CHM 3410 - Physical Chemistry 1
Third Hour Exam
November 26, 2009
There are five problems on the exam. Do all of the problems. Show your work.
1. (32 points) Consider the following galvanic cell
Pt(s)|H2(g, 1 bar)|HBr(b)|AgBr(s)|Ag(s) (1.1)
where b is the molality of the HBr solution.
a) Give the half-cell oxidation reaction, the half-cell reduction reaction, and the net cell reaction for the above galvanic cell.
b) The standard cell potential for the above galvanic cell, measured at T = 25.0 C, is Ecell = 0.0732 v. The rate of change of the standard cell potential with temperature is dEcell/dT = 1.85 x 10-4 v/K. Based on this information find Gcell, Hcell, and Scell for the cell reaction at T = 25.0 C.
c) What is the value for , the mean activity coefficient, predicted using simple Debye-Huckel theory for HBr in an HBr solution with b = 0.0250 mol/kg, and at T = 25.0 C?
d) The experimental value for Ecell for the above galvanic cell at T = 25.0 C and b(HBr) = 0.0250 mol/kg is Ecell = 0.2712 v. Based on this information find an experimental value for for these conditions.
2. (18 points) Beryllium metal (Be, M = 9.01 g/mol) is often used to manufacture low density metallic alloys. Because of this there is interest in the physical properties of beryllium.
a) What is crms, the root mean square average speed of a beryllium atom in the vapor phase, at T = 2000. K? Give your answer in units of m/s.
b) The Knudsen method can be used to measure the vapor pressure of beryllium. In one such experiment a sample of solid beryllium metal was placed inside a Knudsen cell at a temperature T = 1460. K. The effusion hole of the cell had a diameter d = 0.318 mm. The mass loss observed over a time interval t = 25.00 hours was m = 2.34 mg. Based on this information find the vapor pressure of beryllium metal at T = 1460. K. Give your answer in units of torr.
3. (12 points) The general solution for second order heterogeneous kinetics for a reaction with stoichiometry and rate law
A + B "products"d[A]/dt = - k [A] [B](3.1)
is, as shown in class
kt = 1 ln [A]0 [B]t [B]0 [A]0(3.2)
([B]0 - [A]0) [B]0 [A]t
Consider the specific case where [A]0 = 0.0100 M, [B]0 = 0.0200 M, and k = 0.0100 L/mol.s. How much time will it take for the concentration of A to decrease to a value [A] = 0.0050 M?
4. (26 points) In the Arrhenius model for the temperature dependence of the rate constant for a chemical reaction, k, is given by the expression
k = A exp(-Ea/RT)(4.1)
where A is the pre-exponential factor and Ea is the activation energy for the reaction.
The rate constant for the decomposition of peroxyacetyl nitrate (PAN = CH3C(O)OONO2), a molecule important in tropospheric chemistry, is k = 3.6 x 10-4 s-1 at T = 25.0 C and k = 5.6 x 10-6 s-1 at T = 0.0 C.
a) What is t1/2, the half-life for PAN, at T = 25.0 C?
b) Assuming the Arrhenius equation applies to the decomposition reaction for PAN, find the values for A and Ea for this reaction.
c) The temperature dependence of the rate constant for many atmospheric reactions is often fit to an equation of the form
k = B Tn exp(-C/T) (4.2)
where B, n, and C are constants found by fitting this equation to experimental data. When this equation is used for k we can use the following relationship to define the activation energy for the reaction
Ea = - R d(ln k) (4.3)
d(1/T)
where R is the gas constant. Note that for reactions that do not obey the Arrhenius equation Ea will depend on temperature.
Find an expression for Ea for a reaction whose rate constant is given by equn 4.2.
5. (12 points) Gas phase recombination reactions play an important role in gas phase chemistry. One common mechanism for such reactions is the following
stoichiometric reactionA + B AB(5.1)
step 1A + B AB*(k1, k-1)(5.2)
step 2AB* + M AB + M(k2)(5.3)
All reactants and products in the above mechanism are in the gas phase. AB* represents an "energized" reaction intermediate, and M represents any gas phase molecule.
a) Based on the above mechanism find an expression for d[AB]/dt and d[AB*]/dt.
b) Using the steady state approximation the following expression can be obtained for the rate of the above reaction
rate = - d[A] = k1k2[A][B][M] (5.4)
dt ( k-1 + k2[M] )
What are the individual and overall reaction orders in the low pressure limit ( [M] 0) and in the high pressure limit ( [M] )?