Let's try the oxidation number rules on some examples:

- H
_{2}O_{2}: Rule 1 & 6*exception*(H cannot be more + than +1) H = +1, O = -1 - KO
_{2}: Rule 1, 3 & 5*exception 1*K = +1, O = -1/2 - OH
^{-}: Rule 1 & 5 -2 + H = -1, H = +1 - (-2) = -1 - MgH
_{2}: Rule 1 & 3 +2 + 2H = 0, 2H = -2, H = -1 - C
_{2}H_{3}O_{2}^{-}: Rule 1 & 5 & 6 2C + 3(+1) + 2(-2) = -1, 2C = -1 - (+3) - (-4) = 0, C = 0 - MnO
_{2}: Rule 1 & 5 Mn + 2(-2) = 0, Mn = - (-4) = +4

Finally, note that in writing formulae, the element with the more positive oxidation number comes first. There are, of course, a few exceptions, the most well known being ammonia: NH_{3} (by the rules it should be H_{3}N).

**Gases:** Briefly discussed overall properties of gases (fills container, compressible, lo density, lo viscosity).

- Gas particles exert pressure.
- implication - gas particles have momentum (mass and velocity).

**What is Pressure?** Pressure is the force/unit area. Due to collisions of particle with walls of container etc.

Units of Pressure:

- mmHg - based on manometers. Two types:

- open tube - measures pressure relative to current atmospheric pressure.
- closed tube - measures pressure relative to contents of the enclosed volume at the closed end. (A barometer is an example where the enclosed space is "empty", that is it contains a vacuum since the vapor pressure of mercury is very low.)

- atm = 760 mmHg at 1 gravity = 1.01 Bar
- others include: psi (pounds/square inch), pascal, Torr (= 1 mmHg), millibar, etc.

## Gas Laws

Gas Laws describe the relationships between the four properties characterizing any gas:

- Amount of substance,
*n*(in moles) - Volume, V (in Liters)
- Pressure, P (in atm, though often measured in mmHg)
- Temperature (in K)

Boyle's Law describes the relationship between pressure and volume *when the temperature and amount of substance are held constant.*

Plotting pressure volume data (keeping n and T constant) gives a graph for a hyperbola (xy = c), as seen below:

*public domain image courtesy of Wikipedia commons*

Notice that we can rearrange this equation to give a straight-line relationship:

Thus, "At constant temperature the volume of any quantity of gas is inversely proportional to its pressure." V = k (1/P) & P_{1}V_{1} = P_{2}V_{2}.

(Aside on straight-line plots: Very popular in science. Traditionally, we will do almost anything to get a straight line. Why? Because straight lines easy to recognize and evaluate. Also easy to evaluate statistically.)

The relationship between volume and temperature was determined much later because accurate thermometers had to be developed first. But once thermometers were available a number of workers determined that volume is directly proportional to temperature. Plotting data for the relation of volume of a gas to temperature between 0° C and 100 ° C gives a plot similar to that below:

*public domain image courtesy of Wikipedia commons*

Extrapolating this data to V = 0 we can find an absolute minimum value of temperature on the assumption that negative volumes can't exist:

The intercept on the volume axis is then taken as absolute zero = -273.15 °C = 0 K for an ideal or "perfect" gas with particles of zero volume and no interactions other than collisions.

Algebraically we then find that V = k'T, & V_{1}/T_{1} = V_{2}/T_{2}.

We can combine Boyle's and Charles' relationships (T was part of the constant for Boyle's Law and P is part of the constant for Charles' Law) to give:

V = an, where n = moles of stuff. So we have a linear relation between volume and moles; and V_{1}/n_{1} = V_{2}/n_{2}.

**Ideal Gas Law ("Perfect Gas Law"): **The constant for the combined law includes amount of stuff, and breaking that out we then get

where R = the gas constant with units appropriate to the various measurements. We will use atm, L, K, and moles, so that

I will base all of my examples on this equation because that requires a minimum of memorization. However you may find it easier to memorize a series of equations such as the "combined gas law equation" etc.

As an example, let's find the density of sulfur hexafluoride at a temperature of 25 °C and a pressure of 767 mmHg. The first thing we should do is determine what we want to know, mainly the mass of gas in a one Liter sample.

To do this we need to find 1) moles/L and 2) grams/mole. So let's write out the Ideal Gas Law:

Syllabus / Schedule |

*© R A Paselk*

*Last modified 20 February 2013*