This problem provides information about the decomposition of copper(II) nitrate to copper(II) oxide and dinitrogen monoxide; for example, it is endothermic, the enthalpies of formation and the chemical reaction, as well as copper (II) sulfate which when dissolved in water, exhibits a temperature decrease:
[tex]2Cu(NO_3)_2(s) \rightarrow 2CuO(s) + 4NO_2(g) + O_2(g)[/tex]
First of all, we can draw the reaction pathway as shown on the attached figure, by taking into account the positive enthalpy change as it is endothermic, so that the products turn out with higher energy than the reactants, for it to be positive. In addition, keep in mind that top point is the activation energy the reaction needs to take place.
Next, we calculate the enthalpy change for this reaction by using the general formula which subtracts the enthalpy of formation of products and reactants with each species' correct stoichiometric coefficient:
[tex]\Delta H=2\Delta _fH_{CuO}+4\Delta _fH_{NO_2}+\Delta _fH_{O_2}-2\Delta _fH_{Cu(NO_3)_2}[/tex]
So we plug in the given enthalpies of formation:
[tex]\Delta H=2(-157.3)+4(33.2)+(0)-2(-302.9)=424.0 kJ/mol[/tex]
Finally, we go over the calorimetry experiment, whereby the total heat absorbed by the copper(II) sulfate is calculated via the general heat equation, which includes the heat loss from the solution of water and the salt:
[tex]Q_{rxn}=-mC_w\Delta T\\\\Q_{rxn}=-(100+25)g*4.18\frac{J}{g\°C}*-2.9\°C=1515.25J[/tex]
By dividing the previous answer by the moles of salt:
[tex]n=25.0g*\frac{1mol}{249.7g}=0.100mol[/tex]
We can obtain the enthalpy change of solution of the copper salt:
[tex]\Delta _{dissolution}H=\frac{1,515.25J}{0.100mol} \\\\\Delta _{dissolution}H=15,134J/mol=15.1kJ/mol[/tex]
To conclude, it is important to note that one possible source of error is we are assuming the solution has the same specific heat to that of water and that is not necessarily true. Also, we are neglecting any heat transfer to and from the surroundings despite the polystyrene beaker is considered a heat isolator, which means the results cannot necesarilly be accurate and the enthalpy change could have turned out higher or lower in a rigoruous experiment.
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