To begin, gases differ greatly from liquids and gases in that they expand to fill containers, are highly compressible, and have extremely low density. Temperature, pressure, volume, and number of moles are four of the most important aspects of gases that I had to learn. Temperature is the measure of the average kinetic energy of a sample of molecules. When dealing with gas laws, all calculations must be done in Kelvin (K). Pressure is the amount of force applied to an area by a sample. The common units of pressure are atmospheres (atm) and mmHg (a.k.a. torr). The number of moles is the number of molecules present (obviously) and the volume is the amount of space taken up. There are several basic gas laws that establish relationships between these variables, which are as follows:
Boyle's Law
Boyle's Law states that at fixed temperature, volume is inversely proportional to temperature. It is modeled by this equation:
P1V1 = P2V2
Charles' Law
Charles' Law states that at a fixed pressure, volume is directly proportional to temperature. It is modeled by the following equation:
V1/T1 = V2/T2
Gay-Lussac's Law
Gay-Lussac's Law states that at a fixed volume, pressure is directly proportional to volume. It is modeled by the following equation:
P1/T1 = P2/P2
Combined Gas Law
Boyle's Law, Charles' Law, and Gay-Lussac's Law can be combined to form the combined gas law:
P1V1/T1 = P2V2/T2
Avagadro's Law
Avagadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas. It is modeled by the following equation:
V1/n1 = V2/n2
I first modeled these gas laws using the Java applet and the spreadsheet activity. Using the applet, I was able to produce data that proved the direct relationship between volume and temperature, pressure and temperature, the number of moles and volume, as well as the inverse relationship between pressure and volume. Additionally, the Ideal Gasses Parts I & 2 lectures covered this material. This subject matter was not hard conceptually. However, I sometimes have trouble matching the correct name with the correct law.
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| A slight mishap with the Java applet. |
Combining the laws listed above produces perhaps the most important equation of the unit: the ideal gas law. The ideal gas law is as follows:
PV = nRT
This law states that pressure multiplied by volume is equivalent to the number of moles of gas multiplied by the gas constant multiplied by temperature. R, also known as the constant of proportionality, is equivalent to 0.08206 L-atm/mol-K (or 8.134 J/mol-K or 62.36 L-torr/mol-K). There are several variations on the ideal gas law which which allow for the calculation of density and molar mass. They are as follows:
PV = (m/M)RT
Pressure multiplied by volume is equivalent to the mass of the sample divided by the molar mass of the substance of the gas multiplied by the gas constant multiplied by temperature.
d = PM/RT
Density is equivalent to pressure multiplied by molar mass divided by the gas constant multiplied by temperature.
To help learn this concept, I completed several worksheets in class, including the Gases I and Gases II worksheets. The ideal has law was also featured in the Ideal Gasses lectures. Although this equation seems fairly straightforward, when I was asked to find pressure or temperature when given the mass of a sample in grams or given the density, I often had no idea what to do. To prepare myself for the upcoming test, I will find it necessary to familiarize myself with the variations on the ideal gas law.
The ideal gas law ties in closely with Kinetic Molecular Theory (KMT). When a variable like pressure or temperature is being calculated using the ideal gas law, several assumptions are being made. These assumptions are the main ideas behind KMT. In KMT, it is assumed that gases consist of large numbers of molecules that are in continuous, random motion. It is assumed that the the volume of the molecules of gas is negligible. It is also assumed that attractive and repulsive forces between gas molecules is negligible. Kinetic energy is assumed to be conserved when gas molecules collide. It is also assumed that as long as the temperature of the gas remains constant, the average kinetic energy of the molecules remains constant. When the tenants of KMT are fully considered, a gas is considered to be "ideal." Under standard temperature and pressure (1.000 atm and 0˚C) one mole of an "ideal" gas has a volume of 22.4 L.
However, in real life, many aspects ignored in KMT such as intermolecular forces have an effect on the pressure and volume of a gas. Although the ideal gas equation is good for predicting pressure, temperature, volume, etc. at high temperatures and low pressures, these predictions break down at low temperatures and high pressures. This is because the intermolecular forces and volume have a substantial effect on the variables in the ideal gas equation. The ideal has equation fails to account for intermolecular forces. Pressure is calculated by measuring how hard gas particles hit the side of the wall in which they are being housed. Intermolecular forces between gas molecules pull gas molecules towards each other and away from the wall of the chamber. Thus, the pressure is lowered. Since the ideal gas equation fails to account for these intermolecular forces, the pressure values calculated using PV = nRT are often higher than the actual pressure under non ideal conditions. The ideal gas equation works poorly at low temperatures because at low temperatures molecules move slowly and thus have ample time to interact with one another. This exacerbates the effect of the intermolecular forces as the intermolecular forces now have more time to effect molecules, thus pulling gas molecules towards each other and away from the container wall. Furthermore, the ideal gas equation fails to account for the volume of the molecules. When the pressure is low and there are few molecules and/or there is a large volume, the volume of the gas particles is relatively negligible when compared to the volume of the container. However, when the pressure is high and there is a large number of molecules, the volume of the particles is significant when compared to the total volume of the container. Thus, in situations when pressure is high and the ideal gas law fails to take account for the volume of the molecules, the calculated volume is usually lower than the actual volume. In non ideal conditions, one can use a modified version of the ideal gas equation, the van der Waals equation. The van der Waals equation is as follows:
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| The van der Waals equation. |
The (n^2 x a)/(V^2) portion of the equation adjusts the pressure upwards to what it should be if it acted ideally. The V – nb portion of the equation adjusts the volume downwards to what it would be if it was ideal. The concept of real gases and KMT was covered in the lecture on these subjects as well as in the concept tests that we covered in class. I found it a little hard to comprehend how the volume affects the ideal gas equation under non ideal conditions. This website helped bring some clarity to the topic.
Additionally, this week I learned the concept of partial pressures and mole fractions. They are fairly straightforward concepts. If there is mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. Partial pressures are governed by Dalton's Law of partial pressures, which is as follows:
Ptotal = P1 + P2 + P3 + …
A mole fraction is the relative or percent composition by moles of a single component in a mixture, represented in its decimal. The mole fraction (Xa) is equivalent to the moles of one component in a mixture divided by the sum of all components in the mixture. When one has a mixture of gases and known mole fractions, one can multiply the mole fraction by the total pressure to calculate the partial pressure of one gas. This concept was covered in the partial pressures and mole fractions lecture as well as in the Gases II worksheet. I found this subject easy to understand.
Finally, I also learned the concept of effusion and diffusion this week. Effusion is the escape of gas molecules through a tiny hole into an evacuated space. The lighter the molecule, the faster it effuses. Effusion rates are governed by Grahm's Law of Effusion, which is as follows:
V1/V2 = (M2/M1)^0.5
Diffusion is the spread of one substance throughout a space or throughout a second substance. It follows the same relationship as Grahm's Law.
All in all, I feel relatively good about these topics and the upcoming test. As always, I could just use a bit more practice on the topics. To study for the test on Wednesday, I will do over the Gases I and II worksheets. I felt as though I was comprehending the Taskchains well, with the exception of the forth one. If given the opportunity, I will cover that quiz again.
