Problem 76 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following equations represent standard heat of formation of \(\mathrm{C}_{2} \mathrm{H}_{4} ?\) (a) \(2 \mathrm{C}\) (diamond) \(+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\) (b) \(2 \mathrm{C}\) (graphite) \(+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\) (c) \(2 \mathrm{C}\) (diamond) \(+4 \mathrm{H}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\) (d) \(2 \mathrm{C}\) (graphite) \(+4 \mathrm{H}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\)

Step-by-Step Solution

Answer

The correct equation is (b).

Step 1: Understand the Definition of Standard Heat of Formation

The standard heat of formation of a compound is defined as the change in enthalpy when one mole of that compound forms from its elements in their standard states. Therefore, we need one mole of \( \mathrm{C}_2\mathrm{H}_4 \) and the elements \( \mathrm{C} \) and \( \mathrm{H}_2 \) in their standard states.

Step 2: Identify the Standard States of Elements

In standard conditions, carbon exists as graphite, and hydrogen exists as \( \mathrm{H}_2 \) gas. Therefore, we should look for equations that use \( \mathrm{C} \) (graphite) and \( \mathrm{H}_2 \) (gas) as reactants.

Step 3: Analyze Each Given Equation

Check each given equation to see if elements are in their standard states:- **(a)** Uses \( \mathrm{C} \) (diamond) and \( \mathrm{H}_2 \) (gas).- **(b)** Uses \( \mathrm{C} \) (graphite) and \( \mathrm{H}_2 \) (gas).- **(c)** Uses \( \mathrm{C} \) (diamond) and \( \mathrm{H} \) (gas), not a diatomic molecule.- **(d)** Uses \( \mathrm{C} \) (graphite) and \( \mathrm{H} \) (gas), not a diatomic molecule.

Step 4: Choose the Correct Equation

The standard heat of formation requires the elements in their standard states. Thus, option **(b)** \(2 \mathrm{C} \) (graphite) \( + 2 \mathrm{H}_2(g) \longrightarrow \mathrm{C}_2\mathrm{H}_4(g) \) correctly represents this, as it uses graphite and \( \mathrm{H}_2 \) in their standard forms.

Key Concepts

Enthalpy Change

When discussing chemistry, it's crucial to understand the concept of enthalpy change. This refers to the heat absorbed or released during a chemical reaction at constant pressure. It is symbolized by \( \Delta H \). For instance, in exothermic reactions, heat is released, making \( \Delta H \) negative, whereas for endothermic reactions, heat is absorbed, rendering \( \Delta H \) positive.

The enthalpy change involved in forming 1 mole of a compound from its constituent elements in their standard states is known as the standard enthalpy change of formation (\( \Delta H_f^\circ \)). This tells us about the energy required for the synthesis of a compound, such as ethylene (\( \mathrm{C}_2\mathrm{H}_4 \)).

• The sign of \( \Delta H \) provides insights into the stability of the products compared to the reactants.
• It's a critical factor in determining whether a reaction is thermodynamically favorable.

This makes enthalpy change an essential concept in understanding chemical thermodynamics.

Standard States of Elements

For accurate calculations in chemical reactions, specifically the standard heat of formation, elements must be in their standard states. A standard state refers to the most stable physical form of an element at 1 atmosphere of pressure and a specified temperature, generally 25°C (298 K).

Take carbon for example: its standard state is graphite, even though it also exists as diamond. Hydrogen's standard state is as a diatomic gas, \( \mathrm{H}_2 \), which is how it naturally occurs under standard conditions. Therefore, when addressing the standard formation of compounds:

• Carbon should be used as graphite, not diamond.
• Hydrogen should appear as \( \mathrm{H}_2 \), not atomic \( \mathrm{H} \).

Recognizing the correct standard state of elements ensures the accuracy in thermodynamic calculations, especially when determining the heat change in formation reactions.

Chemical Equations Analysis

Analyzing chemical equations requires a keen eye to ensure they are balanced and represent actual chemical processes. This involves verifying that elements appear in their correct standard states and ensuring stoichiometric coefficients reflect the correct proportionality of elements involved.

Assessing an equation like \(2 \mathrm{C} \) (graphite) \( + 2 \mathrm{H}_2(g) \longrightarrow \mathrm{C}_2\mathrm{H}_4(g) \) involves checking each element:

• Are carbon and hydrogen in their standard states? Yes, as graphite and \( \mathrm{H}_2 \).
• Does the equation show the formation of one mole of the compound from elements in their minimal given form? Yes, it accurately reflects the formation from basic elements.
• Are the stoichiometric coefficients balanced? Yes, two moles of carbon and hydrogen gas form one mole of ethylene.

By understanding these aspects, one can correctly identify the right equation that represents a compound's standard heat of formation.