Equilibrium Basics and Thermo Equilibrium

The past few weeks in class we have been discussing equilibrium. We have learned that at equilibrium, the forward and reverse reactions are happening at the same time and at the same rate. We learned that the "products" and "reactants" are evenly distributed throughout the container/solution and that they are freely moving. We also learned that brackets denote concentration for the substance in question.

The equation seen above, is a demonstration of how to write a Q equation and a K equation. We learned that Q is the reaction quotient and is is used at any conditions that are not equilibrium. K is the equilibrium expression which is the reaction quotient at equilibrium. When writing this type of expression, you must make sure that it is Reactants/ Products and that if there are stochiometric coefficients they become the exponents. Also we learned that the partial pressures can be used in the same way to find Kp. Make sure that solids and liquids are not included in these quotients, only gases and aqueous solutions are included.

We learned that if Q is larger than K, this means that the reaction is product favored (larger numerator) and to reach equilibrium would have to move to the left (towards the reactants). If Q is smaller than K, the reaction is reactant favored and would move to the right to get to equilibrium.

Le Chatelier's Principle:
Once a system is in equilibrium, a change in temperature, pressure, or concentration of the components will cause the equilibrium to shift to counteract the disturbance.  If more product is added to the reaction system, then the equilibrium will shift away to the products to balance out the extra products. The opposite will happen if more reactant is added, the equilibrium will shift toward the products. Another aspect of this principle is that if the volume is expanded, the equilibrium will shift to increase the pressure. To do this the equilibrium will shift towards the "side" with the most moles. Likewise if the volume is decreased (compressed), the equilibrium will shift towards the "side" with the least moles to decrease the pressure. We learned that the Keq stays the same if volume or concentration are changed.
If there is a change in temperature there will be a change in the Keq value for a reaction. If the reaction is endothermic, and heat is added the equilibrium will shift to the products. This is because heat can be thought of as a reactant for an endothermic reaction. On the other had if the reaction is exothermic adding heat will cause the reaction to shift to the left towards the reactants. This is because heat can be thought of as a product and increasing a product means that it will shift to the reactants (left). When cooling, the endothermic reactions move to the reactants and when cooling an exothermic reaction the equilibrium moves to the products.

Therom Equilibrium
The next thing that we learned about was thermo equilibrium. We already know that if ΔG is positive that the reaction is unfavorable and endothermic and that if ΔG is negative the reaction is favorable and exothermic.We learned that ΔG° has only one value at a given temperature and ΔG has infinite possible values at a temperature. ΔG°=ΔG at standard state conditions of 1.00 atm, 298K, and 22.4L. The equation that we learned to relate ΔG° to ΔG  is ΔG=ΔG°+RTlnQ, where R= 8.314 J/molK and Q is the reaction quotient. To find ΔG°, we learned that ΔG°=-RTlnKeq. So what can we tell from a ΔG° of a system? If the ΔG°  is greater than 0, the reaction at equilibrium is mostly reactants, and if ΔG° is less than 0, the reaction is mostly products at equilibrium. By looking at ΔG, if it is larger than 0 the reaction is non-spontaneous and cannot happen, if it is smaller than 0 the reaction is spontaneous and is moving toward equilibrium from either direction, and if it is = to 0 the system is at equilibrium.

Overall I feel that this material is very confusing and takes a while to grasp understanding. I think that I have a fair amount of understanding about the basic concepts, but I do need to do more of the calculations to prepare for the test. For this reason I would give my understanding a 7/10.

Ideal Gases, Kinetic Molecular Theory, Real Gases, Partial Pressure, and Mole Fractions

This past week and a half we have spent time talking about ideal gases, kinetic molecular theory, and then real gases and how they deviate from the ideal gases. We also worked through problems dealing with partial pressure and mole fractions.

First we learned about ideal gases. We reviewed that gases expand to fill their container, are highly compressible, and they have extremely low densities. Next we talked about pressure which is the amount of force applied to an area.

Equation: Pressure = Force / Area. 

The most common unit of pressure used is atmospheres (atm). But pressure can also be measured in Pascals, Bar, and torr (mmHg).

Standard pressure, which is normal atmospheric pressure at sea level is equal to:
-1.00 atm
-760 torr
-101.325 KPa

We then learned different equations that can be used to relate volumes, pressures, temperatures, and numbers of moles of gases.

Boyle's Law states that the volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. We get the constant K when multiplying pressure by volume.

Boyle's Law:

This law can be rewritten to solve for an unknown pressure or volume if 2 of one and 1 of the other variables are known.


The next law that we learned about was Charles' Law which states that at fixed pressure, volume is directly proportional to its absolute temperature. The constant K is found by dividing volume by temperature.

Charles' Law:

This law can be rearranged with temperature on the top and volume on the bottom, depending on whether you are solving for volume or pressure. Remember that the temperature must be written in Kelvin which can be converted from°C by this formula: °C+ 273=K

We then learned about  Gay-Lussac's Law which is very similar to Charles' Law as it uses the same basic set up. This law states that at a fixed mass and volume, pressure and temperature are directly proportional to each other. 

