Question

Gas cylinders, each containing 30 kg of a mixture of 75 mol% acetylene (c2h2) and balance n2 are available. how many cylinders are needed to produce 1.5 m3 of the gas mixture at 200 atm (abs) and 150°c?

Answer 1

Answer:- 8 cylinders are needed to produce the required amount of the gas.

Solution: First we calculate the moles of the gas for it's volume $1.5m^3$ at 200 atm and 150 degree C using ideal gas law equation:

PV = nRT

$n=\frac{PV}{RT}$

V = $1.5m^3$ = 1500 L

P = 200 atm

T = 150 + 273 = 423 K

R = $0.0821\frac{atm.L}{mol.K}$

Let's plug in the values in the equation:

$n=\frac{200*1500}{0.0821*423}$

n = 8638.5 mol

Acetylene and nitrogen are 75 mol% and 25 mol% respectively in the cylinder.

So, moles of acetylene = $\frac{8638.5*75}{100}$ = 6478.9 moles

moles of nitrogen = 8638.5 - 6478.9 = 2159.6 moles

mass of acetylene = 6478.9*26 = 168451.4 g

mass of nitrogen = 2159.6*28 = 60468.8 g

Total mass of mixture = 168451.4 g + 60468.8 g = 228920.2 g = 228.92 kg

number of cylinders = $\frac{228.92}{30}$ = 7.63 = 8

So, 8 cylinders are needed.