Question

Suppose you burned 0.414 g of solid carbon in an excess of oxygen gas in a constant-volume calorimeter to give carbon dioxide gas.

C(s) + O2(g) → CO2(g)

The temperature of the calorimeter, which contained 770. g of water, increased from 23.02°C to 26.31°C. The heat capacity of the bomb is 901. J/K. Calculate ΔU per mole of carbon.

Answer 1

specific heat capacity of water is 4.184 J/g·K

m = Mass of water in gm

dT = temperature differnce

C= specific heat capacity

dH = m C dT + C dT
dH = 770 g (4.184 J/g-K) (26.31-23.02) + 901 J/K (26.31-23.02)

dH = 770 g (4.184 J/g-K) (3.29 K) + 901 J/K (3.29 K)

dH = 10599 + 2964.3 = 13563.6

dH = 13563.6 Joules

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find moles:
0.414 g of C @ 12.01 g/mol = 0.0345 moles Carbon


find ΔU per mole of carbon
13563.6 Joules / 0.0345 moles Carbon = 393,147 Joules/mol
aka
393 kJ/mol

since your ereaction was exothermic:
ΔU = - 393 kJ per mole of carbon