Chapter 5 Gases



5.1 Substances That exist as gases:


Our world is a world surrounded by gases. They are vital to our existence. Breathing, probably one of the most important involuntary actions, is comprised of the body taking in the air around us and having our bodies use the oxygen in that air. Air, being made of gases, is comprised of the two abundant gases: Nitrogen and Oxygen. Air is comprised of 78% Nitrogen or (N2) and 21 percent Oxygen or (O2). That 21% level at sea level is vital to our existence. As elevation is increased that percentage of oxygen decreases, thus we feel lightheaded. This happens also because pressure is decreased. Pressure is a concept we will talk about later in this chapter.

There are 11 elements that occur as gases at STP (standard temperature and pressure) on the period table. They are Hydrogen, Helium, Nitrogen, Oxygen, Fluorine, Neon, Chlorine, Argon, Krypton, Xenon, and Radon. Helium, Neon, Argon, Krypton, Xenon, and Radon are special types of gases. They are known as the noble gases because they are generally unreactive with other elements. They have 8 valence electrons, thus these elements don't react with other "inferior" elements.

The other 5 elements are also part of a special group. They are known as the diatomic elements. While diatomics are not limited to gases, these 5 are all diatomic. Diatomic means that when they exist by themselves they exist in groups of 2 atoms bonded together. Instead of just N appearing by itself it appears as N2.

On a molecular level, gases can be ionic compound gases or molecular compound gases. The bonds that create them greatly influence what state the compound appears at room temperature. Molecular compounds, for example CO, CO2, HCl, NH3, and CH4, are either solids or gasses at room temperature, but they easily become gases when they are heated. On the other hand, ionic compound such as NaCl, and KBr, do not appear as gasses at room temperature. To accesses these gases one must raise the temperature of these gases to extraordinary temperatures. For example, NaCl's boiling point is around 1000ºC. It is easier for molecular compounds to form gases because covalent bonds are much easily broken then ionic bonds are. Thus gases such as CO2 will exist at STP, while NaCl will remain a solid until extreme conditions are imposed.



Gases can have a very positive or negative affect on the human body. Some like O2 are essential for survival, but HCN is a very deadly gas. Gases are also usually colorless, except for a few exceptions. Finally, gases have special physical properties pertaining ONLY to gases. They take the shape and volume of their container, are easily compressed to form new pressures, will mix evenly with other gases in their container, and have the lowest of densities of all the states of matter.

chlorine_gas.JPG
This is Chlorine gas it is a greenish color, unlike most gases that are clear

From, http://amazingrust.com/experiments/how_to/Images/Chlorine_gas.jpg



5.2 Pressure of Gas:


Everywhere gas exerts pressure on us. We don’t feel it because we have adapted over many, many generations to not feel the pressure the atmosphere exerts on us. That does not mean there is no pressure in the air. Air pressure, what it is commonly known as, is the force or pressure that the atmosphere exerts on the earth. What is this mysterious pressure and how is it measured? Let us derive the SI unit for pressure….

defining_pressure.JPG
Pascals or Pa is the SI unit for pressure. Since the standard pressure in the atmosphere is 1 atmosphere (atm) there has to be conversions between the various measures of pressures.

1 atm = 101,325 Pa
1kPa = 1000 Pa
1 atm = 760mmHg
1 atm = 760 torr
1 torr = 1 mmHg



Now that we have the units of pressure, how does pressure affect us and how do we measure it? Because air, like everything, is subject to the Earth’s gravitational pull, air pressure is higher at lower elevation than higher altitudes. Atmospheric pressure does not act downwards. Because air is fluid like liquids, the pressure acts from all directions. Thus we are not flattened every time we exist in the atmosphere. How is this pressure determined? A barometer is the easiest tool to measure atmospheric pressure. A simple barometer is made by putting a long glass tube filled with mercury and placing it in a dish of more mercury so a vacuum is created at the top of the glass tube. The pressure acts on the vacuum thus affecting the height of the mercury in the tube. The height of the mercury (in mm of course) is the atmospheric pressure at a given location. While a barometer measures atmospheric pressure, a sweet/totally awesome device called the nanometer measures pressure of other gasses that aren’t the atmosphere. There are two types of nanometers. Closed-tubed and open-tubes are the two types of nanometers. A nanometer takes pressurized gas and has it run through a tube. The gas pushes a certain amount of mercury in the curved tube. The difference in heights reflects the pressure of the gas. In an open-tube nanometer atmospheric pressure must be taken into account too. Mercury is used because of its high density and liquid state at room temperature.



