Question

An ideal gas having a volume of 1.0 liters at 40c and a gauge pressure of 1.0 arm is heated until it's volume is 1.5 liters and its vague pressure is 1.2 arm. Determine A) number of moles contained in the gas and B) final temperature of gas

Answer 1

Initial volume V = 1 lit

                       = 10-3 m 3

Gauge pressure = 1 atm

Absolute pressure P = Po + gauge pressure

Where Po= Atmospheric pressure = 1 atm

So, P = 1 atm + 1 atm= 2 atm

   = 2 x1.01 x10 ⁵ Pa

Initial temprature T = 40 ^o C = 40 + 273 = 313 K      

From ideal gas equation PV=nRT

Number of moles n = PV /RT

Where R = Gas constant = 8.314 J / mol K

Substitute values you get n = (2 x1.01 x10 ⁵) (10 ^-3 ) /(8.314)(313)

                                          = 0.0776 mol

(B). Final temprature T ' ="

Final pressure P ' = Po+ gauge pressure

                           = 1 atm + 1.2 atm

                           = 2.2 atm

Final volume V ' = 1.5 lit

From ideal gas equation PV=nRT

   PV/T = constant

P'V'/T' = PV/T

   T ' = P'V'T / PV

   =(2.2 atm)(1.5 lit) (313) /(2 atm)(1 lit)

           = 516.45 K

           = 516.45-273

            = 243.45 ^o C