Finding molar mass

Question

An unknown gas was analyzed, and the following data was obtained

Mass of the gas sample 1.211 g Volume of the gas 677 mL Temperature 23oC Pressure 750.12 Torr Determine the molar mass of the unknown gas. What is a possible identity of this gas?

Answer 1

Since molar mass is defined as grams/moles, all we need to do is find the moles since we are given the grams.

From the ideal gas law PV = nRT we can solve for n (moles)

n = PV/RT

P = 750.12 torr x 1 atm / 760 torr = 0.987 atm (converted torr to atm)

V = 677 mls x 1 L / 1000 ml = 0.677 L (converted mls to liters)

R = 0.0821 Latm/Kmol

T = 23ºC + 273 = 296K (converted C to K)

n = (0.987)(0.677) / (0.0821)(296)

n = 0.0275 moles

molar mass = g/mol = 1.211 g / 0.0275 moles

molar mass = 44.0 g / mole

Possible identity of the gas might be carbon dioxide (CO₂), but there could be many gases that have a similar molar mass. CO₂ would be the most common.

Answer 2

Hey Stephen! Since we are dealing with a gas in this problem, let us use the trusted Ideal Gas Equation:

PV= nRT

where P is the pressure of the gas in atm, V is the volume of the gas in L, n is the number of mols of the gas and T is the temperature in K. R is the universal gas constant (0.08206 L-atm / mol-K)

The ideal gas equation can be manipulated in a variety of ways. In this instance, we want an equation with a variable of Molecular Weight (let’s call that “MW”). We know from the definition of the molecular weight that:

MW = m/n, where m is the mass of the substance in grams divided by the mols of that substance. We can then rearrange this to solve for n:

n= m/MW, which we can plug back into the ideal gas equation:

PV = (m/MW)RT, and solve for MW:

MW = mRT/PV, which has all the variables we are given in the question (mass, pressure, volume, temp and R is always a given)

The last step is to make sure all of the given quantities are in the proper units as stated above. Remember these conversion factors:

K = °C + 273.15, 1 atm = 760 torr, and 1000 mL = 1 L.

Once you convert everything, just plug all the numbers into the manipulated ideal gas equation for MW and you should be good! Consult your periodic table for the identification of the gas. Hope this helps!