Question

which of the following has a \\( \delta h^{\circ}_{f}=0 \mathrm{~kj} / \mathrm{mol} \\)?
a \\( \mathrm{no}(\mathrm{g}) \\)
b \\( \mathrm{cs}_{2}(\mathrm{i}) \\)
c \\( \mathrm{n}_{2}(\mathrm{~g}) \\)
d \\( \mathrm{h}_{2} \mathrm{o}(\mathrm{i}) \\)
question 2
when 18.5 g of \\( \mathrm{hgo}(\mathrm{s}) \\) is decomposed to form \\( \mathrm{hg}(\mathrm{i}) \\) and \\( \mathrm{o}_{2}(\mathrm{~g}), 7.75 \mathrm{~kj} \\) of heat is absorbed at standard-state conditions. what is the standard enthalpy of
formation \\( \left(\delta \mathrm{h}^{\circ} \mathrm{f}\
ight) \\) of \\( \mathrm{hgo}(\mathrm{s}) \\)? (the unit of your answer should be \\( \mathrm{kj} / \mathrm{mol} \\) with three sf and absolute value)
molar mass of \\( \mathrm{hgo} \\) is \\( 216.59 \mathrm{~g} / \mathrm{mol} \\)
add your answer
integer, decimal, or e notation allowed
question 3
find the standard enthalpy of formation of ethylene, \\( \mathrm{c}_{2} \mathrm{h}_{4}(\mathrm{~g}) \\), given the following data: heat of combustion of \\( \mathrm{c}_{2} \mathrm{h}_{4}(\mathrm{~g})=-1411 \mathrm{~kj} / \mathrm{mol} \\);
\\( \delta \mathrm{h}^{\circ} \mathrm{f}\left\mathrm{co}_{2}(\mathrm{~g})\
ight=-393.5 \mathrm{~kj} / \mathrm{mol} ; \delta \mathrm{h}^{\circ} \mathrm{f}\left\mathrm{h}_{2} \mathrm{o}(\mathrm{i})\
ight=-285.8 \mathrm{~kj} / \mathrm{mol} \\). (3 sf and the unit is \\( \mathrm{kj} / \mathrm{mol} \\))
\\( \mathrm{c}_{2} \mathrm{h}_{4}(\mathrm{~g})+3 \mathrm{o}_{2}(\mathrm{~g}) \
ightarrow 2 \mathrm{co}_{2}(\mathrm{~g})+2 \mathrm{h}_{2} \mathrm{o}(\mathrm{g}) \\).
add your answer
integer, decimal, or e notation allowed

Explanation:

Question 1

Step1: Recall the definition of standard enthalpy of formation

The standard enthalpy of formation ($\Delta H_f^{\circ}$) of an element in its standard state is \(0\space kJ/mol\).

Step2: Analyze each option

• Option A: \(NO(g)\)

It is a compound, not an element in its standard state. So, \(\Delta H_f^{\circ}
eq0\).

• Option B: \(CS_2(l)\)

It is a compound, not an element in its standard state. So, \(\Delta H_f^{\circ}
eq0\).

• Option C: \(N_2(g)\)

Nitrogen (\(N_2\)) is an element in its standard state (gaseous state for \(N_2\) at \(25^{\circ}C\) and \(1\space atm\)). So, \(\Delta H_f^{\circ} = 0\space kJ/mol\).

• Option D: \(H_2O(l)\)

It is a compound, not an element in its standard state. So, \(\Delta H_f^{\circ}
eq0\).

Question 2

Step1: Calculate the number of moles of \(HgO\)

The molar mass of \(HgO\) is \(M = 216.59\space g/mol\). The number of moles \(n=\frac{m}{M}\), where \(m = 18.5\space g\). So, \(n=\frac{18.5\space g}{216.59\space g/mol}\approx0.0854\space mol\).

Step2: Relate the heat absorbed to the enthalpy of decomposition

The decomposition reaction is \(2HgO(s)\to2Hg(l)+O_2(g)\). If \(0.0854\space mol\) of \(HgO\) decomposition absorbs \(q = 7.75\space kJ\) of heat. For \(2\space mol\) of \(HgO\) decomposition, the heat absorbed \(Q\) is calculated as follows:

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Since the decomposition reaction \(2HgO(s)\to2Hg(l)+O_2(g)\) has \(\Delta H^{\circ}= + 181\space kJ\) (endothermic), the formation reaction \(2Hg(l)+O_2(g)\to2HgO(s)\) has \(\Delta H^{\circ}_f=- 181\space kJ/mol\) (opposite sign for the reverse reaction). The standard enthalpy of formation of \(HgO(s)\) (per mole) is \(\Delta H^{\circ}_f=-90.5\space kJ/mol\) (rounded to three significant figures).

Question 3

Step1: Write the combustion reaction and its enthalpy change

The combustion reaction is \(C_2H_4(g)+3O_2(g)\to2CO_2(g)+2H_2O(l)\) with \(\Delta H_{comb}^{\circ}=-1411\space kJ/mol\).
The enthalpy of formation of \(CO_2(g)\) is \(\Delta H_f^{\circ}(CO_2(g))=-393.5\space kJ/mol\) and \(\Delta H_f^{\circ}(H_2O(l))=-285.8\space kJ/mol\), and \(\Delta H_f^{\circ}(O_2(g)) = 0\space kJ/mol\).
Using the formula \(\Delta H_{comb}^{\circ}=\sum n\Delta H_f^{\circ}(products)-\sum m\Delta H_f^{\circ}(reactants)\)

$$
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Answer:

Question 1

C. \(N_2(g)\)

Question 2

\(-90.5\)

Question 3

\(52.4\)