Question

Let moles of C₃H₈ = x,   moles of C₂H₂ = y & moles of CO₂ = z.

Calculation of ΔHº_f of C₃H₈(g)

3C(s) + 4H₂. (g) → C₃H₈(g)

ΔHº_f of C₃H₈(g) = [3(718) + 4(435)] – [2(347) + 8 (416)]

= 3894 – 4022 = –128 kJ / mol. 

Calculations of ΔHº_f of C₂H₂.(g)

2C (s) + H₂(g) → C₂H₂(g)

of C₂H₂(g) = [2(718) + (435)] – [(812) + 2(416)]

= (1436 + 435) – [1644]

= 227 kJ/mol.

Calculations of ΔHº_f of C₂H₄(g)

2C (s) + 2H₂(g) → C₂H₄(g)

ΔHº_f of C₂H₄ (g) = 2 (718) + 2 (435) – [615 + 4(416)]

= 2306 – 2279 = 27 kJ/mol.

Calculation of ΔHº_comb of C₃H₈(g)

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O (ℓ)

${\mathrm{\Delta H}}_{\text{comb }}^{º}\text{ of }{\mathrm{C}}_3{\mathrm{H}}_8=\left[3{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{CO}}_2\right)+4{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{H}}_2\mathrm{O},\mathrm{\ell }\right)\right]-{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{C}}_3{\mathrm{H}}_8, \mathrm{g}\right)$

= [3 (–394) + 4 (–286)] – (–128)  = –2198 kJ/mol.

Calculation of ΔHº_comb of C₂H₂(g)

C₂H₂(g) + 2.5O₂(g) → 2CO₂(g) + H₂O (ℓ)

${\mathrm{\Delta H}}_{\text{comb }}^{º}\text{ of }{\mathrm{C}}_2{\mathrm{H}}_2=\left[2{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{CO}}_2\right)+{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{H}}_2\mathrm{O},\mathrm{\ell }\right)\right]-{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left(\mathrm{CH}\right)$

= [2 (–394) + (–286)] – 227 = –1301 kJ/mol.

Now total heat released during combustion

2198 x + 1301 y = 4800  .............(i)

Combustion = 3x + 2y + z = 10   ..........(ii)

Total moles of H.O (ℓ) formed = 4x + y.

moles of C.H.(g) to be prepared = $\frac{3808}{22.4}=170$

Total heat absorbed during evaporation of water formation of 170 moles C.H. = 4800.

[(4x + y) × 0.875 x 40] + (170 x 27) = 4800

4x + y = 6     .........(iii)

on solvent (i), (ii) and (iii)

we get x = 1, y = 2, and z = 3

Let moles of C₃H₈ = x,   moles of C₂H₂ = y & moles of CO₂ = z.

Calculation of ΔHº_f of C₃H₈(g)

3C(s) + 4H₂. (g) → C₃H₈(g)

ΔHº_f of C₃H₈(g) = [3(718) + 4(435)] – [2(347) + 8 (416)]

= 3894 – 4022 = –128 kJ / mol. 

Calculations of ΔHº_f of C₂H₂.(g)

2C (s) + H₂(g) → C₂H₂(g)

of C₂H₂(g) = [2(718) + (435)] – [(812) + 2(416)]

= (1436 + 435) – [1644]

= 227 kJ/mol.

Calculations of ΔHº_f of C₂H₄(g)

2C (s) + 2H₂(g) → C₂H₄(g)

ΔHº_f of C₂H₄ (g) = 2 (718) + 2 (435) – [615 + 4(416)]

= 2306 – 2279 = 27 kJ/mol.

Calculation of ΔHº_comb of C₃H₈(g)

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O (ℓ)

${\mathrm{\Delta H}}_{\text{comb }}^{º}\text{ of }{\mathrm{C}}_3{\mathrm{H}}_8=\left[3{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{CO}}_2\right)+4{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{H}}_2\mathrm{O},\mathrm{\ell }\right)\right]-{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{C}}_3{\mathrm{H}}_8, \mathrm{g}\right)$

= [3 (–394) + 4 (–286)] – (–128)  = –2198 kJ/mol.

