Question

A birthday candle is 2.5 inches long and 0.75 cm in diameter. It’s made of paraffin wax, which is a mixture of various hydrocarbons, but for the sake of argument we’ll assume it’s all C31H64, since that’s the major component. Its density is 0.90 g/cm3 paraffin. If air is 20.95% O2 by volume, and the density of O2 is 1.43 g/L, then how many liters of air will the candle consume if it completely burns up? (Note that paraffin combines with oxygen to make carbon dioxide and water.)

Answer 1

As the birthday candle is cylindrical in shape its volume is = where pi= 3.14, r= radius = diameter/2 h= height

Now r= 0.75/2 = 0.375 cm, h= (30*2.5)/12 = 6.25 cm ( 30 cm= 12 inch)

So the volume of the candle

The density of the major compound of the paraffin wax is C₃₁H₆₄ = 0.90 gcm^-3

so the mass of the candle= (volume* density)=(0.9*2.76)= 2.84 g

The molar mass of C₃₁H₆₄ = (12*31+ 1*64) = 436g/mol

So the candle is made of (2.84/436) = 0.0065 moles of C₃₁H₆₄

Now the combustion reaction is -

C₃₁H₆₄ + 47O₂ = 31CO₂ + 32H₂O

So to combust 1 mole of C₃₁H_64, 47 moles of oxygen is needed.

To combust 0.0065 moles of C₃₁H₆₄,oxygen is needed = (47*0.0065) = 0.31 moles

1 mole of O₂ = 32g

0.31 of O₂ = (0.31*32) = 9.92 g

Now the volume of 9.92 g O₂ =(Mass/density of oxygen) = (9.92/1.43) = 6.94 L

As the oxygen is 20.95% by volume of the total air, when the candle completely burns up it will consume = (6.94*100)/20.95 = 33.12 L of air.

So, If the candle completely burns up it will consume 33.12 L of air.