## Oxidation Numbers

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

• H2O2: Rule 1 & 6 exception (H cannot be more + than +1) H = +1, O = -1
• KO2: Rule 1, 3 & 5 exception 1 K = +1, O = -1/2
• OH-: Rule 1 & 5 -2 + H = -1, H = +1 - (-2) = -1
• MgH2: Rule 1 & 3 +2 + 2H = 0, 2H = -2, H = -1
• C2H3O2-: Rule 1 & 5 & 6 2C + 3(+1) + 2(-2) = -1, 2C = -1 - (+3) - (-4) = 0, C = 0
• MnO2: Rule 1 & 5 Mn + 2(-2) = 0, Mn = - (-4) = +4

#### Additional practice examples are available on the Study Module

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: NH3 (by the rules it should be H3N).

# Gases

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, (in moles)
• Volume, V (in Liters)
• Pressure, P (in atm, though often measured in mmHg)
• Temperature (in K)

### Boyle's Law

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

PV = c @ constant T & n

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:

Divide both sides by V: (PV)/V = c/V

P = c (1/V)

This is now in the form of a straight line: y = ax + b, where b = 0

Thus, "At constant temperature the volume of any quantity of gas is inversely proportional to its pressure." V = k (1/P) & P1V1 = P2V2.

(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.)

### Charles' Law

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, & V1/T1 = V2/T2.

### Combined Gas Law

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:

(PV)/T = constant.

V = an, where n = moles of stuff. So we have a linear relation between volume and moles; and V1/n1 = V2/n2

# Ideal Gas Law

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

(PV)/T = nR, or PV = nRT

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

R = 0.0821 L*atm/mole*K

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:

PV = nRT

### NEXT

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