|Lecture Notes: 27 October||
Gases: Briefly discussed overall properties of gases (fill container, have mass & volume, compressible, lo density, lo viscosity, etc.). Also noted:
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.)
- others include psi (pounds/square inch), pascals, Torr, etc.
Boyle's describes the relationship between pressure and volume when the temperature and amount of substance are held constant.
Or, "At constant temperature the volume of any quantity of gas is inversely proportional to its pressure." V = k (1/P), or PV = k, & P1V1 = P2V2.
Plotting pressure volume data (keeping n and T constant) gives a graph for a hyperbola (xy = c), as seen below:
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) & P1V1 = P2V2.
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:
If we extrapolate the plot to zero volume, V = 0, we can find an absolute minimum value of temperature on the assumption that negative volumes can't exist. Looking at the plot we can find a value for the lowest temperature possible, or absolute zero = 0 K:
The intercept on the volume axis is 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.
We can combine these relationships (T was part of the constant for Boyle's Law and P is part of the constant for Charles' Law) to give"
But of course the constant now includes amount of stuff. I f we keep P and T constant we can find the relationship between V and moles:
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 ("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" on pg 356 of your text etc.
As an example, let's find the molar volume of a gas under standard conditions of temperature and pressure (STP). STP are defined as: P = 1 atm and T = 0° C. Thus we need to solve the gas equation for 1 mole of gas at 273.15 K (= 0°C+ 273.15) and 1 atm:
Let's look at some sample problems.
Example: We can find the MW of a gas given its density. Thus a 1.000 L sample of gas weighed 1.25 g at a temperature of 0.0 °C and a pressure of 1.000 atm. What is the MW of this gas?
© R A Paselk
Last modified 28 October 2009