CHEM 102

The reaction QUOTIENT, Q Given a set of starting concentrations for an equilibrium system, the question often arises whether these concentrations satisfy the equilibrium condition, and if not, in which direction (i.e., to the left, or to the right) will the reaction proceed in order to establish equilibrium. This analysis is accomplished by calculating a reaction quotient. The reaction quotient tests given concentrations to learn whether or not they are equilibrium concentrations. Expressions for K and Q look the same, but K expressions only use equilibrium concentrations, whereas Q expressions can use any concentrations (often these are starting concentrations). Comparison of Q and K values leads to three cases:

a. when Q = K, the given concentrations are equilibrium concentrations, so no net change by forward/reverse Rx

b. Q > K, the concentration of products is too large in the given information, so reverse Rx is favored until equilibrium concentrations are reestablished.

c. Q < K, the concentration of reactants is too large in the given information, so forward Rx is favored until equilibrium concentrations are reestablished.

The following web site: http://links.math.rpi.edu/~warrej/equil.html has a neat reaction quotient calculator showing changes in forward/reverse direction of Rx - as a function of changing given concentrations for:
H _{2 (gas)} + I _{2 (gas)} = 2 HI _(gas)

1. For the reaction N_{2 (gas)} + O _{2 (gas)} = 2 NO _{2 (gas)} the equilibrium constant has a value of 6.2E-14 at 2000 C. Suppose that 0.020 mol nitrogen, 0.060 mol oxygen, and 0.00031 mol nitric oxide, are placed in a 2 Liter flask. The flask is sealed and the temperature raised to 2000 C. Are the initial concentrations equal to the equilibrium concentrations, and if not, in which direction (i.e., left or right) will the reaction shift in order to establish equilibrium?

Equilibrium Overview It's important to keep in mind what conditions apply when considering equilibrium systems:

a. the system is closed. Reactant and products are in contact with each other and cannot escape from the reaction vessel. In some cases materials can be added to, or removed from the reaction vessel. But, this represents a disturbance to the closed equilibrium system so it must respond (by favoring forward or reverse Rx) until the equilibrium state is reestablished.

b. the equilibrium reaction is dynamic. Forward and reverse reactions are operating continuously, products and reactants are constantly being formed and used. However, once equilibrium is established, concentrations of products and reactants remain unchanged because rates of forward and reverse reactions are the same.

c. the equilibrium constant ( K or Kp ) has a constant value only as long as temperature does not change. K has different values at different temperatures depending on the magnitude of thermal character (i.e., endo- or exothermicity) for forward and reverse reactions.

Solving Equilibrium Problems Recall and apply the suggested format for solving equilibrium problems as shown in Thursday's handout (1/29) involving the balanced equation followed by three rows of information labeled, start, change and equilibrium. Read the problem carefully and place given information under the appropriate formula and in the corresponding row. When using the equilibrium expression, and only enter information from the at equilibrium row. Solve. Several example problems follow:

2. At some specified temperature, a system at equilibrium contains the following concentrations of gases:
[ P Cl ₃ ] = 0.035 M [ P Cl ₅ ] = 0.017 M [ Cl ₂ ] = 0.074 M
What is the value for the equilibrium constant at this temperature?

3. The decomposition of solid ammonium chloride, NH₄Cl , forms ammonia and hydrogen chloride gases. After establishment of equilibrium in a 5 Liter closed vessel, there was 0.243 mols of ammonia gas, 2.48 g of ammonium chloride, and 0.683 mol of hydrogen chloride gas. What is the value for the equilibrium constant at the temperature of this experiment?

4. A one liter reaction flask was charged with 0.500 mole of pure sulfur trioxide gas, SO ₃ . The flask was sealed and the temperature elevated and held constant. After establishment of equilibrium, the concentration of sulfur dioxide gas, SO ₂ , was 0.350 M. What are the equilibrium concentrations of all gases present, i.e., [ SO ₃ ], [ SO ₂ ],
and [ O ₂ ] , and what is the value for the equilibrium constant at the temperature of this experiment?

5. An amount of 0.450 mol hydrogen, and 0.350 mol iodine, were introduced into a one liter reaction vessel. The vessel was sealed, the temperature raised, and some hydrogen iodide was produced. All substances were present as gases. When equilibrium was established it was found that 30.0 % of the iodine had reacted. Find the equilibrium concentrations of all gases present, and determine the value for the equilibrium constant at the temperature of this experiment.

6. For the reaction: N _{2 (gas)} + 3 H _{2 (gas)} = 2 NH _{3 (gas)} the value for K = 5.2E-5 at 25 C. What mass of ammonia would be present in a 10.0 Liter reaction vessel if equilibrium concentrations of nitrogen and hydrogen gases are 2.00 and 0.80 M respectively?

