(a) Define the standard enthalpy of combustion of a substance and state the standard conditions. (3 marks) (b) Given the following standard enthalpies of combustion: carbon (graphite) $-394$ kJ mol$^{-1}$, hydrogen $-286$ kJ mol$^{-1}$, methane $-890$ kJ mol$^{-1}$. Use Hess's law to calculate the standard enthalpy of formation of methane, C(s) + 2H$_2$(g) → CH$_4$(g). (6 marks) (c) When 0.5 g of ethanol (C$_2$H$_5$OH, molar mass 46 g mol$^{-1}$) was burnt, the heat produced raised the temperature of 100 g of water from 20 °C to 45 °C. Calculate the enthalpy of combustion of ethanol from these data. (Specific heat capacity of water $= 4.2$ J g$^{-1}$ K$^{-1}$.) (6 marks)