Question

A student is seen at the Madise om at the Madison Bear Garden with her hand and their environmental engineering textbook in the other. When the professor suddenly walks in the student pours table and starts reading the to e professor suddenly walks in the student nours the beer down the floor drain underneath the is reading the textbook. If the nint of her (500 mlis 5% ethanol (CH.CH,OH) by volume, determine the theoretical oxygen demand. Thod of the her that went into the sewer. The density of ethano Beer that went into the sewer The density of ethanol is 789 mg/mL. Anotlie DO

Answer 1

Theoretical Oxygen Demand is the amount of Oxygen needed to fully oxidise the compound. The compound here is ethanol which is oxidised according to following reaction. Rest of the beer is water which is already fully oxidised.

$C_2H_5OH+3O_2\rightarrow 2CO_2+3H_2O$

Step 1: Calculate Mass of ethanol

Volume of solution = 500 mL

Ethanol is 5% by volume.

Volume of ethanol in the solution = 5% of 500 mL = 5*500/100 mL = 25 mL

Density of ethanol = 789 mg/mL

Mass of ethanol = Volume * Density = 25 mL * 789 mg/mL= 19725 mg = 19.725 g

Step 2: Calculate moles of ethanol

Molar Mass of Ethanol= 46.07 g/mol

Moles of ethanol = Mass/ Molar mass = (19.725 g)/(46.07 g/mol)= 0.428 mol

Step 3: Calculate moles of Oxygen needed

The reaction is

$C_2H_5OH+3O_2\rightarrow 2CO_2+3H_2O$

thus, Ethanol and Oxygen reacts in the ratio 1:3.

Thus, Oxygen needed for 0.428 mol ethanol = 3 * 0.428 mol = 1.284 mol

Step 4: Calculate mass of oxygen needed

Molar Mass of Oxtgen = 32.00 g/mol

Mass of Oxygen needed = Moles of Oxygen * Molar Mass = 1.284 mol * 32.00 g/mol = 41.10 g

Final Answer: ThOD of the beer is 41.10 g