IFAP - Properties & Calculations With Gases (Lesson)
Properties & Calculations With Gases
Combined Gas Law
When the physical laws from the last lesson are considered all together - the relationship between one set of variables and another can be established in what is referred to as the Combined Gas Law.
Since this is a single sample of gas, the number of moles is a constant. The pressure, volume, and temperature conditions in one set of circumstances are related to the values of those three variables for that constant amount in all other circumstances.
Since pressure and volume are inversely related, as established by Boyle's Law, and volume and temperature are directly related, as established by Charles' Law, these three variables can be used to find a missing variable under different pressures, volumes, or temperatures.
All temperatures must be in the absolute Kelvin scale and the units used for pressure and volume will be the units of the secondary pressure and volume. The formulas for converting temperatures are shown below.
Temperature is related to the average kinetic energy of a chemical. While kinetic energy and temperature are not exactly the same thing, they can be used to make interpretations about each other. For example, if a substance has a higher temperature than another, you also know that the particles have a higher average kinetic energy. Notice that there is no degree sign when using the Kelvin scale. Since on the Kelvin scale, zero is not arbitrarily defined, the temperatures on the Kelvin scale are not divided into degrees. Temperatures on this scale are reported in units of "Kelvin," not in "degrees Kelvin."
In the United States, we measure temperature in Fahrenheit, while most other countries use Celsius. Most scientific calculations require that temperature be measured in Celsius. However, when doing calculations involving gases, temperature must be expressed in Kelvin.
Pressure can be measured in several different units as illustrated below. The Pascal (Pa) is the SI unit for pressure, but kPa is often used. Different industries have histories of using different units of pressure; therefore, all of these are used at different times. As you go through the module, you will see that some equations will require you to use specific units of pressure. For this reason, you will need to be able to convert between any of these units. The values shown in the list below represent average atmospheric pressure at sea level. Converting between these units can be done easily using simple dimensional analysis.
| UNITS OF PRESSURE |
|---|
| 1 atm = 101.3 kPa |
| 1 atm = 760 Torr |
| 1 atm = 760 mmHg |
| 1 atm = 14.7 lb/in2 |
Volume
You know that volume is the amount of space something takes up. Gases are unique in that they take up the volume of whatever container they are placed in. Whatever size container they are in, they will spread out to consume the entire container. This happens because the intermolecular attractions (discussed in the previous module) as so weak that they are virtually zero. With no attractions between the gas molecules, they spread out as much as possible.
Standard Temperature and Pressure (STP) and Molar Volume
Avogadro's Law states that the volume occupied by a certain number of moles of any gas must be identical for all gases under the same conditions of pressure and temperature. Because constant conditions of pressure and temperature are used so frequently, scientists agreed to establish a standard set of conditions. The standard conditions of temperature and pressure, or STP, are 1 atm and 273.15 K (0°C).
The volumes of numerous gases have been measured at STP. For 1 mole of any gas, the volume of that gas at STP is 22.4 L and is known as molar volume.
You Try It!
Ideal Gas Law
Did you notice that in the combined gas law examples that the amount of gas was not included? This is because it was held constant. So, how would we determine that amount of gas? Or, what would happen if the amount of gas were not held constant? We need another equation that puts all of this together, the ideal gas law.
From all the previous gas laws, we know that the product of pressure and volume is proportional to the product of temperature and amount in moles.
To change that proportionality to an equality, units need to be defined and a constant (multiplier) introduced to make the mathematical products of equal value. That constant is known as the Universal Gas Constant, R.
For example:
Gas Density and Molar Mass
Finding the molar mass of a gas sample can be used to identify the gas, along with density. Some rearranging of the ideal gas law permits these types of calculations.
For example:
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