Find ΔrU for this reaction.

Question

The heat of combustion of liquid pentane (C5H12)(C5H12) to carbon dioxide and liquid water at 298 K is -3535  kJmol−1. Find ΔrU for this reaction.

my solution:

so i used the equation ΔrU= ΔrH - ΔnRT

substituted the values as follow,

ΔrH= -3535kJ , Δn= -3 , R= 8.3143 and T= 298K and i got the answer as 3898kJmol-1.

But the correct answer was -3528 kJ⋅mol−1.

can i please know where I went wrong?

Thanks

Answer 1

I believe you forgot to account for the difference in units.

R has units J•K^-1•mol^-1. So to convert it to kJ•K^-1•mol^-1, you have to divide it by 1000.

So we have, according to the formula:

ΔrU = ΔrH - ΔnRT

What you did:

ΔrU = -3535 - (-3)(298)(8.3143) ≠ 3898 kJ•mol^-1 (wrong because the R and ΔrH units do not match up)

What you should do instead:

ΔrU = -3535 kJ - (-3)(298 K)(8.3143 J•K^-1•mol^-1)(1 kJ/1000 J) = -3528 kJ•mol^-1 which is the correct answer.

Remember to write out the units!