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2.15 g of an unknown gas at 71 degrees C and 1.10 atm is stored in a 1.75 L flask. Solve for the density and the molar mass of the gas.

Verified Answer :

Explanation:

The given data is as follows.

         mass = 2.15 g,          T = \(71^{o}C\) = (71 + 273) K = 344 K

          P = 1.10 atm,             V = 1.75 L

Now, according to the ideal gas equation PV = nRT

and,        n = \(\frac{mass}{\text{molar mass}}\)  

Hence, calculate the molar mass of unknown gas as follows.

                      PV = \(\frac{mass}{\text{molar mass}} \times RT\)

             \(1.10 atm \times 1.75 = \frac{2.15 g}{\text{molar mass}} \times 0.0821 \times 344 K\)

                     Molar mass = \(\frac{60.721}{1.925}\) g

                                         = 31.54 g

As, density is the amount of mass present in liter of volume.

Mathematically,          Density = \(\frac{mass}{volume}\)

                                                 = \(\frac{2.15 g}{1.75 L}\)

                                                  = 1.22 g/L

Thus, we can conclude that mass of unknown gas is 31.54 g and its density is 1.22 g/L.

ardni313

Density :  0.01229 g/ml

Molar mass  : 31.525 g/mol

Further explanation

Some of the laws regarding gas, can apply to ideal gas (volume expansion does not occur when the gas is heated),:

  • Boyle's law at constant T, P = 1 / V
  • Charles's law, at constant P, V = T
  • Avogadro's law, at constant P and T, V = n

So that the three laws can be combined into a single gas equation, the ideal gas equation

In general, the gas equation can be written

\(\large {\boxed {\bold {PV = nRT}}}\)

where

P = pressure, atm

V = volume, liter

n = number of moles

R = gas constant = 0.08206 L.atm / mol K

T = temperature, Kelvin

Density is a quantity derived from the mass and volume

density is the ratio of mass per unit volume

The unit of density can be expressed in g / cm3 or kg / m3

Density formula:

\(\large {\boxed {\bold {\rho ~ = ~ \frac {m} {V}}}}\)

ρ = density

m = mass

v = volume


2.15 g of an unknown gas at 71 degrees C and 1.10 atm is stored in a 1.75 L flask.

so density = mass : volume

\(\rm density=\rho=\dfrac{21.5}{1750}=\boxed{0.01229\dfrac{g}{ml}}\)

To find the molar mass, we first look for the number of moles with the ideal gas equation:

PV = nRT

T = 71 °C + 273 = 344 K

\(\rm n=\dfrac{PV}{RT}\\\ =\dfrac{1.10\times 1.75}{0.08206\times 344}\\\ =\boxed{0.0682}\)

\(\rm molar\:mass=\dfrac{mass}{mol}\\\\molar~mass=\frac{2.15}{0.0682}\\\\molar\:mass=\boxed{\bold{31.525\:\dfrac{g}{mol} }}\)


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