Calculate the density in grams per liter of an equi-molar mixture of CH4 and C2H6 at 100 degrees celicius and 700mmHg pressure.

Gasses obey the Ideal Gas Law.  The Ideal Gas Law
is

PV = nRT

In general the
volume that gas will occupy is proportional to the number of moles present.  In the
stated problem, there is not a specific number of moles given.  However, this is not
critical as we are asked to find the density of the gas at a specific set of
conditions.  The density at a given temperature and pressure will be constant regardless
of the number of moles present because the volume occupied is directly proportional to
the number of moles.  Thus doubling the moles (doubling the mass of the gas) will double
the volume.  Density being the ratio of mass to volume will remain the
same.

We are free to choose any number of moles we wish as
long as the methane (CH4) and ethane (C2H6) are equi-molar.  Equi-molar simply means
there must be the same number of moles of methane as there are moles of ethane.  Being
free to choose allows us to select one mole of
each.

Applying this and the other conditions of the problem
allows us to calculate the volume of the gas

P = 700 mmHg =
(700/760)atm = 0.921 atm

n = 2 moles (1 mole CH4 + 1 mole
C2H6 = 2 mole of gas)

T = 100 deg C = 373.15
K

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

Solving PV = nRT for V results in V =
(nRT)/P

V = (2mol)X(0.0821 L atm/mol K)X(373.15K)/0.921
atm

V = 66.5 L

To get the
density we must know the mass of the gas.  This can be obtained by calculating the molar
mass of each of the gasses.

The 1 mole of CH4 has a mass of
12.01g + 4(1.008g) =16.042 g

The 1 mole of C2H6 has a mass
of 2(12.01g) + 6(1.008g) = 30.068 g

The total mass of the
gas is thus 16.042g + 30.068g = 46.11 g

The density is
determined from D = m/V = 46.11g/66.5L

D =
0.693 g/L.

Some attention should be given to
the number of significant digits in the problem.  There is some ambiguity in the problem
concerning the number of signficant digit in each of the stated quantities, and thus the
answer may need to be rounded to the nearest tenth of a gram/L.