Question

why did my prof chose to right the stoichiometry of the combustion reaction for propane like this:

1/20 C3H8(g) + 1/4 O2(g) --> 3/20 CO2(g) + 1/5 H2O(l)

why did he write it in fractions, and its not because O2 is a diatomic.

he told does we have to get used to writing equations in fraction.

Answer 1

1 C₃H_8(g)           +          5 O_2(g)   ------>    3 CO_2(g) +          4 H₂O_(l)             - simple balanced equation

Where the stoichiometry coefficients represent the number of moles of the respective reactants and product.

Multiplying or dividing both side of the equation with same number does not affect the equation. For example, diving the coefficients (representing number of moles) of all components of the reaction yields-

            (1/20) C₃H₈       +          (5/20) O₂           ------>    (3/20) CO₂        +          (4/20) H₂O

= (1/20) C₃H_8(g) +          (1/4) O_2(g)                ------>   (3/20) CO_2(g)      +          (1/5) H₂O_(l)

One purpose for writing the coefficients in fraction may be the ease of calculating the amount of all other components relative to one reactant, or determination of limiting reagents or reagent in excess.   

For example, calculate the amount of CO2 and H2O formed when 1/20 moles of C3H8 is combusted in presence of excess of air. So, the relative number of the product is calculated with respect to 1/20 moles of C3H8 and their mass can be calculated by multiplying moles with respective molecular mass.