**Gases**

Molar Mass and Gas Densities

Molar Mass and Gas Densities

**Density**

- Has the units of mass per unit volume

- (n/V) has the units of
. If we know the molecular mass of the gas, we can convert this into*moles/liter*(mass/volume). The*grams/liter*(*molar mass*) is the number of grams in one mole of a substance. If we multiply both sides of the above equation by the molar mass:__M__

- The left hand side is now the number of grams per unit volume, or the mass per unit volume (which is the
)*density* - Thus, the density (
) of a gas can be determined according to the following:*d*

- Alternatively, if the density of the gas is known, the molar mass of a gas can be determined:

Example:

What is the density of carbon tetrachloride vapor at 714 torr and 125°C?

The molar mass of CCl_{4} is 12.0 + (4*35.5) = 154 g/mol. 125°C in degrees Kelvin would be (273+125) = 398K. Since we are dealing with torr, the value of the gas constant, R, would be 62.36 L torr/mol K.

Caesar's Las Breath

Of the molecules in Caesar's last gasp, how many of them are in the breath you just took?

Given:

- One breath= 2 liters of air at a pressure of 730 mmHg and 37 degrees Celsius.
- Earth is a sphere with a radius of 6370 Km and an average barometric pressure of 760mm Hg. (D of Hg=13.6g/cm
^{3}) - The avg. molecular mass of air is 29 g/mol.

1. Number of moles in Caesar’s last breathe:

n = PV/RT = (0.96 atm)(2L)/(0.0821 L atm/mol K)(310 K)

n = 0.075 mol

2. Number of moles in the atmosphere:

a. Surface area of earth:

Area = (4)(p)(r^{2})

Area = 5.10 x 10^{14} square meters

b. Pressure of the atmosphere on the earth’s surface:

Pressure = 760 mm Hg = 1.01 x 10^{5} Pascals = 1.01 x 10^{5} Newtons/square meter

Pressure = 1.01 x 10^{5} kg/m s^{2}

c. Force of the atmosphere on the earth

Pressure = Force/Area

Therefore

Force = (Pressure)(Area)

Force = (1.01 x 10^{5} kg/m s^{2})(5.10 x 10^{14} m^{2})

Force = 5.15 x 10^{19} kg m /s^{2}

d. Mass of the atmosphere

Force = (mass)(acceleration)

therefore

mass = Force/acceleration

mass = (5.15 x 10^{19} kg m/s^{2})/(9.8 m/s^{2}) note: this is the acceleration due to gravity

mass = 5.26 x 10^{18} kg or 5.26 x 10^{21} g

e. Moles in the atmosphere

mol = (5.26 x 10^{21} g)(1 mol/29 g)

mol = 1.81 x 10^{20} mol

3. Fraction of atmosphere which represents molecules from Caesar’s last breath:

(0.075 mol)/(1.81 x 10^{20} mol) = 4.14 x 10^{-22}

4. Moles of Caesar’s last breath in your last breath:

Assume your breath holds 0.075 mol:

(0.075 mol)(4.14 x 10^{-22}) = 3.11 x 10^{-23}mol

5. Number of molecules:

(6.022 x 10^{23} molecules/mol)(3.11 x 10^{-23}mol) = 18.7 molecules

(*An even more disconcerting fact is that he probably had flatulence as well.*)

*1996 Michael Blaber*