The amount of energy required to break a bond is the same as the amount of energy released when the same bond is formed. In a gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond Strength. BDE is affected by the s-character of the bond and the stability of the radicals formed. Shorter bonds are typically stronger bonds. BDEs for some bonds are given below:
Correct match of the C–H bonds (shown in bold) in Column J with their BDE in Column K is
Column J | Column K | ||
---|---|---|---|
P | \(\text{H--CH(CH}_3\text{)}_2\) | i | 132 |
Q | \(\text{H--CH}_2\text{Ph}\) | ii | 110 |
R | \(\text{H--CH}=CH_2\) | iii | 95 |
S | \(\text{H--C≡CH}\) | iv | 88 |
P – iii, Q – iv, R – ii, S – i
P – i, Q – ii, R – iii, S – iv
P – iii, Q – ii, R – i, S – iv
P – ii, Q – i, R – iv, S – iii
Order of stability of free radical
\(Q > P > R > S\)
\(\text{Stability of free radical } \alpha \frac{1}{\text{Bond energy}}\)
∴ Order of bond energy :
\(S > R > P > Q\)
For the following reaction,
\(\text{CH}_4\text{(g)} + \text{Cl}_2\text{(g)} \overset{\text{light}}{\longrightarrow} \text{CH}_3\text{Cl (g)} + \text{HCl(g)}\)
the correct statement is
Initiation step is exothermic with \(\Delta\)H° = –58 kcal mol–1
Propagation step involving ·CH3 formation is exothermic with \(\Delta\)H° = –2 kcal mol–1
Propagation step involving CH3Cl formation is endothermic with \(\Delta\)H° = +27 kcal mol–1
The reaction is exothermic with \(\Delta\)H° = –25 kcal mol–1
Step (1) → Endothermic (bond breaking)
Step (2) → ∆H = 105 – 103 = 2 kcal/mol (Endothermic)
Step (3) → ∆H = 58 – 85 = –27 kcal/mol (Exothermic)
For complete reaction
\(\text{CH}_4\text{(g)} + \text{Cl}_2\text{(g)} \overset{\text{light}}{\longrightarrow} \text{CH}_3\text{Cl (g)} + \text{HCl(g)}\)
∆H = 58 + 105 – 85 – 103
= –25 kcal/mol
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____