2.7 Practice Problems

1. Calculate the kinetic energy of an oxygen atom moving at a speed of \(\pu{100 m s−1}\). Hint: convert mass of an \(\ce{O}\) atom from \(\pu{amu}\) to \(\pu{g}\).

2. Calculate \(\Delta_{rxn}H^\circ\) for the following reactions using thermodynamic data:

\[\begin{split}\begin{align*} \ce{H2 + F2 &-> 2 HF\\ 2 NO2 &-> N2O4 } \end{align*}\end{split}\]

3. How is the system defined in this chemical reaction? Where does the energy go?

4. According to a Clif Bar nutrition label, it contains \(\pu{240 Cal}\) of energy. How much is this energy in \(\pu{J}\)?

5. What would be good examples of open, closed, and isolated systems in nature?

6. Of mass and concentration, which property is conserved in a system?

7. Is a mixture of different gases a single phase?

8. What component defines a pure \(\ce{H2O}\) system?

9. What component(s) defines an aqueous system composed of \(\ce{CO2}\) and \(\ce{CaCO3}\)?

10. How many properties are required to define a system of \(\pu{1 L}\) pure \(\ce{H2O}\)?

11. If \(\Delta_{rxn}H^\circ = \pu{2803 kJ mol-1}\) for photosynthesis reaction shown in the reaction below. Calculate the solar energy required to produce \(\pu{75 g}\) of \(\ce{C6H12O6}\).

\[\ce{6 H2O(l) + 6 CO2(g) ->[Sunlight] C6H12O6(s) + 6 O2(g)}\]

12. If \(\Delta_{rxn}H^\circ = \pu{-72.4 kJ mol-1}\) for the reaction shown below. Calculate the heat released when \(\pu{1 kg}\) of \(\ce{Br2}\) is consumed in this reaction.

\[\ce{H2(g) + Br2(l) -> 2 HBr(g)}\]

13. If \(\Delta_{rxn}H^\circ = \pu{333.8 kJ mol-1}\) for the thermochemical equation shown below, calculate the mass of copper produced when \(\pu{1.47e4 kJ}\) is consumed in this reaction.

\[\ce{2 Cu2O -> 4 Cu + O2}\]

14. Determine the enthalpy change for each reaction using the reaction data provided in the table below each reaction:

\[\ce{NO(g) + O(g) -> NO2(g)}\]

Reaction	\(\Delta_{rxn}H^\circ\), \(\pu{kJ mol-1}\)
\(\ce{NO(g) + O3(g) -> NO2(g) + O2 (g)}\)	\(-198.9\)
\(\ce{O3(g) -> 3/2 O2 (g)}\)	\(-142.3\)
\(\ce{O2(g) -> 2 O (g)}\)	\(-571.6\)

\[\ce{ 3 H2 + O3 -> 3 H2O }\]

Reaction	\(\Delta_{rxn}H^\circ\), \(\pu{kJ mol-1}\)
\(\ce{2 H2 (g) + O2(g) -> 2H2O (g)}\)	\(-483.6\)
\(\ce{3 O2(g) -> 2 O3 (g)}\)	\(284.6\)

\[ \ce{ P4O6 + 2 O2 -> P4O10} \]

Reaction	\(\Delta_{rxn}H^\circ\), \(\pu{kJ mol-1}\)
\(\ce{P4 (s) + 3 O2(g) -> P4O6 (s)}\)	\(-1640.1\)
\(\ce{P4(s) + 5O2(g) -> P4O10(s) }\)	\(-2940.1\)

15. Calculate \(\Delta_{rxn}S^\circ\)of the following reactions at \(\pu{25 ^\circ C}\):

\[\begin{split} \begin{align*} \ce{ N2 + 3 H2 &-> 2 NH3\\ H2 + Cl2 &-> 2 HCl\\ H2 + CuO &-> Cu + H2O\\ 2 Al + 3 ZnO &-> Al2O3 + 3 Zn\\ CH4 + 2 O2 &-> CO2 + 2 H2O } \end{align*} \end{split}\]

16. Determine the sign of \(\Delta_{sys}S\) for the following systems using the rules outlined in the section on the qualitative prediction entropy of substances:

    1. Freezing ethanol

    2. Evaporating water

    3. Heating water

    4. Condensing bromine vapor

17. Calculate \(\Delta_{rxn}G^\circ\) for the following reactions at \(\pu{25 ^\circ C}\):

\[\begin{split} \begin{align*} \ce{ 2 MgO &-> 2 Mg + O2\\ H2 + Br2 &-> 2 HBr\\ 2 C2H6 + 7 O2 &-> 4 CO2 + 6 H2O } \end{align*} \end{split}\]

18. Determine the \(T\) at which the following reactions reach equilibrium:

\[\begin{split} \begin{align*} \ce{ 2 MgO &-> 2 Mg + O2\\ H2 + Br2 &-> 2 HBr\\ 2 C2H6 + 7 O2 &-> 4 CO2 + 6 H2O } \end{align*} \end{split}\]