Elaine Teto
Chem101-6
Due: 7/5/04
In chapter six of the textbook, the topic, states of matter and the kinetic theory are covered. In this chapter one will find such concept headings as the gaseous state; the pressure-volume-temperature relationships for fixed amounts of gas; the Ideal Gas Law; Dalton’s Law of Partial Pressure; the kinetic theory of gases; the liquid states; vapor pressure, dynamic equilibria and changes in state; water and the hydrogen bond; and the solid state. Although this seems like an overabundance of concepts, they do in fact; play in an intricate role in tying into one another. To begin embarking on this information one shall first familiarize oneself with some basic terminology and formulas.
Firstly, there are three primary states of matter, the solid state, the liquid state, and the gaseous state. The gaseous state obviously pertains to matter in a gas form. A gas has no fixed volume or shape, but takes both the shape and volume of its container. In addition, a gas is highly compressible, especially in comparison to the other two states of matter. The particular state that a system takes depends to a large degree on the intermolecular forces (which bind the individual particles into its bulk form.) However, there are also additional physical parameters that define the state of matter. Temperature, pressure, and volume, in addition to the actual amount of particles present (moles) are major contributing factors. In breaking down each individual parameter we will also cover many laws and formulas, such as The Ideal Gas Law, Dalton’s Law of Partial Pressure, and the Pressure-Volume-Temperature relationship for a fixed amount of gases.
Temperature is an indicator of the average kinetic energy that a sample of matter (gases in this case) possesses. Temperature can be recorded in three different forms, Fahrenheit, Celsius, and Kelvin. It is accustom to predominantly use the Fahrenheit scale in the United States, however, as with most areas of science, the scale used, differs from that of day-to-day life. Therefore, for all intensive purposes one may as well familiarize with the Kelvin scale and the way in which to convert from one scale to another.
The conversion between Celsius (oC) and Fahrenheit (oF) temperature scales is:
When dealing with the parameter of temperature, in this chapter, one will always use the Kelvin scale, because it is measured from the Absolute Zero of temperature. Absolute Zero is the point at which all internal motion of matter ceases. With no internal motion, matter has no kinetic energy and thus no temperature. On the Celsius scale, this temperature is -273.15 oC. The Kelvin scale (K) is therefore defined from Celsius (oC) according to:
The next parameter is pressure. Pressure, unlike temperature, has a formula in and of itself, before its relevance to this concept is even discussed.
Pressure = force/area
The SI unit of pressure is the Pascal (Pa). Since force is measured in Newtons:
The pressure applied by the entire column of air above a point at sea level (at 25oC) is by definition one atmosphere (atm) of pressure.
1 atm = 760 Torr
The third parameter of gas is the actual number of gas particles. This is measured in moles (n.)
N = mass/molar mass
The final parameter of gas is the volume. Volume is measured in liters. Some helpful conversions, when dealing with volume are as follows:
1L = 1000Ml = 1000 cm3
Now that one has become familiarized with the four parameters of gases, there are a few laws, pertaining to gases that are also imperative to know, before moving forward in this chapter. Firstly, the Ideal Gas Law, which relates the pressure, temperature, and volume of an ideal gas, was derived from Charles’ Law (V1/T1=V2/T2=K2) and Boyle’s Law (P1V1=P2V2=K1). The equation of the Ideal Gas Law is as follows:
PV=nRT
P represents the pressure, V represents the volume, n is the number of moles present, R is the universal gas constant (whose formula will be given below), and finally, T represents the temperature.
The universal gas constant (R) formula is;
PV=NkT
In the preceding formula, N is the number of atom of gas present and k is Boltzmann’s constant, which is related to the universal gas constant by;
R=NAk
Where NA is Avogadro’s number. Furthermore, the original Ideal Gas Law equation can be written in terms of mass density and molar mass, providing the equation:
Although numerous equations have been addressed, the execution of the Ideal Gas Law is rather uncomplicated. An example of such an equation is:
If 333mL of an ideal gas at a temperature of 25 degrees Celsius and a pressure of 750 torr has its temperature lowered to -11 degrees Celsius and its pressure lowered to 730mmHg what will its new volume be in milliliters?
