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Explanation:

Given parameters:

Mass of the sample = 0.622g

Volume of the gas = 2.4L

Temperature = 287K

Pressure of the gas = 0.85atm

Unknown

Molar mass of the gas = ?

Solution

To find the molar mass of the gas, we first assume that the gas in question is an ideal gas i.e. it obeys Boyle's and Charles's law.

On this premise, we can find the unknown which is the molar mass of the gas.

We first use the ideal gas equation to find the number of moles of the gas since all the parameters apart from the number of moles are given:

   Solving for number of moles:

   The ideal gas equation is given as PV = nRT

  We make the unknown "n" the subject of the equation

                           n =

     R is the gas constant whose value is 0.082atmdm³mol⁻¹K⁻¹

                n =  

                n = = 0.087mole

Now, we know the number of moles of the gas. We can proceed to find the molar mass from the given mass and the number of moles calculated using the equation below:

                       molar mass =  

                    molar mass =   =7.15gmol⁻¹

Part 2:

If the sample was placed under a low temperature, we want to consider what would happen to the volume:

Since we assume that the gas is an ideal gas, we can explain what will happen to the gas using Charles's law. The law states that "The volume of a fixed mass of a gas varies directly as its absolute temperature if the pressure is constant".

  If we assume the pressure is constant for this gas, the volume of the gas would decrease as the temperature becomes lower. We would get lower values for both actual volume and predicted volume.