NAME CEE 330 Spring 2014 Exam 1 Write legibly if you want to receive all deserving points Closed book closed notes no cheat sheets nothing from class or book stored on calculators List of relevant formulas and equations is given Question 1 Question 2 Question 3 Question 4 Question 5 20 20 20 30 10 Problem 1 20 pts Approximate estimate of CO2 emissions due to driving Assume you consume 500 gallons of gasoline per year in your car and that gasoline can be represented entirely by C8H18 Gasoline has a density of 0 85 g cm3 Combustion of C8H18 leads to CO2 and H2O a Write and balance the combustion reaction 5 points b How many kg of CO2 does your driving contribute to the atmosphere every year 10 points c How many ppbv CO2 are added to the atmosphere 5 points d There is a claim that 1 billion vehicles now cruise the planet If they all are similar consumers as you how much CO2 they add to the atmosphere overall per year 5 points Approximate number of moles of air in the atmosphere 1 8 x 1020 moles 1 gallon 3 78 L C 12 H 1 O 16 Solution a C8H18 25 2 O2 8CO2 9H2O b Convert 500 gallons to L 500 gallons yr 3 78 L gallon 1890 L yr Total mass of gasoline 1894 L yr x 0 85 g cm3 x 1000 cm3 L 1 6 x 106 g yr Convert this mass to mole 1 6 x 107 g yr 12x8 18 14122 moles yr According to the chemical reaction number of moles of CO2 produced is 8x14122 moles yr 1 13 x 105 moles yr Mass of CO2 emitted 1 13 x 105 moles yr x 44 x 0 001 kg g 4 970 kg yr c Ratio of moles of CO2 added over the total number of mole 1 13 x 105 moles yr 1 8 x 1020 moles 6 26x 10 16 Convert to ppbv 6 28x 10 15x 109 6 26x 10 7 ppbv yr d If we have 109 cars then emission 626 ppbv yr 1 Question 2 20 points Chemical 4 methylcyclohexane methanol used to clean coal was spilled into a river in West Virginia in Jan 2014 The discharge was estimated as 1 105 m3 day for 5 days The river flow rate is 9 105 m3 day This chemical is decaying with first order kinetics with a rate constant of 0 10 day The concentration of the chemical in the spill flow is 1000 mg L The concentration of the pollutant in the incoming river is 0 mg L a What would the chemical concentration be in the river water after it received the waste Assume steady state You can also assume that the chemical is mixed instantaneously throughout the width of the river right after it was added to the river b Unfortunately the river is the source of drinking water for 300 000 people Now we need to consider the chemical traveling with the river which can be modelled as a plug flow reactor without mixing along the length of the river The river is flowing at a velocity of 10 km day Calculate the concentration of the chemical in the river water 20 km downstream from the spill where the intake for the local water treatment is located Solution a Mass balance calculation to determine C in the river after mixing with the waste correct mass balance 4 points CaftermixQaftermix CupstreamQupstream CinQin Caftermix C upstreamQupstream CinQin Qaftermix Caftermix Qupstream 0 Qin 9 105 1 105 106 m3 s 0mg L 9 105 m3 s 1000mg L 1 105 m3 s Cdownstream 100mg L 106 m3 s Correct mass balance equation 4 points correct answer 1 point b The travel time for 20 km is t 20 km 10km day 2 days dC 0 0 VkC first order kinetics reaction dt C dC kC t 2 days exp kt dt C0 V Ct 2 days C0 exp kt 100mg L exp 0 1 2 82mg L Correct equation for concentration 7 points Correct answer 3 points 2 Question 3 20 points 20 of the energy produced from a nuclear power plant is converted to 1000 MW of electrical energy The remaining 80 of the energy from this plant is converted to heat waste 20 of the heat waste is released out of the smoke stack 80 of the heat waste is taken away by cooling water that is drawn from a nearby river Specific heat of water 4 184 kJ kg C a How much of the heat waste is taken away by the cooling water MW b How fast does the cooling water need to be pumped to remove this heat from part a so that the temperature of the cooling water only increases by 10 C The density of water is 1000kg m3 Solution a the total energy produced by the plant 1000 MW 0 2 5000 MW of fuel energy Energy loss 5000 1000 4000 MW 5 points Energy goes to cooling water 4000 0 8 3200 MW 5 points b The rate of change in internal energy for the cooling water m C T m is the mass flow rate of cooling water E in E out 3200MW E in m c T E in 3200MW m 76 48 103 kg s c T 4184 J kg C 10 C 1MW 106 J s Mass flow rate m can be converted to flow rate 5 points for correct m 2 points if correct equation is used m kg s 76 48 103 kg s Q 76 48m3 s kg m3 1000kg m3 5 points for correct Q 2 points if correct equation is used 3 Question 4 30 points Pristine rainwater falls through cracks into a limestone CaCO3 aquifer In the aquifer the water is isolated from the atmosphere Set up an analysis to determine the pH of the rainwater in the bowl a Write the list of species 5 points b Write the equilibrium relationship between these species and express the concentration of each species in terms of the equilibrium constants H and concentration of CO2aq 10 points c Write the electroneutrality equation 5 points d Write the mass balance equation 5 points e Use the results from part a b c and d to find 2 equations with 2 unknowns that could be used to solve for the concentration of each species and pH You do not have to solve these equations for species concentrations or pH 5 points Solution a List species present in the aqueous phase Ca2 H HCO3 CO32 OH CO2aq b Because water is on contact with limestone then we need to consider the solubility for CaCO3 solid CaCO3 Ca 2 CO32 Ca 2 CO32 K sp 4 57 10 9 K sp Ca 2 CO32 CO32 will react with H2O HCO3 H CO32 H CO32 H CO32 K 2 HCO3 K2 HCO3 H HCO3 CO2 aq H 2O H HCO3 K1 CO2 aq HCO3 CO32 K1 CO2 aq H CO2 aq K1K 2 H 4 2 H CO32 K2 K …