9.4 STP

1  The molar volume of a gas

You will recall that the molar mass of a pure substance is the mass of 6.02 x 10²³ (Avogadro’s number) of particles or molecular units of that substance. Molar masses are commonly expressed in units of grams per mole (g mol^–1) and are often referred to as molecular weights.

As was explained in the preceding lesson, equal volumes of gases, measured at the same temperature and pressure, contain equal numbers of molecules (this is the “EVEN” principle, more formally known as Avogadro’s law.)

STP

Avogadro’s law allows us to compare the amount of any two gases by comparing their volumes. Often amounts of gas are compared at a set of standard conditins of temperature and pressure called STP.

STP conditions are: 1 atm ( 760 mm of Pr) and 273 K ( (0⁰C)

At STP, one mole of any gas has the same volume 22.4 L called the standard molar volume.

Converting Between Moles and Liters of a Gas at STP

Example:

 1mol= 22.4 L

Q: How many mols are present Moles of 5.00 L of O₂ at STP?

1mol                 = x mol

22.4 L                   5.00L        x= 0.223 mols

Figure 9.47 STP Condition and molar volume

Ref: common.wikimedia.org/

At STP all different gases occupy same volume.

Questions:

1. Burning 1mol of propane in a gas grill occupies 150. grams of CO₂. What volume of CO₂ does it occupy at STP?

Standard temperature and pressure: 273K, 1 atm

The magnitude of this volume will of course depend on the temperature and pressure, so as a means of convenient comparison it is customary to define a set of conditions T = 273K and P = 1 atm as standard temperature and pressure, usually denoted as STP. Substituting these values into the ideal gas equation of state and solving for V yields a volume of 22.414 litres for 1 mole.

Figure 9.48 Muana Kea Hawaii

Ref: commons.wikimedia.org/

Problem Example 1

Estimate the volume of one mole of air at 20°C on top of Muana Kea, Haw’aii (altitude 4.2 km) where the air pressure is typically around 60 kPa.

Solution: Apply Boyle’s and Charles’ laws as successive correction factors to the STP molar volume. (Recall that
1 atm =101.3 kPa)

The standard molar volume 22.4 L mol ^–1 is a value worth memorizing, but remember that it is valid only at STP. The molar volume at other temperatures and pressures can easily be found by simple proportion.

The molar volume of a substance can tell us something about how much space each molecule occupies, as the following example shows.

Problem Example 2

Estimate the average distance between the molecules in a gas at 1 atm pressure and 0°C.

Solution: Consider a 1-cm³ volume of the gas, which will contain

(6.02E23 mol^–1)/(22400 cm³ mol^–1) = 2.69E19 cm^–3.

The volume per molecule (not the same as the volume of a molecule, which for an ideal gas is zero!) is just the reciprocal of this, or 3.72E–20 cm³. Assume that the molecules are evenly distributed so that each occupies an imaginary box having this volume. The average distance between the centers of the molecules will be defined by the length of this box, which is the cube root of the volume per molecule:

(3.72 × 10^–20)^1/3 = 3.38 × 10^–7 cm = 3.4 nm

Pure gases or mixtures: it makes no difference

Under conditions at which the ideal gas model is applicable (that is, almost always unless you are a chemical engineer dealing with high pressures), “a molecule is a molecule”, so the volume of Avogadro’s number of molecules will be independent of the composition of the gas. The reason, of course, is that the volume of the gas is mostly empty space; the volumes of the molecules themselves are negligible.