Question

How many moles of gas must be forced into a 4.6 l tire to give it a gauge pressure of 31.2 psi at 26 âc? the gauge pressure is relative to atmospheric pressure. assume that atmospheric pressure is 14.8 psi so that the total pressure in the tire is 46.0 psi?

Answer 1

Use the Ideal Gas Law to the air in the tire : 

( P ) ( V ) = ( n ) ( R ) ( T ) 
n = ( P ) ( V ) / ( R ) ( T ) 
P = P gauge + P baro = 31.2 psig + 14.8 psia = 46 psia 
P = ( 46 psia ) ( 1 atm / 14.696 psia ) = 3.13 atm 
n = ( P ) ( V ) / ( R ) ( T ) 
n = ( 3.13 atm ) ( 4.6 L ) / ( 0.08206 atm - L / mol - K ) ( 26.0 + 273.2 K ) 
n = 0.5864 moles 
m = ( n ) ( M ) 
m = ( 0.5864 mol ) ( 28.96 g/ mol ) = 16.98 g