The following reaction was carried out in a calorimeter with
a heat capacity of 2000 J K-1. The specific heat capacity
of the solutions should be taken as 4.2 J K-1 cm-3. You may
assume that the mass of excess metal in the
experiments are negligible. In the first
experiment, excess magnesium powder was added to 100 cm3 of a 1.00
mol dm-3 solution of copper (II) sulfate. The temperature rose from
19.5 °C to 41.2 °C. In the second experiment, excess copper powder
was added to 100cm3 of a 0.50 mol dm-3 solution of silver nitrate.
The temperature rose from 19.5 °C to 20.9 °C.
Calculate the enthalpy change of reactions in both
experiments, as well as the expected enthalpy change, per mole of
magnesium, for the reaction (not carried out
experimentally) between magnesium and silver nitrate.
Solution
:
The heat capacity of the entire system is the sum of the heat
capacities for the individual components, ie. the calorimeter and
the aqueous solution.
Total Heat Capacity = Heat Capacity of Water + Heat
Capacity of Calorimeter
= (100cm3 x 4.2 J K-1 cm3) + (2000 J K-1)
= 2420 J K-1
Heat transferred in Experiment 1 = Total Heat
Capacity x Change in Temperature
Q = (2420 J K-1) x (41.2 - 19.5)
Q = 5.2514 x 10^4 J
Heat transferred in Experiment 2 = Total Heat
Capacity x Change in Temperature
Q = (2420 J K-1) x (20.9 - 19.5)
Q = 3.3880 x 10^3 J
Note that because the temperature rose, the reactions are
exothermic, and therefore you must write the negative sign for
the enthalpy change value.
Mg(s) + Cu2+(aq) ---> Mg2+(aq) + Cu(s)
Enthalpy change of 1st experiment in regard to either Mg or
Cu2+
= Heat transferred / (moles of reactant of either Mg or
Cu2+)
= - (5.2514 x 10^4 J) / (100/1000 x 1.0)
= - 5.2514 x 10^2 kJ/mol
of Mg or Cu2+
Cu(s) + 2Ag+(aq) ---> Cu2+(aq) + 2Ag(s)
Enthalpy change of 2nd experiment in regard to Ag+
= Heat transferred / (moles of reactant of Ag+)
= - (3.3880 x 10^3 J) / (100/1000 x 0.5)
= - 6.7760 x 10^1 kJ/mol
of Ag+
Enthalpy change of 2nd experiment in regard to Cu
= Heat transferred / (moles of reactant of Cu)
= - (3.3880 x 10^3 J) / (100/1000 x 0.5) / 2
= - 1.3552 x 10^2 kJ/mol
of Cu
By Hess Law, enthalpy change of reaction between magnesium and
silver nitrate
= (enthalpy change of reaction between magnesium and copper)
+ (enthalpy change of reaction between copper and silver
nitrate)
= (-5.2514 x 10^2)kJ + (-1.3552 x 10^2)kJ
= -6.6066 x 10^2
kJ/mol of Mg