5.3 The Gas Laws:

Over the years many scientists have explored relationships with the properties of gasses. The relationships of pressure, volume, and temperature have eluded scientists for years. In the end, some very lucky scientists unlocked the special formulas that have helped chemistry students endure gasses. Let’s begin with Boyle’s Law.

Boyles Law: Boyle concluded that the pressure of a fixed amount of gas at a fixed temperature is inversely proportional to the volume of said gas. Basically, when pressure of a gas decreases, the volume increases. Also, when pressure increases, the volume decreases.

boyles_law.JPG
Charles-Guy-Lussac’s Law: This law concludes that the relationship between volume and temperature. They concluded that the volume of a gas is directly proportional to the temperature of said gas. So when temperature increases, as does pressure and vice-versa.
charles_law.JPG
guy_lassacs_law.JPG
Side note: Shortly after these two laws were published, Lord Kelvin calculated absolute zero to be -273.15°C.
Avagadro’s Law: This law states that at constant pressure and temperature, the volume of a gas is directly proportional to the number of moles of the gas present. This equation is a precursor to the idea gas equation that will be covered in the next section.
avagadros_law.JPG



5.4 The Ideal Gas Equation:


What if all the equations could be combined into one master equation? This master equation could predict the behavior of a gas at ideal conditions! It would be able to help predict to the behavior of Pressure, Volume, Temperature, and number of moles! Just speaking of this makes the world sound like a sweeter place!
…Wait such an equation exists!!!!


YOU_ARE_ALL_PVNERTS.JPG

This equation is used for gasses in ideal states. For a gas to be considered “ideal” the molecules would neither attract nor repel each other, and the volume is negligible compared to the mass of the container. Unfortunately there is no such thing as an ideal gas, BUT discrepancies in behaviors of real gasses do not deviate from ideal gasses that much, so the ideal gas equation can be used! HOORAY!!!
Some things to remember:
1 mole of gas usually takes up 22.4 L in space.
The R constant changes for the unit of pressure used. R is .0821 for atm and 8.31 for kPa

The idea gas equation can be manipulated very easily to do other useful calculations. The ideal gas equation is the Chuck Norris of gas equations. The first manipulation we can do is to find density of a gas.
After rearranging the equation we get this:

pvnert_density_1.JPG



Number of moles is given by: (m is mass and M is molar mass)
pnvert_density_2.JPG

This can be placed into our original equation to form:

pvnert_density_3.JPG

Density is defined as mass over volume, so with some reworking we have our final equation for density of a gas:

pvnert_density_4.JPG
Using the ideal gas equation, with a little help from molar mass, we can easily create a useful equation for density of a gas.


Using the density equation, we can figure out the molar mass of a gas. Sometimes when doing an experiment the gas used is unknown, so a nice equation would be helpful to figure out the gas’s molar mass. Taking the density equation it can be manipulated to form:

molar_mas_pvnert.JPG


5.5 Gas Stoichiometry:


As learned in chapter3 stoichiometry is used to calculate relationships between moles and mass in reactions. For gases we can use stoichiometry to find relationships between moles and volumes using the gas laws.

5.6 Dalton's Law of Partial Pressure:

Question. How do you measure the pressure of one gas when there are multiple gases in a container and all you know is the total pressure? Use Dalton’s law of partial pressures!
We know this:

partial_pressures_part1.JPG


Partial_pressures_part2.JPG
Partial_Pressures_Part3.JPG

5.7 Kinetic Molecular Theory of Gases:

As Sales will soon go over in chapter 6 one of the types of energy is Kinetic Energy. Kinetic Energy applies to many generalizations about gasses known as the kinetic molecular theory of gas. The kinetic molecular theory has 4 basic assumptions:

1. A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be “points”; that is, they possess mass but have negligible.
2. Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic. In other words, energy can be transferred from one molecule to another as a result of a collision. Nevertheless, the total energy of all molecules in a system remains the same.
3. Gas molecules exert neither attractive nor repulsive forces on one another.
4. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy. The average kinetic energy of a molecule is given by:

mean_square_speeed_1.JPG
M is the mass of the molecule and u is its speed. The horizontal line denotes and average for the Kinetic Energy and the speed of the molecule. The u^2 quantity denotes the mean square speed, and it is the average of all the speeds divided by the number of molecules.
mean_square_speeed_2.JPG
With assumption 4 we can rewrite the means square speed equation as:
mean_square_speed_3.JPG

In this equation C is a constant and T is the absolute temperature. As we learned that the pressure is a result of collisions between molecules, this equation is the expression for temperature. This equation shows that the absolute temperature based on the average kinetic energy, so absolute temperature is an index of the random motion of molecules. The higher the kinetic energy, the higher the temperature.

