Law, think of energy as a ledger. Regardless of how you get from the starting balance (reactants) to the ending balance (products), the total "transaction" is the same. This means you can add up enthalpy changes from different reactions to find the total enthalpy change of the overall chemical reaction.

• Use known enthalpies of other reactions to find unknowns.
• If reactions need to be flipped, reverse the sign of the enthalpy change.
• Scale enthalpy changes proportionately if reaction coefficients are multiplied.

In our exercise, by using the enthalpy of combustion of carbon and carbon monoxide, Hess's Law allowed us to calculate the enthalpy of formation for carbon monoxide.

Combustion Reactions

Combustion reactions are a class of chemical reactions where a substance combines with oxygen to produce oxides and energy in the form of heat and light. They are highly exothermic reactions and are critical for a wide range of applications including energy production and propulsion.

In the context of the given exercise, understanding combustion reactions helps highlight how these reactions release specific amounts of energy, measured in kilojoules per mole ( ext{kJ/mol}). This gives insight into the enthalpy changes that occur during the reaction.

• Complete combustion of carbon forms carbon dioxide and releases (-393.5 kJ/mol of energy).
• Complete combustion of carbon monoxide forms carbon dioxide and releases (-283 kJ/mol of energy for two moles).

Tracking these energy changes allows scientists to use combustion information to back-calculate formation enthalpies for substances, such as carbon monoxide.

Carbon Monoxide

Carbon monoxide (CO) is a colorless, odorless gas that can be quite deadly in high concentrations. Its formation and combustion are integral parts of studying chemical energetics.

CO forms from the incomplete combustion of carbon-containing fuels. Unlike carbon dioxide (CO_2), which forms when there is plenty of oxygen, CO forms when oxygen is limited. This makes understanding its enthalpy of formation crucial for safe energy production.

• Its incomplete combustion nature demonstrates incomplete oxidation of carbon.
• Enthalpy of formation of CO is derived from its reaction pathways using Hess's Law.
• CO, by its nature, highlights the importance of controlled fuel burning for efficiency and safety.

In our calculation, the enthalpy of formation of CO was found to be -110.5 (kJ/mol), reflecting its energetic state relative to pure elements in their standard states.