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 at 200 atm and 150 degree C using ideal gas law equation:

PV = nRT

V = = 1500 L

P = 200 atm

T = 150 + 273 = 423 K

R =

Let's plug in the values in the equation:

n = 8638.5 mol

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

So, moles of acetylene = = 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 = = 7.63 = 8

So, 8 cylinders are needed.