## Physical Properties of Gas and Gas Law

#### Physical Properties of Gas and Gas Law

##### Gas Properties

The state of matter distinguished from the solid and liquid states by relatively low density and viscosity, relatively great expansion and contraction with changes in pressure and temperature, the ability to diffuse readily, and the spontaneous tendency to become distributed uniformly throughout any container. Therefore gases have the following characteristic properties: they are easy to compress, they expand to fill their containers, and they occupy far more space than the liquids or solids from which they form.

Since one of the properties of a gas is compressibility, a gas at a certain volume can be compressed by adding pressure. The mass of the gas will remain unchanged. Since the mass remains the same and the volume decreases, the density of the gas is greater. This can be observed by using the density equation D=m/V. If the mass of the gas is .50 grams and the volume of the gas is one liter then the density of the gas is .50 grams/liter. However, if the gas is compressed to only take up one half a liter then the density will change to 1 gram/liter.

Many of the properties of gases can be measured in different ways. Conversion from one unit of pressure to another is very important. To achieve this there has to be a conversion factor to move from one unit to another. Here is a list of equivalent amounts of pressure:

*1 atmosphere (atm) = 14.7 PSI (pounds per square inch) = 760 mm Hg (also known as 1 Torr) = 101.325 KPa (kiloPascals)*

##### Gas Laws

**i) Boyle's Law **states the volume of a definite quantity of dry gas is inversely proportional to the pressure, provided the temperature remains constant. Mathematically Boyle's law can be expressed as P1V1 = P2V2

- V1 is the original volume
- V2 is the new volume
- P1 is original pressure
- P2 is the new pressure

Suppose you have a gas with 45.0 ml of volume and has a pressure of 760.mmHg. If the pressure is increased to 800mmHg and the temperature remains constant then according to Boyle's Law the new volume is 42.8 ml. (760mmHg)(45.0ml) = (800mmHg)(V2) . Therefore V2=42.8ml

**ii) Charles' law: **States that, at constant pressure, the volume of a given mass of gas varies directly with its absolute temperature (T):

V / T =constant. V is the volume & T is the absolute temperature (measured in Kelvin)

V1 / T1 = V2 / T2

- V1 is the initial volume
- T1 is the initial temperature
- V2 is the final volume
- T2 is the final temperature

**iii) The combined gas law** is a combination of Boyle's Law and Charles's Law; hence its name the combined gas law. In the combined gas law, the volume of gas is directly proportional to the absolute temperature and inversely proportional to the pressure.

This can be written as PV / T = constant. Since for a given amount of gas there is a constant then we can write P1V1 / T1 = P2V2 / T2.

- P1 is the initial pressure
- V1 is the initial volume
- T1 is the initial temperature (in Kelvin)
- P2 is the final pressure
- V2 is the final volume
- T2 is the final temperature (in Kelvin)

For example if you have 4.0 liters of gas at STP, and you want to know the volume of the gas at 2.0 atm of pressure and 30o C, the equation can be setup as follows:

(1.0)(4.0) / 273 = (2.0)(V2) / 303

(V2)(2)(273) = (1)(4)(303)

V2 = 2.2

Therefore the new volume is 2.2 liters.

**Clinical Application of the Gas Law**

Two methods are commonly used to express the concentration of gas or vapor is partial pressure and volume percent.

*Partial pressure:* a mixture of gases in a closed container will exert a pressure on the walls of the container. The part of the total pressure due to any one gas in the mixture is called the partial pressure of that gas. The total pressure of the mixture is the sum of the partial pressures of the constituent gases. Under the usual conditions of vaporization, the total pressure will be equal to atmospheric pressure).

*Volume percent:* The concentration of gas in a mixture can also be expressed in terms of its percentage of the total volume. The term volumes percent is defined as the number of units of volume of gas in relationship to a total of 100 units of volume for the total gas mixture. In a mixture of gases, each constituent gas exerts the same proportion of the total pressure as its volume is of the total volume. In other words, volumes percent express the relative ratio of gas molecules in a mixture, while partial pressure expresses an absolute value. E.g., At sea level (1 atm = 760mmhg) the partial pressure of oxygen is 159mmhg, the volume percent of oxygen is 20.9%

A 'full' cylinder of oxygen on an anesthetic machine contains compressed gaseous oxygen at a pressure of 137 atm. If the cylinder of oxygen empties at constant temperature, the volume of gas contained is related linearly to its pressure. In contrast, the pressure in a cylinder of nitrous oxide remains relatively constant as the cylinder empties to the point at which liquid has totally vaporized. Subsequently, there is a linear decline in pressure proportional to the volume of gas remaining within the cylinder.