A 2.25-L container filled with CO2 gas at 25∘C and 225 kPa pressure springs a leak. When the container is re-sealed, the pressure is 185 kPa and the temperature is 10 ∘C. How many moles of gas were lost?

0.001mol

Explanation:

First let us determine the new volume

P1 = 225kpa

V1 = 2.25L

T1 = 25°C = 25 + 273 = 298k

P2 = 185 kPa

T2 = 10°C = 10 + 273 = 283k

V2 = ?

P1V1/T1 = P2V2/T2

225x2.25/298 = 185xV2/283

298x185xV2 = 225x2.25x283

V2 = (225x2.25x283) / (298x185)

V2 = 2.6L

Now let us find the number of mole at each state

State 1:

V = 2.25L

P = 225kpa = 225000Pa we must covert this to atm

101325Pa = 1atm

225000Pa = 225000/101325 = 2.22atm

T = 25°C = 25 + 273 = 298k

R = 0.082atm. L/mol/K

n = ?

PV = nRT

n = PV/RT

n = 2.25x2.22/0.082x298

n = 0.204mol

State 2:

V = 2.6L

P = 185 kPa = 185000Pa we must covert this to atm

101325Pa = 1atm

185000Pa = 185000/101325 = 1.83atm

T = 10°C = 10 + 273 = 283k

R = 0.082atm. L/mol / k

n = ?

PV = nRT

n = PV/RT

n = 1.83x2.6/0.082x283

n = 0.205mol

Change in number of mole

= 0.205 - 0.204 = 0.001mol