Question

Guinness is one of the most popular beers in the world with almost 2 billion pints sold around the world every year (1 million a day in Great Britain alone) and 95 megaliters sold in the US. Guinness is usually consumed by the imperial pint and draft Guinness is 4.2% ethanol by volume. If the ethanol in 2.24 imperial pint of Guinness is burned in a sealed bottle containing 78.4 grams of oxygen, how many molecules of each of the products will be formed?

(Useful information? ethanol = C₂H₅OH, density of ethanol = 0.789 g/cm3, 1 gal. = 4 qts., 1 imperial pint = 19.215 fl. oz., 1 pint of Guinness has few calories than 1 pint of skim milk)

Answer 1

the question really inspired to try out Guinness once, considering it has fewer calories than slim milk :P ... just kidding

So, firstly we write down the combustion reaction that is occurring here

When ethanol is burned in presence of air , following reaction occurs

C₂H₅OH + 3O₂ --------> 2CO₂ + 3H2O

At ideal conditions

1mol C₂H₅OH reacts with 3 mol O2 ------> to give 2 mol CO2 and 3 mol H2O

46 g  C₂H₅OH reacts with 96 g O2 ------> to give 88 g CO2 and 54 g H2O.........................(1)

So for ease of calculation, i will convert all units in grams

we have 2.24 imperial pint of beer

= 2.24 X 19.215 X 29.5735 cm3 of beer ( 1 imperial pint = 19.215 fl. oz & 1 fl. oz = 29.5735 cm3)

= 1272.89 cm3 of beer

ethanol % = 4.2 %

hence, ethanol = 1272.89 X .042 = 53.46 cm3

As Mass = density X Vol

Mass of ethanol = 42.18 g

Now From (1)

46 g  C₂H₅OH reacts with 96 g O2 ------> to give 88 g CO2 and 54 g H2O.........................(1)

42.18 C₂H₅OH reacts with 88.03 g O2

but only 78.4 grams of O2 is present, which makes it a limiting reactant

Hence, 78.4 g O2 will react with ------> (46/96)X 78.4 = 37.57 g of C₂H₅OH

CO2 formed

= (88/96)X 78.4

= 71.9 g = 1.63 molecules of CO2

H2O formed

= (54/96)X 78.4

= 44.1 g = 2.45 molecules of H2O