Calculation of ΔHº_comb of C₂H₂(g)

C₂H₂(g) + 2.5O₂(g) → 2CO₂(g) + H₂O (ℓ)

${\mathrm{\Delta H}}_{\text{comb }}^{º}\text{ of }{\mathrm{C}}_2{\mathrm{H}}_2=\left[2{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{CO}}_2\right)+{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{H}}_2\mathrm{O},\mathrm{\ell }\right)\right]-{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left(\mathrm{CH}\right)$

= [2 (–394) + (–286)] – 227 = –1301 kJ/mol.

Now total heat released during combustion

2198 x + 1301 y = 4800  .............(i)

Combustion = 3x + 2y + z = 10   ..........(ii)

Total moles of H.O (ℓ) formed = 4x + y.

moles of C.H.(g) to be prepared = $\frac{3808}{22.4}=170$

Total heat absorbed during evaporation of water formation of 170 moles C.H. = 4800.

[(4x + y) × 0.875 x 40] + (170 x 27) = 4800

4x + y = 6     .........(iii)

on solvent (i), (ii) and (iii)

we get x = 1, y = 2, and z = 3

Let moles of C₃H₈ = x,   moles of C₂H₂ = y & moles of CO₂ = z.

Calculation of ΔHº_f of C₃H₈(g)

3C(s) + 4H₂. (g) → C₃H₈(g)

ΔHº_f of C₃H₈(g) = [3(718) + 4(435)] – [2(347) + 8 (416)]

= 3894 – 4022 = –128 kJ / mol. 

Calculations of ΔHº_f of C₂H₂.(g)

2C (s) + H₂(g) → C₂H₂(g)

of C₂H₂(g) = [2(718) + (435)] – [(812) + 2(416)]

= (1436 + 435) – [1644]

= 227 kJ/mol.

Calculations of ΔHº_f of C₂H₄(g)

2C (s) + 2H₂(g) → C₂H₄(g)

ΔHº_f of C₂H₄ (g) = 2 (718) + 2 (435) – [615 + 4(416)]

= 2306 – 2279 = 27 kJ/mol.

Calculation of ΔHº_comb of C₃H₈(g)

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O (ℓ)

${\mathrm{\Delta H}}_{\text{comb }}^{º}\text{ of }{\mathrm{C}}_3{\mathrm{H}}_8=\left[3{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{CO}}_2\right)+4{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{H}}_2\mathrm{O},\mathrm{\ell }\right)\right]-{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{C}}_3{\mathrm{H}}_8, \mathrm{g}\right)$

= [3 (–394) + 4 (–286)] – (–128)  = –2198 kJ/mol.

Calculation of ΔHº_comb of C₂H₂(g)

C₂H₂(g) + 2.5O₂(g) → 2CO₂(g) + H₂O (ℓ)

${\mathrm{\Delta H}}_{\text{comb }}^{º}\text{ of }{\mathrm{C}}_2{\mathrm{H}}_2=\left[2{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{CO}}_2\right)+{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left({\mathrm{H}}_2\mathrm{O},\mathrm{\ell }\right)\right]-{\mathrm{\Delta H}}_{\mathrm{f}}^{º}\left(\mathrm{CH}\right)$

= [2 (–394) + (–286)] – 227 = –1301 kJ/mol.

Now total heat released during combustion

2198 x + 1301 y = 4800  .............(i)

Combustion = 3x + 2y + z = 10   ..........(ii)

Total moles of H.O (ℓ) formed = 4x + y.

moles of C.H.(g) to be prepared = $\frac{3808}{22.4}=170$

Total heat absorbed during evaporation of water formation of 170 moles C.H. = 4800.

[(4x + y) × 0.875 x 40] + (170 x 27) = 4800

4x + y = 6     .........(iii)

on solvent (i), (ii) and (iii)

we get x = 1, y = 2, and z = 3