Question

How many moles of gas must be forced into a 3.5 L ball to give it a gauge pressure of 8.8 psi at 22 ∘C? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.5 psi so that the total pressure in the ball is 23.3 psi .

Answer 1

Answer : The number of moles of gas forced into a 3.5 L ball must be 2.28 moles.

Explanation :

Using ideal gas equation:

$PV=nRT$

where,

P = pressure of gas = 23.3 psi = 1.58 atm

conversion used : (1 atm = 14.7 psi)

V = volume of gas = 3.5 L

T = temperature of gas = $22^oC=273+22=295K$

n = number of moles of gas = ?

R = gas constant = 0.0821 L.atm/mole.K

Now put all the given values in the ideal gas equation, we get:

$(15.8atm)\times (3.5L)=n\times (0.0821L.atmK^{-1}mol^{-1})\times (295K)$

$n=2.28mole$

Therefore, the number of moles of gas forced into a 3.5 L ball must be 2.28 moles.