2 PCH241P MAYIJUNE 2017 Question 1 A compressed gas cylinder contains 1000 g of

Question

2 PCH241P MAYIJUNE 2017 Question 1 A compressed gas cylinder contains 1000 g of argon gas is 140 atm at a temperature of 18 °c How much gas (in grams) remains in the cylinder if the pressure is decreased to 45 atm at 18°C, by opening and then closing the cylinder? (a) The pressure inside the cylinder HINT Note that the volume of the cylinder and the temperature remain constant (7) A flask of 7 0 L contains a mixture of 6 g of 02 and 15 g of N2 at 30°? Use this information to answer questions -l below (0) What is the mole fraction of the oxygen gas? () What is the partial pressure of the oxygen gas? (u) What is the total pressure in the flask? (b) (10) (c) Denve the following expression (from the ideal gas equaton) for the density (c) of a gas PM RT where M is the molar mass, Pis the pressure and T, the temperature of the gas 1201

Explanation / Answer

Ans 1

Part a

Moles of Ar gas = mass/molecular weight

= 1000g / 39.948g/mol

= 25.0325 mol

Pressure P = 140 atm

Temperature T = 18 + 273 = 291 K

From the ideal gas equation

Volume = nRT/P

= 25.0325 mol x 0.0821 L-atm/mol-K x 291 K / 140 atn

= 4.2718 L

New pressure P2 = 45 atm

Moles of gas = P2V/RT

= (45 atm x 4.2718 L) / (0.0821 L-atm/mol-K x 291 K)

= 8.046 mol

Mass remains in cylinder = moles x molecular weight

= 8.046 mol x 39.948g/mol

= 321.43 g

Part b

Moles of O2 = mass/molecular weight

= 6g / 32g/mol

= 0.1875 mol

Moles of N2 = mass/molecular weight

= 15g / 28g/mol

= 0.5357 mol

Total Moles = 0.5357 + 0.1875 = 0.7232 mol

Mol fraction of O2 = moles of O2 / total moles

= 0.1875/0.7232 = 0.26

Mol fraction of N2 = 1 - 0.26 = 0.74

Partial pressure of O2 = moles of O2 x RT/V

= 0.1875 mol x 0.0821 L-atm/mol-K x (30+273)K / 7L

= 0.666 atm

Partial pressure of N2 = moles of N2 x RT/V

= 0.5357 mol x 0.0821 L-atm/mol-K x (30+273)K / 7L

= 1.904 atm

Total pressure = 0.666 + 1.904 = 2.570 atm

Part c

From the ideal gas equation

PV = nRT

PV = (mass/M) RT

PM = (mass/V) RT

PM = dRT

Density d = PM/RT

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