Question

A cylinder of compressed gas rolls off a boat and falls to the bottom of a lake. Eventually it rusts and the gas bubbles to the surface. A chemist collects a sample of the gas with the idea of trying to identify the gas. The wet gas collected occupies a volume of 285 mL at a pressure of 726 torr and temperature of 28.0oC. The vapor pressure of water at 28.0oC is 0.0372 atm.
1. Calculate the volume (L) that the gas occupies after it is dried (the water vapor removed) and stored at STP.

The mass of the dry gas is 214 mg. A fragment of the tank indicates that the gas is a monoatomic element.

2. Write out the full name of the gas.

Answer 1

Answer:

The volume that the gas occupies at STP is 237mL.

Gas is neon.

Explanation:

Using general gas law, the volume that the gas occupies after is dried at STP (273,15K; 1atm) is:

P1V1/T1 = P2V2/T2

The pressure of the wet gas is:

726torr×$\frac{1atm}{760torr}$ = 0,955atm

As vapor pressure of water is 0,0372atm, the pressure of the wet gas is:

0,955atm-0,0372atm = 0,9178atm.

Replacing:

0,9178atm×285mL/301,15K = 1atm×V2/273,15K

V2 = 237mL

To solve this problem it is necessary to obtain the moles of gas using gas law and, knowing the mass of the dry gas, it is possible to obtain the atomic mass of the element to know which one is.

Gas law is:

PV = nRT

n = PV/RT

Where P is pressure. The pressure of the wet gas is:

726torr×$\frac{1atm}{760torr}$ = 0,955atm

As vapor pressure of water is 0,0372atm, the pressure of the wet gas is:

0,955atm-0,0372atm = 0,9178atm.

V is volume: 0,285L.

R is gas constant: 0,082atmL/molK

And T is temperature (28°C + 273,15 = 301,15K)

Replacing:

n = 0,0106moles

As mass of dry tank is 214mg=0,214g. The atomic mass of the gas is:

0,214g/0,0106mol = 20,189 g/mol

Thus, gas is neon, because atomic mass of Ne is 20,18g/mol

I hope it helps!