Question

2.50 Liters of CO2 gas (ideal) at 25^{\circ }C and 1.o atm of pressure is allowed to expand in volume until the final pressure and temperature are 0.50 atm and 15^{\circ }C , respectively:

a) Calculate the final volume of the gas.

b) Calculate the # of moles, n, of the gas.

c) Calculate the # of grams of the gas.

Answer 1

Initially   P1 = 1 atm , V1 = 2.5 L ,   T1 = 25C = 25+273 = 298 K

final P2 = 0.5 atm , T2 = 15C = 15+273 = 288 K

we find   moles of gas using PV = nRT    equation using initial conditions

where R = gas constant = 0.08206 liter atm/molK

b) 1 atm x 2.5 liter = n x 0.08206 liter atm/molK x 298 K

n = 0.10223

a) now using moles we calculate final volume since P , T , V changed but not moles as gas is not added or removed.

0.5 atm x V = 0.10223 mol x 0.08206 liter atm/molK x 288 K

V = 4.83 L

c) CO2 moles = 0.10223

CO2 mass = Moles x molar mass of CO2               ( molar mass of CO2 = 44 g/mol)

hence mass = 0.10223 x 44 g/mol

           = 4.5 g