# Solve question 7: 7. The difference between heat of reaction at constant volume and constant pressure of the reaction. ${\mathrm{C}}_{2}{\mathrm{H}}_{2}\left(\mathrm{g}\right)+\frac{5}{2}{\mathrm{O}}_{2}\left(\mathrm{g}\right)\to 2{\mathrm{CO}}_{2}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{l}\right)$ At 300 K in Kcal is [Given: R=2 cal/mol. K] (A) -0.3 Kcal             (B) +0.3 Kcal           (C) -0.9 Kcal        (D) None of these.

Dear student,

The given reaction is;  C2H2(g)  + $\frac{5}{2}$ O2(g)  $\to$2 CO2(g)  + H2O(l)
Again we know that ; heat at constant volume = $∆$U ( Change in internal energy )
heat at constant pressure = $∆$ H ( Change in enthalpy )
Now from the first law of thermodynamics for the reactions; $∆$H = $∆$ U - $∆$ng RT ........(i)
From the above relation $∆$ng = number of moles of gaseous products - number of moles of gaseous reactants
= 2 - ( $\frac{5}{2}$+ 1) =  - $\frac{3}{2}$
Now on putting the values inequation (i) ; $∆$H = $∆$ U - (- $\frac{3}{2}$$×$2$×$300 )
Then ; $∆$H - $∆$ U = 900 cal /mol or 0.9 kcal/mol
Again according to the question asked ;
$∆$ U - $∆$H = - 0.9 kcal/mol (Option C)
Regards

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