Q1 (a) Calorimetry results for a typical beer (3.5 % alcohol by volume, or 2.8% alcohol by mass) show a fuel value (energy content) of 1.1 kJ g-1.
i) Use the data given to calculate enthalpy of combustion of ethanol, C2H5OH(l).
ii) Hence, calculate the fuel value of the ethanol, in kJ per gram of beer.
iii) What accounts for the remaining energy content of the beer?
Concentration in beer
1.2 % by mass
0.3 % by mass
-278 2.8% by mass
(b) The manufacturers of a new engine want to know how efficient it is. They think that the petrol used to run the engine can be approximated well by octane and have asked you to tell them how much energy is available from burning octane, according to the following equation:
C8H18(l) + 12.5O2(g) → 8CO2(g) + 9H2O(l)
(i) Use the equation and the data given to calculate values of ΔrHo298 and ΔrUo298 for this reaction.
(ii) Comment on the relative magnitudes of the values you obtain.
Substance ΔfHo298 /kJ mol-1
Octane C8H18(l) −249.9
Carbon dioxide CO2(g) −393.5
Water H2O(l) −285.8
Next, the chief scientist points out that the chemical equation as written does not exactly mimic the operating conditions of the engine. The exhaust gases are hot and contain water in the vapour phase; octane is also in the vapour phase (boiling point 399K).
(iii) Estimate ΔrHo for the reaction at 1000 K. The enthalpy of vaporisation of water, ΔvapHo, is +40.7 kJ mol-1 and the enthalpy of vaporisation of octane, ΔvapHo, is +41.5 kJ mol-1.
Substance Cp, m /J K-1 mol-1
Octane C8H18(l) 187.8
Oxygen O2(g) 29.4
Carbon dioxide CO2(g) 37.1
Water H2O(l) 75.3
(a) Choose the substance with the greater molar entropy in each of the following pairs, and give a brief reason for each answer:
(i) O2 (g) (0.5 atm, 298 K); O2 (g) (1.0 atm, 298 K)
(ii) butan-1-ol C4H9OH (l) (298K); diethyl ether C4H10O (l) (298K)
(b) 4 moles of an ideal gas are compressed isothermally and reversibly from
150 dm3 to 75 dm3 at 298 K.
(i) Calculate the entropy change of the system.
(ii) What is the entropy change of the surroundings?
(iii) What is the entropy change of the system if the process is carried out irreversibly?
(c) Use the following data to estimate the normal boiling point (in K) of bromine.
Br2(l) : Sm0 = 152.2 J mol-1 K-1.
Br2(g) : Sm0 = 245.4 J mol-1 K-1; ΔfH0 = 30.91 kJ mol-1.
(d) 1 mole of liquid water is frozen at a temperature of −5 oC. The molar heat capacity of liquid water is 75.3 J K−1 mol−1 and the molar heat capacity of ice is 37.6 J K−1 mol−1. The molar enthalpy of fusion of ice is 6.01 kJ mol−1 at 273K.
(i) Calculate the entropy change for the freezing process at −5 oC. Hint:
split the process into
H2O(l) (-5 oC) → H2O(l) (0 oC) → H2O(s) (0 oC) → H2O(s) (-5 oC)
(ii) Calculate the entropy change of the surroundings. Hint: First calculate the enthalpy of fusion of ice at –5 oC. (5 marks)
(iii) Deduce whether the process is spontaneous.