VF= (nR) TF/PF This formula will give us the final volume (Which is what was asked for); however, there are some other unknowns we must solve for, before we can use this formula!
N=VIPI/TIR This formula will solve for the amount of gas (moles) which is also unknown. After arranging the formulas, one would end up with:
VF=PITF/PFTI(VI)
The given information is:
Pi= 750 torr
TI= 25 degrees Celsius (25+273) 298K
VI= 333Ml
TF= -11 degrees Celsius (-11+273) 262K
PF= 730mmHg (torr=mmHg)
Solution: (750 Torr) (262 K)/ (730 Torr) (298 K) x (333mL)
301mL
The next law, Dalton’s Law of Partial Pressure, explains that the total pressure of a mixture of gases equals the sum of the pressure that each would exert if it were present alone. The previous explanation can be summarized very simply, through the formula:
PT= P1+P2+P3+…
Furthermore, one can relate the amount of a given gas in a mixture to its partial pressure. This can be achieved through the formula:
P1/PT= (n1RT/V) / (nTRT/V) which summarizes to;
P1/PT = n1/nt which is equal to;
X1 (The mole fraction of a gas)
After rearranging the formula above, the final equation one can derive is as follows:
P1 = X1PT
An example of the Dalton’s Law of Partial Pressure is as follows:
A sample of hydrogen gas is collected over water at 14.0 oC. The pressure of the resultant mixture is 113.0 kPa. What is the pressure that is exerted by the dry hydrogen alone?
Pdry gas = Ptotal - Pwater vapor
Look up the vapor pressure of water at 14.0 oC à1.6 kPa
The knowns are:
Ptotal = 113.0 kPa
Pwater vapor = 1.6 kPa
Pdry gas = 113.0 kPa - 1.6 kP
Pdry gas = 111.4 kPa
Continuing through Chapter 6, one will come across a section titled Kinetic Theory of Gases. This topic is exceptionally interesting because it actually explains some of the phenomenon that one may encounter in day-to-day life. Because of the obvious differences between a gas and a solid (such as the size of the molecules and its correlation to the actual size of the sample), when we do math problems, dealing with ideal gases, we treat the particles as point masses (particles with mass but no volume). In real gases, there will be an attraction between the particles involved. These attractions are often minor and we ignore them when we do math problems involving gases. It is important to remember the differences between real gases and ideal gases.
Pressure, also plays a huge role in the Kinetic Theory of Gases. One should already be familiar with the definition of pressure, being a force over an area. However, this force can be measured in quit a few different ways. For example, pressure can be measured in kilopascals (kPa), millimeters of mercury (mmHg), or atmospheres (atm). Due to the variety of measurements one should be able to convert from one unit to another, in order to ensure proper execution of equations one may encounter. Therefore, the following conversions are very important to remember, for this topic:
Standard Atmospheric Pressure = 101.3 kPa = 760 mm of Hg = 1.0 atm
1 kPa = 7.50 mm of Hg
The next significant topic in this section is temperature. As previously stated, although one may be accustomed to dealing with temperature measurements in units of Celsius or Fahrenheit, in chemistry the units are measured in Kelvin. The reason for this is the fact that it is possible to have negative numbers on the Celsius scale, and that would cause problems when measuring the volume of a gas at low temperatures. Therefore, in order to do any gas law calculations involving temperatures, you must first convert the temperature to Kelvin. The following equations are the conversions, necessary for temperature:
Co + 273 = K
K - 273 = Co
As one may already know standard temperature has been set at 273 Kelvin, which is equal to 0oC. Standard temperature and pressure is abbreviated as STP. STP is often called upon to ensure equality in measurements taken either in different labs, or on different days. The following equation will aid in equating STP:
STP = 101.3 kPa and 273 K (or any equivalent values, i.e. 1 atm and 0oC)
Now that an understanding about the kinetic’s of gases has been established, the topic of equilibria can be discussed. Dynamic equilibria is established when no further change is occurring, however, the reaction is still continuing. Dynamic equilibria is illustrated in an equation by the use of a special set of double arrows:
There are different types of reactions that may occur. Firstly, there are reversible reactions, meaning the reaction can go in either direction, depending upon the conditions. An example of a reversible reaction is as follows:
If you pass steam over hot iron the steam reacts with the iron to produce a black, magnetic oxide of iron called triiron tetroxide, Fe3O4.
