62 
Some T/F questions about chemical potentials. 
63 
An exercise in calculating equilibrium constants in several forms. Please remember that the only form of the equilibium constant that can be used in the formula DG^{o}=RTln K_{p}° (where DG^{o} is calculated from the D_{f}G^{o} values in standard tables) is K_{p}°. The difference between K_{p}° and K_{p} is that the latter may have units because the individual factors are pressures rather than pressures divided by the standard pressure (which is 1 bar). (K_{p} values are used in General Chemistry courses and are fine for doing equilibrium problems but K_{P}° is the only form that can be used to calculate D_{rxn}G^{o}). In part (a) it is necessary to convert from mole fraction to pressure using Raoult’s Law (X_{i} = P_{i}/P_{tot}); the pressures must be calculated in bar if DG^{o} is to be calculated. In part (c) the value K_{c}° refers to the equilibrium constant as calculated from concentrations with each concentration being divided by a standard concentration of 1 mol/L. The concentrations in mol/L of perfect gases are just c = n/V = P/RT. (Some of this is a review of material from General Chemistry). 
66 
An exercise in determining whether or not a system is at equilibrium with
respect to a specific chemical reaction, i.e., the calculation and
interpretation of the quantity Q_{p} (The value Q_{P}
has the same form as the equilibrium constant but the gas pressures do not
necessarily correspond to a set of equilibrium pressures). If Q_{p}
is equal to K_{p} then the reaction is at
equilibrium; if Q_{p}
is less than K_{p} then the reaction must
go forward (more reactants must be converted to products) for the reaction to
come to equilibrium. If Q_{p} is greater than K_{p}
then the reaction must go backwards for the reaction to come to
equilibrium. (Review of material from
General Chemistry). 
610 
A T/F question about equilibrium constants. (Most of this material was covered in General Chemistry). In part (d) it is true that K_{p}° is independent of P because all the pressures used in calculating K_{p}° = exp(D_{rxn}G^{o}/RT) are defined to be exactly 1 bar. (If the gases were not perfect the calculation would be more complicated). 
634 
An exercise that relates the magnitude of the equilibrium constant to the form of the balanced reaction. If the relationship is not obvious write out K_{p}° for each of the reactions and compare their forms. (Review of material from General Chemistry). 
637 
A demonstration of how a modest error in the D_{rxn}G^{o} value can make a very significant difference in the value of the corresponding K_{p}^{o}. To answer this question just do some simple calculations. Write K_{p}° as D_{rxt}G°±error and remember that exp(a+b) = [exp(a)][(exp(b)]. 
656 
Very short question. (Review of material from General Chemistry). Remember that the question only applies to equilibria involving perfect gases, for which P_{i}V = n_{i}RT. 
extra 
Calculate DG_{m} = Dm in kJ/mol for water (1.00 g/mL, 18.0 g/mol)
when 


614 
Use data in Tables to find K_{p}° at 298
K and then to estimate the value at 400 K. 
616 
The value of K_{p}^{o} is given
as a mathematical function of T. Remember that Levine's notation "(T/K)", where K means units of Kelvin, can be confusing; it is probably easiest to just ignore all the factors "/K" and to remember that temperature must be given in degrees Kelvin. 
617 
(Calculation only). Shows how the temperature dependence of DH^{o}_{rxn} affects the equation for the variation of the equilibrium constant with temperature. This derivation assumes that the C_{p}^{o} values for all substances are independent of T, but remember that this assumption is less important than the assumption that DH^{o}_{rxn} is independent of T. In any event DC_{p}^{o} changes only very slowly with T. This problem uses the same chemical reaction and the same temperature as problem 616, so comparisons are possible. Note that K_{p} values seldom have more than 2 significant digits; uncertainties of 20% or more are common. Please do not memorize this equation! 
623 
Short T/F exercise. For part (a) the equation given just above will be needed. 
648 
A question that can be answered if Le Chatelier's principle is understood. This principle says that if an equilibrium system is “stressed” the system will adjust to (partially) relieve that stress. So adding a reactant results in production of more product, raising the pressure favors the side of the reaction with the fewer number of gas molecules, and raising the temperature favors the direction of the reaction that is endothermic. (Review of material from General Chemistry). 
662 
For what kind of reaction is the equilibrium position independent of
pressure? (For all other reactions the
equilibrium position does depend on the sum of the P_{i}'s even
though K_{p}° itself does not depend on pressure because it is
calculated from D_{rxn}G^{o},
where the ° means at 1 bar). 


627 
Use data in a Table to calculate D_{rxn}G^{o}, then compute K_{p}^{o} and finally do the equilibrium problem by the method of successive approximations. The reaction itself is interesting. 
628 
An equilibrium problem very similar to the one done in class. The equilibrium expression for part (a) reduces to a quadratic equation after factoring and cancellation of terms. It can then be solved using the quadratic formula. (Two roots will be found but one of them is not physically reasonable). The equation can also be solved by the method of successive approximations. No cancellation of terms is possible in part (b). 
extra 
Calculate the equilibrium pressures for the N_{2}+3H_{2} «
2NH_{3} gasphase reaction at 400 K, where K_{P}° = 36,
given that the initial pressures are P_{N2} = 0.500 bar, P_{H2}
= 0.200 bar, and P_{NH3} = 2.00 bar.
In doing this problem it is very important to get the limits on x
correct. First calculate whether x is
>0 or <0, then work out the limits on x, and then solve the equilibrium
problem by the method of successive approximations. 