Gay-Lussac's Law:

 This law can also use the reciprocal of the equation given above. You can divide the temperature by the pressure. We learned that when using any gas law equation the temperature must be in Kelvin.

By learning the three gas laws explained above, we were able to come to the combined gas law equation. This equation multiplies pressure and volume together and then divides it by temperature. 

Combined Gas Law:

 

Another important gas law is Avogadro's Law. This law states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles (n) of gas. This means that the volume of a gas divided by the number of moles is equal to the volume of another gas divided by the number of moles. 

Avogadro's Law: 

This law can be rearranged to solve for an unknown volume by multiplying both sides of the equation by n1.

This now brings us to the Ideal Gas Equation. We fondly refer to it as "pivnert" to help us remember the different variables that are included. The ideal gas equation is pressure times volume is equal to the number of moles times the gas constant times the temperature. 

Ideal Gas Equation:

R is the ideal gas constant and is equal to 0.008206. This equation can be rearranged to solve for volume by dividing both sides by pressure. Likewise it can be rearranged to solve for any of the variable as the unknown.

After we learned about the ideal gas equation, we learned about the ideal gas law. This law is referring to ideal gases that are at standard temperature (0º C) and pressure (1.00 atm). We also learned that the standard volume for one mole of an ideal gas is 22.4 L. 

We talked about doing calculations with the ideal gas laws, focusing mainly on the ideal gas equation. We learned that molar mass (mass/moles) can be substituted into the ideal gas equation for moles (n). We also learned that density can be found many different ways. One way is to use some of the information from the ideal gas equation: Density= (Pressure x Volume) / (gas constant x temperature).

The next major topic that we covered was Kinetic-Molecular Theory (KMT). We reviewed that kinetic energy is the energy of motion. We talked about how kinetic energy is proportional to kelvin temperature. We learned that there are several different types of kinetic energy that gas molecules experience. The most common is transitional energy which is the movement through space in straight lines. Other types of kinetic energy include rotational energy, and vibrational energy.  

We then talked about the main points of Kinetic-Molecular Theory. 

-Gases consist of large numbers of molecules that are in continuous random motion. 

-The combined volume of the gas particles is negligible compared to the total volume. The molecules of gas are considered volumeless points of mass. 

-There are no attractive forces between the gas molecules

-Elastic collisions means that kinetic energy is conserved during collisions with the wall. (KE initial = KE final) 

- Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change over time if the temperature remains constant.

Another thing that we learned about KMT is root mean square speed (U) also known as RMS. This can be calculated by adding together the squared speeds of each object, dividing it by the number of objects, and then taking the square root of that number. Remember that molecules with lower molecular masses have higher RMS.

Next we discussed effusion and diffusion. Effusion is the escape of gas through a tiny hole into an evacuated space. This helps to explain why balloons deflate over time. We can describe the relationship of effusion by Graham's Law of Effusion. This law says that the rates of effusion for two substances are  inversely proportional to the square root of their molar masses.

Graham's Law of Effusion:

Remember to match up rate 1 with M1 on the bottom of the fraction and R2 with M2 on the top of the fraction. 

We learned that diffusion is the spread of one substance throughout a second substance. This relationship is the same as the relationship for  effusion. as described by Graham's Law: the rates of effusion for two substances are  inversely proportional to the square root of their molar masses.

After discussing KMT and ideal gases we began to talk about real gases, and the differences that they have compared to ideal gases. We learned that real gases only conform to ideal gas law under relatively high temperature and low pressure. There are two types of deviations that real gases have from the ideal gas equation. These are volume and pressure. The assumptions made in KMT were that gas molecules have no volume and that there are no forces of attraction between molecules. Since these assumptions are not true when the gas is at high pressure or low temperature the ideal gas equation must be corrected and include these extra factors. 

The van der Waals equation is the equation that adjusts the ideal gas equation and makes it work for unideal gases.

van der Waals Equation:

The first part of the equation adjusts the pressure upward and accounts for the attractive forces between molecules, because these forces are causing the pressure to be lower than in an ideal gas. The attractive forces cause the pressure to be lower because they pull the molecules of gas away from the wall where the pressure is measured. The "a" is the part of the equation that represents the attraction part of the molecules. 

The second part of the equation adjusts the volume downward to account for the fact that gas molecules have volume, this causes the volume to be higher than that of an ideal gas. Real gas molecules take up real space. The "b" represents the volume of the gas particles. 

The final thing that we learned about this week was partial pressures and mole fractions. The partial pressure of a gas in a mixture of gases is the pressure that is exerted by that gas if it was occupying the same amount of volume as the total gas. Partial pressure can be found by using pV=nRT. The partial pressures of gases in a solution can be added together to find the total pressure. A mole fraction is the relative or percent composition by moles of a single component in a mixture, represented in decimal form. It is a unitless number.

Where ni is the moles of that component and n total are the total moles of the mixture of gases.

Over all I think that we learned a lot about gases and their properties this past week and a half. I think that I have come to a better understanding of how to use the different equations to solve problems given. I feel like I have a 7/10 understanding of the material. I say a 7 because I still need to practice using some of the equations and  mole fractions as well. But I think that I have a solid base of understanding.