The Kinetic Molecular Theory of Gases is a very complex mathematic theory, but it can be applied to many concepts to show the range of kinetic molecular theory’s range.

Compressibility of Gases: Gas molecules are separated by large distances (assumption 1 states this), thus they can be compressed easily.

Boyle’s Law: The pressure of a gas is determined by the number of collisions, and the collision rate (number of collisions per second) is proportional to the density of the gas. Decreasing the volume of the gas increases the density, which increases the collision rates, which increases the pressure of the gas. Thus, pressure is inversely proportional to volume (as volume decreases, pressure increases).

Charles’s Law: Since average kinetic energy is proportional to a gas’s absolute temperature (assumption 4), thus as temperature increases as does average kinetic energy. We’ve also learned that as average kinetic energy increases the pressure does also.

Avagadro’s Law: The last two laws have shown that pressure of a gas is directly proportional to both the density and the temperature of a gas. Since moles are directly proportional to the number of moles of the gas, so we can rewrite density as n/V. Thus:


kinetic_avagadro.JPG
In these equations C is a constant. Thus, under the same conditions the moles for each gas is the same, which is a mathematical expression of Avogadro’s law.

Dalton’s Law of Partial Pressure: If molecules do not attract or repel each other (assumption 3), the pressure exerted by one gas does not affect the pressure of the other gas. Thus, the total pressure is the sum of the two gases in a container.

The kinetic theory of gases helps us explain molecular motion in more detail. If there are a large number of molecules in a space with a constant temperature, the mean square speed and average kinetic energy will remain unchanged and the motion of the molecule is completely random. At a given time how many molecules are moving a certain speed? Luckily, Maxwell Speed Distribution Curves are graphs that show that number of molecules moving at a certain speed. The peak of the graph represents the most probable speed, or the speed of the largest number of molecules. As temperatures increases, the most probably speed increases as well.


MaxwellBoltzmann.gif

From: http://upload.wikimedia.org/wikipedia/commons/3/37/MaxwellBoltzmann.gif

How are these graphs formulated? A device using an oven at a constant temperature and two rotating disks are used to formulate these graphs. A beam of atoms (or molecules) are shot from the oven and pass through a slit on the first rotating disk and accumulate on the second disk. Molecules with fast speeds will pass through the first disk faster. After the atoms have accumulated on the second disk, the density of atoms in a certain area determine the distribution of molecular speeds at that particular temperature.

On any temperature (T) we can calculate the speed of a molecule using the Root-mean-square speed. We know that the total kinetic energy of a mole of any gas equals 3/2RT. So we can write the equation as:


rms1.JPG
N is Avagadro’s number, and since Nm=M (molar mass) the original equation can be rewritten as:

rms2.JPG
This is the equation for the roots-mean-square speed. Because molar mass is in the denominator of this equation, heavier gases move slower than lighter gases. Root-mean-square speed is calculated in m/s.
Since gases move in random motion, a direct demonstration of this is known as diffusion. Diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. Diffusion occurs when areas of high concentrations of gas diffuse to lower concentration.



5.8 Deviation from Ideal Behavior:

As we have discussed earlier, it is concluded that there is no such thing as an ideal gas. At different pressures the ratio of PV/RT (or n) does not stay constant like it should for an ideal gas.

PVRT.JPG

From: http://www.mikeblaber.org/oldwine/chm1045/notes/Gases/Deviate/IMG00004.GIF

As you can see in the graph, this is rarely the case. Luckily, gases behave ideally at very low atmospheres (>5 atm) and these deviations occur at extreme pressures. Pressure is not the only way to expose nonideal gasses; by lowering temperatures the particles in gases deviate from their normal behavior and the particles break from their mutual attractions. To compensate for this deviation, a Dutch chemist named J.D. van der Waals realized that the real pressures is lower than the ideal measured and found the correction term to bring the real pressure to the ideal pressure.

vanderwallls_equation.JPG
In this equation a is a constant, n is the number of moles, and V is the volume of the gas. This correction term is put in place to take account for nonideal behavior. Basically, nonideal behavior is influenced by how frequently two molecules approach each other closely. The square of the number of molecules pre unit (n/V)^2 increases because the presence of each of the two molecules is proportional to n/V. P(ideal) is measured without any interactions, thus a is proportionally constant.

