When 0.602 g of biphenyl (C12H10) undergoes combustion in a bomb calorimeter, the temperature rises from 26.5 ∘C to 30.4 ∘C. What is the ΔErxn for the combustion of biphenyl? The heat capacity of the bomb calorimeter is 5.86 kJ/∘C.

Express the energy in kilojoules per mole to three significant figures.

1 Answer
Truong-Son N.
May 15, 2018

#DeltaE_"rxn" = -5.85 xx 10^3 "kJ/mol"#

What is this value in #"kJ/g"#?

A bomb calorimeter operates at constant volume, i.e. it is rigid.

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The biphenyl is placed into the sample holder and ignited from the outside. The temperature of the water inside (typically approx. #"2 L"#) will rise, as the reaction releases heat, and the cited heat capacity accounts for both the dry device and the water .

At constant volume, we obtain from the first law of thermodynamics:

#DeltaE = q + w#

#~~ q - cancel(PDeltaV)^(0)#

#-= q_V#

where #q_V# is the heat flow out from the reaction towards the surrounding water at constant volume.

By unit conversion (no equation required),

#q_V = "5.86 kJ"/cancel(""^@ "C") xx (30.4cancel(""^@ "C") - 26.5cancel(""^@ "C"))#

#=# #"22.9 kJ" = DeltaE_"soln"#

due to combusting #"0.602 g biphenyl"#. By conservation of energy,

#q_V + q_"rxn" = 0#

Therefore,

#q_V -= DeltaE_"soln" = -q_"rxn" -= -DeltaE_"rxn"#

and from this,

#color(blue)(DeltaE_"rxn") = -q_V/(n_"reactant")#

#= -("22.9 kJ")/(0.602 cancel"g biphenyl") xx (154.21 cancel("g C"_12"H"_10))/"1 mol"#

#= color(blue)(-5.85 xx 10^3 "kJ/mol")#

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