Using the data (all values are in kilocalories per mole at 25^ C ) given below, calculate the bond energy of C - C and C - H bonds. H ^ combustion (ethane) =-372.0 H ^ combustion (propane) =-530.0 H ^ for C ( graphite ) C ( g )=172.0 Bond energy of H - H =104.0 _ f H ^ of H _2 O ( l )=-68.0 H ^ for CO _2(g)=-94.0

We are given, 1. C_2H_6(g)+7 2 O_2(g) 2CO_2(g)+H_2O; ^ =-372.0kcal 2. C_3H_8(g)+5O_2(g) 3CO_2(g)+4H_2O; ^ =-530.0kcal 3. C(s) C(g); ^ =172.0kcal 4. H_2(g) 2H(g); ^ =104.0kcal 5. H_2(g)+1 2 O_2(g) H_2O(l); ^ =-68.0kcal 6. C(g)+C_2(g) CO_2(g); ^ =-94.0kcal Suppose the bond energy of C-C bond = xkcal mol^ -1 . and that of C-H bond = ykcal mol^ -1 . Then for C_2H_6 (g), H H | | -C-C-H 2C(g)+6H; | | H H =x+6y (vii) and for C_3H_8(g); i.e., H H H | | | -C-C-C-H 3C(g)+8H(g); | | | H H H =2x+8y (viii) To get eq. (vii), operate eq. (i) + 2 × eq. (iii) + 3 × eq. (iv) - 3 × eq. (v) - 2 × eq. (vi). It gives =676kcal It get eq. (viii) operate eq. (ii) + eq. (iii) + 4 × eq. (iv) - 4 × eq. (v) - 3 × eq. (vi) It gives =956kcal Thus, x + 6y = 676, 2x + 8y = 956 On solving these equations, we get x = 82, y = 99 Hence, C-C bond energy = 82kcal mol^ -1 and C-H bond energy = 99kcal mol^ -1 .

Using the data (all values are in kilocalories per mole at 25^ C …

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Using the data (all values are in kilocalories per mole at $25^{\circ} C$ ) given below, calculate the bond energy of $C - C$ and C -
H bonds. $\Delta H ^{\circ}$ combustion (ethane) $=-372.0$
$\Delta H ^{\circ}$ combustion (propane) $=-530.0 \Delta H ^{\circ}$ for $C ($ graphite $) \rightarrow C ( g )=172.0$ Bond energy of $H - H =104.0 \Delta_{ f } H ^{\circ}$ of $H _2 O ( l )=-68.0 \Delta H ^{\circ}$ for $CO _2(g)=-94.0$

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Answer

We are given,

$\text{C}_2\text{H}_6(\text{g})+\frac{7}{2}\text{O}_2(\text{g})\overrightarrow{\ \ \ \ \ }\ 2\text{CO}_2(\text{g})+\text{H}_2\text{O};$ $\Delta\text{H}^\circ=-372.0\text{kcal}$
$\text{C}_3\text{H}_8(\text{g})+5\text{O}_2(\text{g})\overrightarrow{\ \ \ \ \ \ }\ 3\text{CO}_2(\text{g})+4\text{H}_2\text{O};$ $\Delta\text{H}^\circ=-530.0\text{kcal}$
$\text{C(s)}\overrightarrow{\ \ \ \ \ }\ \text{C(g)};$ $\Delta\text{H}^\circ=172.0\text{kcal}$
$\text{H}_2(\text{g})\overrightarrow{\ \ \ \ \ }\ 2\text{H(g)};$ $\Delta\text{H}^\circ=104.0\text{kcal}$
$\text{H}_2(\text{g})+\frac{1}{2}\text{O}_2(\text{g})\overrightarrow{\ \ \ \ \ \ }\ \text{H}_2\text{O(l)};$ $\Delta\text{H}^\circ=-68.0\text{kcal}$
$\text{C(g)}+\text{C}_2(\text{g})\overrightarrow{\ \ \ \ \ }\ \text{CO}_2(\text{g});$ $\Delta\text{H}^\circ=-94.0\text{kcal}$

Suppose the bond energy of C-C bond = xkcal $mol^{-1}.$ and that of C-H bond = ykcal $mol^{-1}.$ Then for $C_2H_6 (g),$
$\ \ \ \ \ \ \ \ \text{H} \ \ \ \ \ \text{H}\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ |\\\text{H}-\text{C}-\text{C}-\text{H}\overrightarrow{\ \ \ \ \ }\ 2\text{C(g)}+6\text{H};\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ |\\ \ \ \ \ \ \ \ \ \text{H}\ \ \ \ \text{H}$ $\Delta\text{H}=\text{x}+6\text{y}\dots(\text{vii})$
and for $C_3H_8(g)$; i.e.,
$\ \ \ \ \ \ \ \ \text{H} \ \ \ \ \ \text{H} \ \ \ \ \ \text{H}\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ |\ \ \ \ \ \ |\\\text{H}-\text{C}-\text{C}-\text{C}-\text{H}\overrightarrow{\ \ \ \ \ }\ 3\text{C(g)}+8\text{H(g)};\\ \ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ |\ \ \ \ \ \ |\\ \ \ \ \ \ \ \ \ \text{H} \ \ \ \ \ \text{H}\ \ \ \ \text{H}$ $\Delta\text{H}=2\text{x}+8\text{y}\dots(\text{viii})$
To get eq. (vii), operate eq. (i) + 2 × eq. (iii) + 3 × eq. (iv) - 3 × eq. (v) - 2 × eq. (vi).
It gives $\Delta\text{H}=676\text{kcal}$
It get eq. (viii) operate eq. (ii) + eq. (iii) + 4 × eq. (iv) - 4 × eq. (v) - 3 × eq. (vi)
It gives $\Delta\text{H}=956\text{kcal}$
Thus, x + 6y = 676, 2x + 8y = 956
On solving these equations, we get x = 82, y = 99
Hence, C-C bond energy = 82kcal $mol^{-1}$ and C-H bond energy = 99kcal $mol^{-1}.$

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