V. Equilibrium Problems 2 main categories of equilibrium problems:  Finding K c or K p from known equilibrium concentrations or partial pressures  Finding one or more equilibrium [ ]’s or partial pressures w/ a known K c or K p

V. Finding K c or K p To find equilibrium constants, we must be given information as to what [ ]’s to use in the equilibrium expression. Often, we will need to set up a table to organize the information.

V. Sample Problem An equilibrium was established for the reaction CO (g) + H 2 O (g)  CO 2(g) + H 2(g). At equilibrium, the following [ ]’s were found: [CO] = M, [H 2 O] = M, [CO 2 ] = M, [H 2 ] = M. What’s the value of K c ?

V. Sample Problem In the reaction 2CO (g) + O 2(g)  2CO 2(g), it was found the concentration of O 2 dropped by mole/L. When the reaction reached equilibrium, how had the [CO] and [CO 2 ] changed?

V. Sample Problem A student placed mole PCl 3(g) and mole Cl 2(g) into a 1.00 L container at 250 °C. After the reaction PCl 3(g) + Cl 2(g)  PCl 5(g) came to equilibrium, mole PCl 3 was found. What’s the value of K c for this reaction?

V. Key Points 1)Only use equilibrium [ ]’s in the K c /K p expression. 2)Initial [ ]’s should be in molarity if using K c. 3)Changes in [ ]’s always occur in agreement with stoichiometry in the balanced equation. 4)When entering the “Change” row, make sure all reactants change in one direction and all products change in the opposite direction.

V. Finding Equil. [ ]’s This second type of problem is more challenging than the first. Key is interpreting information given and organizing it into a concentration table.

V. Sample Problem At 25 °C, K c = 4.10 for the reaction CH 3 COOH (l) + CH 3 CH 2 OH (l)  CH 3 C(O)OCH 2 CH 3(l). At equilibrium, it was found that [CH 3 COOH] = M, [H 2 O] = M, [CH 3 C(O)OCH 2 CH 3 ] = M. What’s the equilibrium [ ] of CH 3 CH 2 OH?

V. Sample Problem The reaction CO (g) + H 2 O (g)  CO 2(g) + H 2(g) has a K c of 4.06 at 500 °C. If mole CO and mole H 2 O are placed in a 1.00 L reaction vessel at this temperature, what are the equilibrium concentrations of reactants and products?

V. Sample Problem Using the same reaction and conditions from the previous problem, suppose we now add mole of CO, mole H 2 O, mole CO 2, and mole H 2 in a 1.00 L reaction flask. What will be the equilibrium [ ]’s of everything?

V. Sample Problem During an experiment, mole of H 2 and mole of I 2 were placed in a 1.00 L flask in which the reaction H 2(g) + I 2(g)  2HI (g) came to equilibrium. If K c = 49.5 at the temperature of the experiment, find the equilibrium [ ]’s of all species.

V. Sample Problem At a certain temperature, K c = 4.50 for the reaction N 2 O 4(g)  2NO 2(g). If mole N 2 O 4 is placed in a 2.00 L flask at this temperature, what will be the equilibrium [ ]’s of both gases?

V. Simplifications Using the quadratic equation can be a drag, so we look for simplifications. When K c or K p is very small or very big, we can treat x as being insignificant.  As such, we discard x in any addition/subtraction operation. We must verify our assumption by comparing the value we obtain for x to the number it was discarded from.  Assumption is valid if value of x is less than 5% of the number it was subtracted from.

V. Sample Problem In air at 25 °C and 1 atm, [N 2 ] = M and [O 2 ] = M. The reaction between molecular nitrogen and molecular oxygen to form nitrogen monoxide has K c = 4.8 x at 25 °C. What is the natural [NO] in the atmosphere?

V. Successive Approximations If the less than 5% criteria is not met, we fall back to the method of successive approximations. In this method, we take the value of x obtained after simplification, and insert it into the equation where x was discarded. The equation is solved again for x, the process repeating until the value of x becomes constant.

V. Sample Problem Hydrogen sulfide decomposes according to the reaction 2H 2 S (g)  2H 2(g) + S 2(g) at 800 °C with a K c of 1.67 x If initially [H 2 S] = 1.00 x M, in a closed reaction vessel, what is the equilibrium concentration of S 2(g) ?

VI. Predicting Qualitative Changes to Equilibrium If a system is at equilibrium, what happens when it is disturbed? Le Châtelier’s Principle allow us to make qualitative predictions about changes in chemical equilibria:  When a chemical system at equilibrium is disturbed, the system shifts in the direction that minimizes the disturbance.

VI. Three Ways to Disturb an Equilibrium We look at three ways that disturb a system at equilibrium: 1)Adding/removing a reactant or product. 2)Changing the volume/pressure in gaseous reactions. 3)Changing the temperature.

VI. Adding Reactant/Product If we add or remove a reactant or product, we’re changing the [ ]’s. The equilibrium will shift in a direction that will partially consume a reactant or product that is added, or partially replace a reactant or product that has been removed.

VI. Adding Product

VI. Changing Volume/Pressure Via PV = nRT, changing volume is related to changing pressure and vice versa.  For example, decreasing volume is equivalent to increasing pressure. Reducing volume (or increasing pressure) of a gaseous reaction mixture shifts the equilibrium in the direction that will, if possible, decrease the # of moles of gas.

VI. Changing Pressure

VI. Changing Temperature To determine the effect of changing the temperature, we need to know the heat of reaction, ΔH rxn. Once we know if a reaction is exo or endo, we can write “heat” as a product or reactant. We then apply Le Châtelier’s Principle in the same manner as when we considered the add product/reactant case.

VI. Changing Temperature

VI. Sample Problem For the reaction N 2(g) + 3H 2(g)  2NH 3(g), ΔH rxn = kJ/mole. Which way will the equilibrium shift when each of the following occurs? a)NH 3 is removed via reaction w/ HCl. b)The reaction vessel is opened. c)The reaction vessel is cooled by 25 °C. d)Some Ar gas is added to the reaction vessel. e)A catalyst is added.