The original pressure (in atm) of argon in the cylinder is 8.062atm
Volume of neon = 4.40L
Volume of argon = 13L
total volume = 17.4L
partial pressure of neon = 4.40l * 4.22atm/17.4L = 1.1552 atm [ partial pressure = original pressure X (volume of the gas/total volume)]
total pressure = 7.01
partial pressure of argon = 5.8548 atm
original pressure of argon = 5.8548*17.9/13 = 8.062atm
Each gas that makes up a mixture of gases has a partial pressure, which is the notional pressure of that gas as if it alone filled the original combination's complete volume at the same temperature.
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