Given the following combustion reactions, what is the enthalpy of combustion of ethane?

#(i)# # C_2H_6(g)rarr 2C(s)+3H_2(g); DeltaH^@=+86*kJ*mol^-1#

#(ii)# #C(s)+O_2(g) rarr CO_2(g); DeltaH^@=-396.8*kJ*mol^-1#

#(iii)""H_2(g)+1/2O_2(g)rarrH_2O(l); DeltaH^@= -287.3*kJ*mol^-1#

1 Answer
anor277
Feb 18, 2018

So you want the enthalpy of combustion of ethane? I make it #DeltaH_"combustion"^@=-1569.5*kJ*mol^-1#

Explanation:

...that is we want #DeltaH_"rxn"^@# for..

#C_2H_6(g) +7/2O_2(g) rarr 2CO_2(g) + 3H_2O(l) + Delta#

We are given...

#(i)# # C_2H_6(g)rarr 2C(s)+3H_2(g); DeltaH^@=+86*kJ*mol^-1#

#(ii)# #C(s)+O_2(g) rarr CO_2(g); DeltaH^@=-396.8*kJ*mol^-1#

#(iii)""H_2(g)+1/2O_2(g)rarrH_2O(l); DeltaH^@= -287.3*kJ*mol^-1#

Let us take #(i)+2xx(ii)+3xx(iii)#

# C_2H_6(g)+cancel(2C(s))+2O_2(g)+cancel(3H_2(g))+3/2O_2(g)rarr 2CO_2(g)+cancel(2C(s)+3H_2(g))+3H_2O(l)#..

...the which gives after cancellation....

# C_2H_6(g)+7/2O_2(g)rarr 2CO_2(g)+3H_2O(l)#..

...the which is the reaction whose #DeltaH^@# we wish to calculate. And to get #DeltaH_"rxn"^@#, we simply add the thermodynamic parameters appropriately, in the same way that we added the reactions...i.e.

#DeltaH_"rxn"^@=DeltaH_(i)^@+2xxDeltaH_(ii)^@+3xxDeltaH_(iii)^@#
...and please note that I observe the sign parameters...

...we gets..#{+86-2xx396.8-3xx287.3}*kJ*mol^-1=-1569.5*kJ*mol^-1#

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