Chemistry question

Question

A  sample of an unknown gas at  and  is stored in a  flask.

What is the density of the gas? (g/L)

What is the molar mass of the gas? (g/mol)

Answer 1

Ideal Gas Law: PV = nRT

Use this to solve for moles (n)

n = PV/RT = (1.05 atm)(2.15 L)/(0.0821 Latm/Kmol)(320K)

n = 0.0859 moles

What is the density of the gas? (g/L): density is mass/volume. We are given both the mass and the volume, so density = 1.75 g/2.15 L = 0.814 g/L

What is the molar mass of the gas? (g/mol): grams = 1.75 g and moles = 0.0859

Molar mass = 1.75 g/0.0859 moles = 20.4 g/mole

Answer 2

Hi.

The first thing we need to do here, as is usually the case when we have a quantity of a substance measured in grams, is to convert to moles. Once we do that, we can then figure out the molar mass of the substance and then determine the density of the gas.

We will start with the ideal gas law.

PV = nRT

Since we need to find the number of moles, we'll rearrange the variables:

n = PV/RT

We also need to convert our temperature units from degrees Celsius to Kelvins.

K = °C + 273.15

K = 47 + 273.15 = 320.15

So now let's solve for n:

n = (1.05 atm) (2.15 L) / (0.08206 L-atm-K^-1-mol^-1) (320.15 K) = 2.2575 / 26.271509 = 0.086 mol

Now we can figure out the molar mass:

1.75 g / 0.086 mol = 20.35 g/mol

Finally, we can solve for the density:

Density = Molar Mass x P/RT = 20.35 x [1.05 atm / (0.08206 L-atm-K^-1-mol^-1) (320.15 K)] = 20.35 x 1.05 / 26.271509 = 20.35 x 0.03996725121 = 0.813 g/L