The hydrogen produced in the reaction is swept away by the stream of steam.
Under different conditions, the products of this reaction will also react together. Hydrogen passed over hot triiron tetroxide reduces it to iron. Steam is also produced.
This time the steam produced in the reaction is swept away by the stream of hydrogen.
These reactions are reversible, but under the conditions normally used, they become one-way reactions. The products aren't left in contact with each other, so the reverse reaction can't happen.
The next type of system is a closed system, in which no substance is either added or lost. However, although no substances are added or lost, energy can still be transferred in or out. Based upon the previous example, one can see that if it were a closed system, one would have established dynamic equilibria. Although equilibria was previously illustrated as a set of double arrows, that is not to say that the reaction always remain in that perfect state. The change from left to right in the equation is known as the forward reaction. The change from right to left is the back reaction. If the conditions of the experiment change (by altering the relative chances of the forward and back reactions happening), the composition of the equilibrium mixture will also change.
The following is an example of an equilibria equation and an explanation as to how a reaction ends up in this state:
At the beginning of the reaction, the concentrations of A and B were at their maximum. That means that the rate of the reaction was at its fastest.
As A and B react, their concentrations fall. That means that they are less likely to collide and react, and so the rate of the forward reaction falls as time goes on.
In the beginning, there isn't any C and D, so there can't be any reaction between them. As time goes on, though, their concentrations in the mixture increase and they are more likely to collide and react.
With time, the rate of the reaction between C and D increases:
Eventually, the rates of the two reactions will become equal. A and B will be converting into C and D at exactly the same rate as C and D convert back into A and B again.
At this point there won't be any further change in the amounts of A, B, C and D in the mixture. As fast as something is being removed, it is being replaced again by the reverse reaction. We have reached a position of dynamic equilibrium.
The final topic in this chapter is water and the hydrogen bond. In a water molecule the electron shell around hydrogen atoms is thin, giving the hydrogen atom a small positive charge. On the other hand the electron shell around oxygen atoms is thick, causing oxygen to carry an extra negative charge. These opposite charges attract, although quite weakly. This weak force is called a hydrogen bond. The hydrogen atoms of one water molecule stick to the oxygen atoms of nearby water molecules, freezing them together into solid ice.
However, not all molecules are sticky. Those which cannot form hydrogen bonds are informally known as slippery. The scientific name for this is "hydrophobic" which means "water fearing". Examples of slippery molecules are fats and oils. On the other hand molecules which stick to water, such as alcohol and sugar, are called "hydrophilic", meaning "water loving".
The difference between slippery and sticky molecules is very important in the process of life. For example the folding of amino acid chains into enzymes relies upon it. So too does the holding together of cell membranes. Not all stickiness of molecules is due to hydrogen bonding. There are very weak bonds, called van der Waals bonds, which occur between nearby molecules because of random fluctuations in their electron shells.
In conclusion, one has learned the fundamental and detailed aspects of the gaseous state. Throughout the chapter such topics as the Ideal Gas Law and the Kinetic Theories of Gases have been touched upon. It is interesting to see the vast differences of the gaseous state, in comparison to the others. Through the study of this chapter, one is even able to walk away understanding some of the phenomenon of day-to-day life.
Works Sited
http://www.chemistry.ohio-state.edu. Viewed on 6/16/04
http://www.gi.alaska.edu. Viewed on 6/16/04
http://www.google.com. Viewed on 6/26/04
http://www2.hawaii.edu. Viewed on 6/29/04
http://www.science.uwaterloo.ca. Viewed on 6/21/04