Question

A 2. 75-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?.

Answer 1

The number of moles of gas lost is  0.0213 mol. It can be solved with the help of Ideal gas law.

What is Ideal law ?

According to this law, "the volume of a given amount of gas is directly proportional to the number on moles of gas, directly proportional to the temperature and inversely proportional to the pressure. i.e.

PV = nRT.

Where,

• p = pressure
• V = volume (1.75 L = 1.75 x 10⁻³ m³)
• T =  absolute temperature
• n = number of moles
• R =  gas constant, 8.314 J*(mol-K)

Therefore, the number of moles is

n = PV / RT

State 1 :

• T₁ = (25⁰ C = 25+273 = 298 K)
• p₁ = 225 kPa = 225 x 10³ N/m²

State 2 :

• T₂ = 10 C = 283 K
• p₂ = 185 kPa = 185 x 10³ N/m²

The loss in moles of gas from state 1 to state 2 is

Δn = V/R (P₁/T₁ - P₂/T₂ )

V/R = (1.75 x 10⁻³ m³)/(8.314 (N-m)/(mol-K) = 2.1049 x 10⁻⁴ (mol-m²-K)/N

p₁/T₁ = (225 x 10³)/298 = 755.0336 N/(m²-K)

p₂/T₂ = (185 x 10³)/283 = 653.7102 N/(m²-K)

Therefore,

Δn = (2.1049 x 10⁻⁴ (mol-m²-K)/N)*(755.0336 - 653.7102 N/(m²-K))

    = 0.0213 mol

Hence, The number of moles of gas lost is 0.0213 mol.

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