7. For the reaction of carbon dioxide and hydrogen gases, to form carbon monoxide and water at 990 C, the equilibrium constant is 1.6. What are the equilibrium concentrations of all gases, if initial concentrations were
[ H ₂ ] = 0.250 M, [ CO ₂ ] = 0.250 M, and [ H ₂ O ] = 0.100 M?

Factors affecting the point of equilibrium Systems in chemical equilibrium can be (and are) subjected to external stresses such as changes in concentrations of substances, volume of vessel, pressure, and temperature.

LeChatelier's Principle informs that in response to an external stress, a system will attempt to change the point of equilibrium and minimize the stress in order to reestablish equilibrium Consider the generic reaction:
2 A _(gas) + B _(solid) = 3 C _(gas) + D _liquid) H = 123 kJ/mol

a. Adding/Removing Substances:
addition of A results in more C being formed, Rx shifts to right (-->).
removal of C more A reacts, Rx shifts to right (-->).
addition/removal of B no change

b. Changing volume of vessel:
decreasing volume favors reaction (of forward/reverse pair) forming less mols of gas.
In the example this would be the reverse Rx. Rx shifts to left (<--).

c. Changing pressure of system:
decreasing pressure favors reaction forming more mols of gas.
In the example this would be the forward Rx. Rx shifts to right (-->).

d. Changing temperature of reaction:
increasing temperature favors the forward/reverse pair that is endothermic.
In the example this would be the reverse Rx. Rx shifts to left (<--).

e. Addition of an inert gas:
no change

8. Consider the reaction: 2 SO _{2 (gas)} + O _{2 (gas)} = 2 SO _{3 (gas)} H = 99 kJ/mol What is the effect of:
a. adding oxygen gas
b. removing SO ₃ gas
c. increasing volume of flask
d. increasing the pressure
e. increasing the temperature

9. Consider the reaction: COCl _{2 (gas)} = CO _(gas) + Cl _{2 (gas)} H = + 107 kJ/mol What is the effect of:
a. decreasing [ CO ]
b. increasing [ Cl ₂ ]
c. reducing volume of container
d. reducing the pressure
e. raising the temperature

(answers to problems 1 - 9 are: left; 6.56; 6.64E-3; 0.953; 0.522; 1240; x=0.121; 11212; 12211)

SUGGESTED HMWK - Chapter 13: 49, 55, 56, 59, 62

The following web site: http://www.chem.vt.edu/RVGS/ACT/notes/chem-eqm.html contains a nice presentation of chemical equilibrium in the gas phase. This is an interactive site that allows answers to be submitted (and checked) for several practice problems.

You are requested to turn-in the following equilibrium problems on Thursday, February 5.

1. An equilibrium system consists of sulfur dioxide and oxygen gases, in equilibrium with sulfur trioxide gas. Equilibrium pressures are found to be 0.32 atm sulfur dioxide, 0.13 atm oxygen, and 0.61 atm sulfur trioxide. Calculate the value of the equilibrium constant, and interpret its magnitude.

2. In a different run for the above equilibrium system - but studied at the same temperature - the equilibrium pressures of oxygen and sulfur trioxide were found to be 0.25 and 1.05 atm respectively. What is the equilibrium pressure of sulfur dioxide?

3. Suppose the following amounts of gases were present in a five Liter reaction vessel at equilibrium: 3 moles of ammonia, 2 moles of hydrogen, and 5 moles of nitrogen. What is the equilibrium constant for the reaction at the temperature of the experiment?

4. Suppose 5.0 moles of carbon monoxide, and 3.0 moles of chlorine are introduced into a one Liter flask. The equilibrium reaction proceeds to form COCl₂ . All substances are gases. Given that the equilibrium constant at the experimental temperature is 2.38, what are the equilibrium concentrations of all substances?

5. Suppose 0.80 mols of nitric oxide (NO), 0.60 mols of oxygen, and 0.30 mols of nitrogen dioxide (NO₂), are introduced into a one Liter reaction vessel. After equilibrium is established, the concentration of nitrogen dioxide is found to be 0.70 mol/L. Determine remaining equilibrium concentrations, and the value of the equilibrium constant.

6. For the equilibrium system consisting of ammonia and its elements, suppose concentrations of 0.12 mol/L nitrogen and 0.20 mol/L hydrogen were present in a reaction vessel. After equilibrium is established, the concentration of ammonia is found to be 0.070 mol/L. Determine remaining equilibrium concentrations, and the value of the equilibrium constant. (Please note correction in ammonia concentration from 0.700 to 0.070 mol/L)

PLEASE NOTE TODAY'S EXAM IS IN CUDAHY  SCIENCE  BLDG,  ROOM 207,  FROM  1:00  to 2:20 PM.

INTEGRATED RATE LAWS AND PERIODIC TABLES WILL BE PROVIDED.