Problem 39
Question
Bond energy of \(\mathrm{N}-\mathrm{H}, \mathrm{H}-\mathrm{H}\), and \(\mathrm{N} \equiv \mathrm{N}\) bonds are \(\mathrm{Q}_{1}\), \(\mathrm{Q}_{2}\) and \(\mathrm{Q}_{3} ; \Delta \mathrm{H}\) of \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}\) is (a) \(\mathrm{Q}_{3}+3 \mathrm{Q}_{2}-2 \mathrm{Q}_{1}\) (b) \(2 Q_{1}-Q_{3}-2 Q_{2}\) (c) \(\mathrm{Q}_{3}+3 \mathrm{Q}_{2}-6 \mathrm{Q}_{1}\) (d) \(\mathrm{Q}_{1}+\mathrm{Q}_{2}-\mathrm{Q}_{3}\)
Step-by-Step Solution
Verified Answer
Option (c): \(\mathrm{Q}_{3} + 3 \mathrm{Q}_{2} - 6 \mathrm{Q}_{1}\).
1Step 1: Understand the Reaction
The given reaction is \( \mathrm{N}_{2} + 3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3} \). This reaction involves breaking \(1\) \(\mathrm{N} \equiv \mathrm{N}\) triple bond and \(3\) \(\mathrm{H}-\mathrm{H}\) single bonds to form \(6\) \(\mathrm{N}-\mathrm{H}\) bonds.
2Step 2: Calculate Bonds Broken
Breaking bonds requires energy. In this reaction, we break \(1\) \(\mathrm{N} \equiv \mathrm{N}\) bond (energy \(\mathrm{Q}_{3}\)) and \(3\) \(\mathrm{H}-\mathrm{H}\) bonds (energy \(3\mathrm{Q}_{2}\)). Therefore, the total energy for bonds broken is \(\mathrm{Q}_{3} + 3 \mathrm{Q}_{2}\).
3Step 3: Calculate Bonds Formed
Forming bonds releases energy. Here, \(6\) \(\mathrm{N}-\mathrm{H}\) bonds will be formed, each with energy \(\mathrm{Q}_{1}\). Thus, the total energy released by forming bonds is \(6 \mathrm{Q}_{1}\).
4Step 4: Calculate Change in Enthalpy (ΔH)
Change in enthalpy (\(\Delta H\)) for a reaction is the energy of bonds broken minus the energy of bonds formed. Therefore, \[ \Delta H = (\mathrm{Q}_{3} + 3 \mathrm{Q}_{2}) - 6 \mathrm{Q}_{1}. \]
5Step 5: Identify the Correct Option
Compare the derived expression for \(\Delta H\) with the given options. The matching expression is the one given in option (c): \(\mathrm{Q}_{3} + 3 \mathrm{Q}_{2} - 6 \mathrm{Q}_{1}\).
Key Concepts
Enthalpy ChangeChemical Bond FormationChemical Bond Breaking
Enthalpy Change
Enthalpy change (9H) in a chemical reaction refers to the amount of heat absorbed or released. This depends on whether bonds are broken or formed. When a chemical reaction takes place, bonds in the reactants need to be broken first. Breaking these bonds requires energy. Then, new bonds are formed to produce the products, and this releases energy.
The overall change in enthalpy (9H) can be determined by considering the energy needed to break the bonds minus the energy released from forming new bonds. If 9H is negative, the reaction is exothermic, meaning it releases energy. If 9H is positive, the reaction is endothermic, which absorbs energy.
In our example reaction \(\mathrm{N}_{2} + 3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}\), the formula we use for enthalpy change is:
The overall change in enthalpy (9H) can be determined by considering the energy needed to break the bonds minus the energy released from forming new bonds. If 9H is negative, the reaction is exothermic, meaning it releases energy. If 9H is positive, the reaction is endothermic, which absorbs energy.
In our example reaction \(\mathrm{N}_{2} + 3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}\), the formula we use for enthalpy change is:
- 9H = Energy of bonds broken - Energy of bonds formed.
Chemical Bond Formation
Chemical bond formation releases energy. This energy release happens because atoms reach a more stable, lower energy state during bond formation.
When atoms come together to form bonds, they achieve a configuration with less energy compared to when they are separate. The energy released during this process bfloat="center"onding signals the system's stability. Just think of it like legos clicking together to make a firm structure.
In our target reaction, six \(\mathrm{N}-\mathrm{H}\) bonds are being formed. For each \(\mathrm{N}-\mathrm{H}\) bond, energy \(\mathrm{Q}_{1}\) is released:
When atoms come together to form bonds, they achieve a configuration with less energy compared to when they are separate. The energy released during this process bfloat="center"onding signals the system's stability. Just think of it like legos clicking together to make a firm structure.
In our target reaction, six \(\mathrm{N}-\mathrm{H}\) bonds are being formed. For each \(\mathrm{N}-\mathrm{H}\) bond, energy \(\mathrm{Q}_{1}\) is released:
- Total energy released from bond formation = \(6 \times \mathrm{Q}_{1}\).
Chemical Bond Breaking
Breaking chemical bonds requires energy. This is because energy is needed to overcome the forces that hold the atoms together in a molecule. It can be thought of as the opposite of bond formation, as now you are pulling the legos apart which requires some effort.
In chemical reactions, existing bonds in the reactants must be broken before new bonds can form in the products. This requires input energy known as bond dissociation energy.
In chemical reactions, existing bonds in the reactants must be broken before new bonds can form in the products. This requires input energy known as bond dissociation energy.
- New-N bond: \( \mathrm{Q}_{3}\) for breaking a single \(\mathrm{N} \equiv \mathrm{N}\) bond.
- H-H bonds: \(3 \times \mathrm{Q}_{2}\) for breaking three \(\mathrm{H}-\mathrm{H}\) bonds.
Other exercises in this chapter
Problem 37
In a constant volume calorimeter \(3.5 \mathrm{~g}\) of a gas (mol.wt.28) was burnt in excess \(\mathrm{O}_{2}\) at \(298 \mathrm{~K}\). The increase in tempera
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The amount of heat required to raise the temperature of one mole of the substance through \(1 \mathrm{~K}\) is called, its (a) molar heat (b) entropy (c) therma
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Which of the following gas molecule has the maxi mum specific heat at constant pressure? (a) helium (b) argon (c) nitrogen (d) oxygen
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A reaction occurs spontaneously if (a) \(\mathrm{T} \Delta \mathrm{S}\Delta \mathrm{H}\) and \(\Delta \mathrm{H}=+\mathrm{ve}, \Delta \mathrm{S}=-\mathrm{ve}\)
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