Quantitative Changes in Equilibrium Systems

Quick review of concepts so far… Chemical equilibria are dynamic equilibria Forward and reverse reaction rates are equal Concentrations of reactants and products remain constant over time

Review cont’d….. Dynamic equilibrium Reaction appears stopped at the macroscopic scale (e.g. no more change in colour, T, ph, etc.) Reaction is continuing at the atomic (microscopic) scale but at equal reverse and forward rates

Review cont’d Conditions for equilibrium Closed system Reaction must be directly reversible Identical reaction conditions Equilibrium position The relative concentrations of reactants and products in a system in dynamic equilibrium

Calculating [ ] in equilibria Use the ICE table given initial and at least one equilibrium [ ] 2NOCl(g)  ----> 2NO(g)  +  Cl2(g) I     2.0                     0            0 C    -2x                  + 2x           x E     2.0 - 2x             2x           x

The math of equilibria Equilibrium Law (or Law of Mass Action) Mathematical description of chemical system at equilibrium Equilibrium constant – the value that defines the equilibrium law for a given system (unitless)

Calculating K Does not change regardless of initial [ ] at given T Does change with T change Only true for elementary processes

Quick review of concepts so far… Magnitude of K K>1 favours K=1 K< 1 Products same [ ] favours reactants

Review…. Homogeneous vs. heterogeneous equilibria Homogeneous – same state of matter Heterogeneous – reactants and products are present in more than one state K in heterogeneous systems only depends on the [ ] of the gases since the [ ] of liquids and solids does not change

Review of Le Chatelier’s Principle When a system in equilibrium is disturbed, it responds in the opposite manner (equilibrium shift) Concentration changes Energy changes (exothermic and endothermic) Gas volume/pressure changes What about catalysts and addition of inert gases?

Applications of chemical equilibria Hemoglobin and oxygen exist in equilibrium in the blood: Hb(aq) + 4O2(g) ⇋ Hb(O2)4(aq) At high altitudes, there is a lack of oxygen, equilibrium shifts where? As a result , a person tends to feel light-headed. What would an oxygen tank do to the equilibrium? What about someone who is born at high altitude? climbers

CO poisoning CO forms stronger bonds with Hb than O2 Hb(aq) + 4CO(g) ⇋ Hb(CO)4(aq) (new equilibrium) No longer available to carry O2, can be fatal Introducing O2 shifts the equilibrium Hb(CO)4(aq) + 4O2(g) ⇋ Hb(O2)4(aq) + 4CO(g) Equilibrium shift to ? CO is exhaled…..

Methanol production Methanol is an important alcohol used in industrial processes CO(g) + 2H2(g) CH3OH(g) (ΔH = -90 kJ mol-1) What conditions would provide the highest yields? -

Quantitative changes What if a system is not @ equilibrium? The reaction quotient, Q, can be used to analyze a chemical reaction that is not at equilibrium. Q can determine: If the system is at equilibrium or not If not at equilibrium, which way will the system shift e.g. if only reactants are present, then reactions will shift to the right But if both reactants and products are present, which way?

Reaction quotient Q is the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants It is calculated using instantaneous concentrations – [ ] that correspond to a particular point in time.

Q For the general reaction aA(g) + bB(g) < = > cC(g) + dD(g) the reaction quotient is expressed as Q = [C]c[D]d/ [A]a[B]b Just like K but system may not be at equilibrium Can use concentrations or partial pressures to get Q

Relationship of Q to K If Q = K, the system is at equilibrium If Q> K, the system must shift to the left ([products] must decrease, [reactants] increase) If Q< K, the system must shift to the right

Calculating Q In order to determine Q we need to know: the equation for the reaction, including the physical states, the quantities of each species (molarities and/or pressures), all measured at the same moment in time. To calculate Q: Write the expression for the reaction quotient. Find the molar concentrations or partial pressures of each species involved. Substitute values into the expression and solve. 

Example: 0. 035 moles of SO2, 0. 500 moles of SO2Cl2, and 0 Example:  0.035 moles of SO2, 0.500 moles of SO2Cl2, and 0.080 moles of Cl2 are combined in an evacuated 5.00 L flask and heated to 100oC.  What is Q before the reaction begins?  Which direction will the reaction proceed in order to establish equilibrium? SO2Cl2(g)  SO2(g) + Cl2(g)       K = 0.078 at 100oC Write the expression to find the reaction quotient, Q. Since K is given, the amounts must be expressed as moles per liter.  The amounts are in moles so a conversion is required. 0.500 mole SO2Cl2/5.00 L = 0.100 M SO2Cl2 0.035 mole SO2/5.00 L = 0.070 M SO2 0.080 mole Cl2/5.00 L = 0.016 M Cl2 Substitute the values in to the expression and solve for Q. Compare the answer to the value for the equilibrium constant and predict the shift.

Write the expression to find the reaction quotient, Q. Since K is given, the amounts must be expressed as moles per liter.  The amounts are in moles so a conversion is required. 0.500 mole SO2Cl2/5.00 L = 0.100 M SO2Cl2 0.035 mole SO2/5.00 L = 0.070 M SO2 0.080 mole Cl2/5.00 L = 0.016 M Cl2

Substitute the values in to the expression and solve for Q. Compare the answer to the value for the equilibrium constant and predict the shift. 0.078 (K) > 0.011 (Q) Since K >Q, the reaction will proceed in the forward direction in order to increase the concentrations of both SO2 and Cl2 and decrease that of SO2Cl2 until Q = K.