2AA0 Sample Exam Solution (1).pdf

2AA0 Sample Exam Solution (1).pdf - Sample Exam Solution...

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CHEN 2AA0 – Progress Assessment I Dr. Mario Richard Eden Department of Chemical Engineering Auburn University Sample Exam Solution
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Problem 1 Evaluate the following definite integral, 1 𝑥 2 1 𝑥 3 −1 −3 𝑑𝑥 = 1 ( 1) + 1 2 1 2 1 ( 3) + 1 2 3 2 1 𝑥 2 1 𝑥 3 −1 −3 𝑑𝑥 = 1 𝑥 + 1 2 𝑥 2 −3 −1 = 1 + 1 2 1 3 + 1 18 = 18 18 + 9 18 6 18 + 1 18 = 27 18 7 18 = 20 18 = 10 9
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Problem 2 What is the empirical formula of the compound containing 72.36 wt% Fe and the rest oxygen? Oxygen Content of Compound: MW Fe = 55.85 MW O = 16.00 Basis: 100 g 72.36 g Fe 27.64 g O 100 – 72.36 = 27.64% = 1.296 mol Fe = 1.728 mol O 1.728 moles of O 1.296 moles of Fe = 1.333 mol O mol Fe = 4 3 mol O mol Fe Fe 3 O 4
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Problem 3 Experiment data known to follow the relationship 𝑦 2 = 𝑎𝑒 −𝑏 / 𝑥 plot as a straight line when ln (y 2 ) is plotted against 1 𝑥 on rectangular coordinates. What are the slope and the intercept? 𝑦 2 = 𝑎𝑒 −𝑏 𝑥 ln 𝑦 2 = ln 𝑎𝑒 −𝑏 𝑥 = ln 𝑎 + −𝑏 𝑥 = ln 𝑎 − 𝑏 1 𝑥
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Problem 4 At 25 ° C, an aqueous solution containing 35 wt% H 2 SO 4 has a specific gravity of 1.2563. A quantity of the 35% solution is needed that contains 195.5 kg of H 2 SO 4 . Calculate the required volume (in L) of the solution. V = 195.5 kg H 2 SO 4 1 kg solution L =444.6 L 0.35 kg H 2 SO 4 1.2563 kg
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Problem 5 A 5-foot tall girl is walking at night toward a 20-foot tall lamppost at the rate of 6 feet per second. How fast is the tip of her shadow (cast by the lamp) moving? Solve for the change in distance over time: 𝑑𝑦 𝑑𝑑 3 𝑑𝑦 𝑑𝑑 = 4 𝑑𝑥 𝑑𝑑 𝐴𝐴 𝐷𝐷 = 𝑦 𝑦 − 𝑥 20 5 = 𝑦 𝑦 − 𝑥 4 = 𝑦 𝑦 − 𝑥 4𝑦 − 4𝑥 = 𝑦 3𝑦 = 4𝑥 𝑑𝑦 𝑑𝑑 = 4 3 𝑑𝑥 𝑑𝑑 = 4 3 6 𝑓𝑑 𝑠 = 8 𝑓𝑑 / 𝑠 Thus the speed of the shadow is: 𝑑𝑦 𝑑𝑑 = 8 𝑓𝑑 / 𝑠
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Problem 6 What is the minimum value of the function 𝑓 𝑥 = 𝑥 3 + 2 𝑥 2 + 𝑥 − 1 on the interval [-1,1]? Hint: Differentiate the function.
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