Question

A 30.0-liter cylinder of gas containing 97.0 mole % CO and 3.0% CO₂ is delivered to your plant. You sign the receipt for it, noting that the gauge on the tank reads 2000 psi. Several days later you notice that the gauge reads 1875 psi, indicating a leak. The storage room in which the cylinder is kept has a volume of 24.2 m³ and is very poorly ventilated. Calculate the maximum mole% of CO in the room at the time the leak is discovered, assuming that the leaking gas spreads uniformly throughout the room and the room temperature is constant at 30^oC. Use Kay’s rule if appropriate.

Hint: You will need to use Kay’s rule/assumption. Compressibility factors work great for this problem.

Answer 1

Given: Volume of the cylinder, V=30 L

Initial pressure reading in gauge, P₁= 2000 psi

Final pressure reading in gauge, P₂= 1875 psi

Mole fraction of CO and CO₂ respectively, y₁=97 mol%=0.97 and y₂ = 3 mol%=0.03

Volume of the room, V_room= 24.2 m³

Temperature, T= 30⁰C= 303.15 K

For CO, the critical temperature and pressure, respectively are T_c1 =133 K and P_c1 = 34.54 atm

For CO₂, the critical temperature and pressure, respectively are T_c2 =304.2 K and P_c2 = 72.93 atm

According to Kay's Rule, the pseudocritical constants are obtained using the expression

where T_c^' and P_c^' are Pseudocritical Constants

y₁ and y₂ is Mole Fraction of CO and CO₂ respectively

T_c1 and P_c1 are Critical Properties of CO

T_c2 and P_c2 are Critical Properties of CO₂

Reduced temperature and pressure at initial conditions are

Reduced conditions at final condition is

As the temperature remains constant, reduced temperature at final condition will remain the same.

From the General Compressibility Chart, obtain the compressibility factor.

Compressibility factor at T_r =2.2 and P_r =3.8 is z₁=0.97

Compressibility factor at T_r =2.2 and P_r=3.6, z₂=0.97

Total moles leaked is

where P₁ and P₂ is Initial and Final Pressure respectively

z₁ and z₂ is the Compressibility Factor at initial and final conditions respectively

V is the Volume

R is Universal Gas Constant, R=0.08206 L atm/mol K

T is the Temperature

(Conversion: 1 atm=14.69 psi)

Moles of CO leaked is n_CO=y₁(n₁-n₂)

n_CO=0.97*10.6 mol

n_CO= 10.28 mol CO

Total Number of Moles in the room, n_total is

where n_total is the Total number of moles present in the room

V_room is the Volume of the room

T is the Temperature

T_s, V_s and n_s is the Temperature, Volume and Number of moles of gas at standard conditions, respectively

(Conversion: 1m³ = 1000 L)

Thus the maximum mole% of CO in the room, at the time the leak is discovered, is

Therefore, the maximum mole% of CO in the room is 1.05%