An unknown amount of helium (He) gas occupies 10.5 L at 1.52 atm pressure and 335 K. What is the mass of helium gas in the container? Use R = 0.0821 L. atm/(mol. K).

The lectures in this unit cover gases. This lecture covers the Ideal Gas Law and partial pressures.

Ideal Gas Law

In our previous lecture we discovered a relationship between the pressure, volume, temperature,

and number of moles in gases. After scientists worked out the individual relationships between

pressure, volume, temperature, and the number of moles, it was clear that a single law could

bring all of these individual laws together. This unifying law is called the ideal gas law. An

ideal gas is one which follows the ideal gas law. Not all gases are perfectly ideal in this sense

but most of them are close enough to it that the law applies well.

I. Ideal Gas Law

The Ideal Gas Law unifies all these independent laws as follows:

PV = nRT

Where P = Pressure, V = Volume, T = Temperature, and n = number of moles.

The remaining value, R, is the constant which makes the rest of these factors work together

mathematically. Once the relationship between all individual factors was found it was trivial to

calculate R: it is the value of

PV

nT for any gas since they all act the same way!

There are several numerical values for R depending on which units you are using (atm or torr or

bars, L or mL, Joules (energy) etc). Our class uses this one:

R = .0821

L·atm

mole·K

The ideal gas law helps us calculate variables such as pressure, volume, temperature, or number

of moles without having to make a comparison.

For example, if 3.5 moles O2 has a volume of 27.0 L at a pressure of 1.6 atm, what is the

temperature of the sample?

Here we are given n = 3.5 moles, V = 27.0 L, P = 1.6 atm. We rearrange the ideal gas law to

solve for temperature as follows:

PV = nRT

PV

nR = T

(1.6 atm)(27.0 L)

(3.5 moles)(0.0821 L·atm/mol·K) = 150.3 K

Explanation:

2.32g

Explanation:

Given parameters:

Volume occupied by gas = 10.5L

Pressure = 1.52atm

Temperature = 335K

R = 0.0821 L.atm/(mol.K)

Unknown:

Mass of helium = ?

Solution:

To find the mass of helium in the container, use the expression below:

     Mass of helium  = number of moles x molar mass

Number of moles;

    Using the ideal gas equation;

           PV = nRT

where P is the pressure

          V is the volume

         n is the number of moles

        R is the gas constant

        T is the temperature

Insert the parameters and solve for n;

       1.52 x 10.5 = n x 0.0821 x 335

                 n  = 0.58moles

So,

        molar mass of He = 4g/mol

 Now, solve;

        Mass of helium  = 4 x 0.58 = 2.32g

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