Now that we have corrected pressure, there must also be a correction for volume. To make the correction we have to start with volume V. The correction becomes (V-nb), where n are the number of moles and b is a constant. The term nb represents the volume occupied by the number of moles of gas.

We can now take these two corrections and place them in the PV=nRT equation, so that nonideal gasses can be taken into account. This new equation is:

vanderwalls_equation_final.JPG
This equation is known as the Van der Waals equation. The constants a and b are easily obtained from a table:

vanderwaals_constants.JPG


From: http://en.wikipedia.org/wiki/Van_der_Waals_constants_(data_page)



Lab!

In this lab we are going to calculate the mass of a magnesium ribbon by using the Ideal Gas Law and gas stoichiometry after the ribbon has reacted with an acid and hydrogen gas has formed. Dalton's law of Partial Pressures will also be applied to help us find all the variables in the Ideal Gas Law.

Materials:
Mg ribbon
Copper Wire
Stopper
Concentrated HCl acid
Gas Collecting tube
250 mL beaker with H2O
Thermometer
Barometer
Internet Connection

Procedure:
1. Take a glass collecting tube and fill it with a known amount of concentrated HCl. Fill the rest of the tube with water.
2. Fill a 250 mL beaker with H2O.
3. Mass the magnesium ribbon.
4. Create a "basket" for the magnesium ribbon with copper wire and attach to the stopper at the bottom of the tube. The copper will not react with the HCl.
5. Slowly invert the tube so that the HCl goes to the bottom and reacts with the Mg ribbon.
6. After inverting the tube place it in the bath of H2O that has been created.
7. Record the temperature of water in the bath and the amount of H2 gas that has been collected.
8. Do Calculations.

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In the end our lab went fairly well. Error could have occured at taking the temperature, measuring the amount of gas, failure to account for gas in the collecting tube already, and not having the stopper on completely. Our lab was overall a success as our percent error was less than 5%.

Questions:
1. Explain how the stoichiometry was done without knowing how many moles of HCl there were in the beginning of the lab?
HCl was the excess reactant, thus in theory there are "infinite" amounts of moles, and the reaction would remain unaffected.
2. 5 moles of HCl and 24.3g of Mg react. What is the volume of H2 formed at 300K at 760 mmHg?
24.63 L of H2

Review Questions

Highlight the area underneath the question to see the answer:
1. The atmospheric pressure on top of Mt. Bauerstein is 524 mmHg. What is the pressure in atm?
.6895 atm

2. At 46 degrees C, CO2 exerts a pressure of 156 atm. What is the new pressure when the volume is decreased by 1/20 and kept at constant pressure?
3120 atm
3. With constant pressure in the system, a gas is cooled from 90 decrees C to an unknown temperature. The volume decreases from 7L to 1L. What's the new temperature?
630 degrees C
4. At 777 mmHg a 5 gram sample of an unknown gas occupies 1 L at 288K. What is the molar mass?
115.74 grams
5. Given there are 7.988 moles of N2 in a 3L container at 340K, what is the pressure of the system in atm?
74.33 atm
6. Given the Reaction S + O2 --> SO2 If 2.54 g of Sulphur reacted with the oxygen, what is the volume in mL of SO gas formed in 200K and 1.5 atm?
868.9 mL
7. .72 grams of CO2 and N2 exist in a container together with a total pressure of 1 atm. What are the pressures of each gas?
.631 atm N2
.3686 atm CO2

8. A 2L container containing 2 atm of .5 moles of O2 and H2 has what partial pressures and temperature?
48.72K
1 atm of each gas

9. At 27 degrees C, compare the root-mean-square speedcs of N2 and O2.
O2 is 483.56 m/s
N2is 516.95 m/s

10. 2.5 moles of CO2 are in a 5L container at 450K. The a value is 3.59 and the b value is .0427 for CO2. Compare the results from the Van der Waals equation to the ideal gas equation.
Ideal gas equation = 180.5 atm
Van der Waals = 187.857atm


Thanks to Our text book at: http://highered.mcgraw-hill.com/sites/0072512644/student_view0/index.html for all the help in the world!

All other pictures were made using equation editor on Microsoft word and captured as images on paint.