Problem 18
The standard enthalpy change of combustion of heptane, \(\left.\mathrm{C}_{7} \mathrm{H}_{16}, \text { at } 298 \mathrm{K}, \text { is }-4817 \mathrm{kJmol}^{-1} \text {. (Section } 1.6\right)\) (a) Write a thermochemical equation for the complete combustion of heptane to carbon dioxide and water. (b) What is the enthalpy change when \(50 \mathrm{g}\) of heptane are bumed? (c) What mass of heptane would be needed to provide \(100 \mathrm{MJ}\) of energy?
Problem 19
(a) List the non-covalent interactions present in liquid water. Which is responsible for the strongest interactions between the molecules? (b) Explain why the value of \(\Delta_{\mathrm{vap}} H^{\mathrm{O}}\left(\mathrm{H}_{2} \mathrm{O}\right)\) is unusually high for a molecule of its size. (c) \(\ln\) a storm, \(3 \mathrm{cm}\) of rain falls on the city of Leeds, which has an area of approximately \(500 \mathrm{km}^{2}\). Estimate the energy released as heat when this quantity of water condenses from vapour to form rain. (Density of water is \(1.00 \mathrm{gcm}^{-3}\) \(\Delta_{\mathrm{vap}} H^{\mathrm{e}}\left(\mathrm{H}_{2} \mathrm{O}\right)=+40.7 \mathrm{kJmol}^{-1}\) at \(298 \mathrm{K}\) (d) The output from a large 2000 MW power station is \(2000 \mathrm{MJs}^{-1}\). How long would it take the power station to deliver the same quantity of energy as was released by the condensation of the rain in (c)? (Sections 1.7 and 1.8 )
Problem 20
Nitrogen dioxide gas is heated in a sealed container at \(700 \mathrm{K}\) until the system comes to equilibrium. The nitrogen dioxide dissociates into nitrogen monoxide and oxygen in an endothermic process (Section \(1.9)\) $$2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$ The equilibrium constant at \(700 \mathrm{K}\) is \(2.78 \times 10^{-2} \mathrm{moldm}^{-3}\) (a) Write an expression for \(K_{c}\) (b) State how the position of equilibrium would be affected by: (1) an increase in temperature (ii) an increase in the total pressure. (c) At equilibrium at \(700 \mathrm{K}\), the concentration of nitrogen monoxide was found to be \(0.017 \mathrm{moldm}^{-3}\). What was the concentration of nitrogen dioxide in the equilibrium mixture?
Problem 21
One stage in the manufacture of methanol from methane involves the conversion of synthesis gas (a mixture of \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) to methanol. The conversion is carried out over a catalyst at a temperature of around \(500 \mathrm{K}\) and a pressure of 100 atm. (Section \(1.9)\) $$\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g}) \Delta H=-90.7 \mathrm{kJmol}^{-1}$$ (a) Write an expression for \(K_{p}\) for the reaction. (b) At \(500 \mathrm{K}\) and 100 atm pressure, an equilibrium mixture contains \(42 \% \mathrm{CH}_{3} \mathrm{OH}\) and \(48 \% \mathrm{CO}\). Calculate a value for \(K_{p}\) at this temperature. (c) Use Le Chatelier's principle to predict what would happen to the percentage of methanol in the mixture if: (i) the temperature increases; (ii) the pressure increases; (iii) hydrogen is added at constant temperature and pressure.
