Question

The reaction \[C{H_{4(g)}} + C{l_{2(g)}} \to C{H_3}C{l_{(g)}} + HC{l_{(g)}}\] has \[\Delta H = - 25kcal\]

Bond	Bond Energy Kcal
\[C - Cl\]	\[84\]
\[H - Cl\]	\[103\]
\[C - H\]	x
\[Cl - Cl\]	y
\[x:y = 9:5\]

From the given data what is bond energy of \[Cl - Cl\] bond
\[(1)\]\[70kcal\]
\[(2)\]\[80kcal\]
\[(3)\]\[67.75kcal\]
\[(4)\]\[57.75kcal\]

Answer 1

Hint: Bond energy can be defined as the amount of energy that is necessary to form the bond or break the bond between two atoms. Energy is released by the system when a bond is formed and energy is given to the system when a bond is broken.

Complete answer:
Let’s write the given chemical question
\[C{H_{4(g)}} + C{l_{2(g)}} \to C{H_3}C{l_{(g)}} + HC{l_{(g)}}\]
From the above reaction we can see that a \[C - H\] bond is broken from the molecule of methane and one \[Cl - Cl\] bond is broken from the chlorine molecule. One the product side we can see the formation of two new bonds, one is \[C - Cl\] bond to form chloroform and other is \[H - Cl\] bond to form hydrochloric acid.
Let us write the given value of bond enthalpies of different bonds.
Bond enthalpy of Carbon-Chlorine bond, \[C - Cl = 84kcal\]
Bond enthalpy of Hydrogen-Chlorine bond, \[H - Cl = 103kcal\]
Bond enthalpy of Carbon-Hydrogen bond, \[C - H = xkcal\]
Bond enthalpy of Chlorine-Chlorine bond, \[Cl - Cl = ykcal\]
Total energy released/given, \[\Delta H = - 25kcal\]
Total released/given energy is given by measuring the difference between energy given during breaking bonds and energy released due to formation of bonds. Now using the formula for total released/given energy according to the given reaction.
\[\Delta H = 4 \times C - H + 1 \times Cl - Cl - 3 \times C - H - 1 \times C - Cl - 1 \times H - Cl\]
Substituting given values in the above equation.
\[ - 25 = 4x + y - 3x - 84 - 103\]
On further simplification we get the relation
\[x + y = 162\]
also, we are given \[x:y = 9:5\] which can be written as \[x = \dfrac{9}{5}y\]
putting this value of x in the obtained relation
\[\dfrac{9}{5}y + y = 162\]
\[y = \dfrac{{162 \times 5}}{{14}}\]
we get the value of y
\[y = 57.75kcal\]
So, the bond energy of \[Cl - Cl\] bond is \[57.75kcal\].

Therefore option \[(4)\] is the right answer.

Note:
Laws of thermodynamics, states that bond enthalpy is positive when a bond is formed and bond enthalpy is negative when bond is broken. The negative sign of total energy released indicates that the energy released by the formation of new bonds is less than the energy required to break the bonds in reactant molecules.