Consider a galvanic cell based upon the following half reactions: Ag+ + e- → Ag 0.80 V Cu2+ + 2 e- → Cu 0.34 V

How would the following changes alter the potential of the cell?

Adding Cu2+ ions to the copper half reaction (assuming no volume change).

Adding equal amounts of water to both half reactions.

Removing Cu2+ ions from solution by precipitating them out of the copper half reaction (assume no volume change).

Adding Ag+ ions to the silver half reaction (assume no volume change)

Calculate the final concentration of each of the following diluted solutions.

0.50 L of a 4.0 M HNO3 solution is added to water so that the final volume is 8.0 L .

Water is added to 0.35 L of a 6.0 M KOH solution to make 2.0 L of a diluted KOH solution.

A 65.0 mL sample of 8.0 % (m/v) NaOH is diluted with water so that the final volume is 200.0 mL .

A 8.0 mL sample of 50.0 % (m/v) acetic acid (HC2H3O2) solution is added to water to give a final volume of 25 mL .

A compressor is to run at 250 rpm and requires 75 kW. The drive is provided by V-belts from an electric motor running at 750 rpm. The pitch diameter of the pulley on the compressor is 750 mm and the centre distance between the motor shaft and compressor shaft is 1500 mm. Determine the number of V-belts required to transmit this power if each belt has a cross-sectional area of 375 mm2, density of 1000 kg/m3 and an allowable stress of 2.5 MPa. The groove angle of the pulley is 35° and the coefficient of friction between the belt and pulley is 0.25.

A quasiparticle of mass m is trapped by an extended crystal defect, which has a shape of a narrow, straight tube of length l. The quasiparticle hence is confined to move within this defect. Consider that the tube of this defect is sealed at both ends with potential V = 0 inside the tube. Treat the defect as a 1D infinite square well. Assume that this tube defect is placed at an angle Θ relative to the surface of the earth. The quasiparticle experiences the usual gravitational potential V = mgh. Calculate the lowest order change in the energy of the ground state due to the gravitational potential.

A quasiparticle of mass m is trapped by an extended crystal defect, which has a shape of a narrow, straight tube of length l. The quasiparticle hence is confined to move within this defect. Consider that the tube of this defect is sealed at both ends with potential V = 0 inside the tube. Treat the defect as a 1D infinite square well. Assume that this tube defect is placed at an angle Θ relative to the surface of the earth. The quasiparticle experiences the usual gravitational potential V = mgh. Calculate the lowest order change in the energy of the ground state due to the gravitational potential.

6. Two continuous random variables X and Y have the joint density that is equal to c(x + y) 2 inside the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 and vanishes everywhere else.

a) Find the value of c

b) Find the marginal density f_X(x) and use it to determine E(X) and V(X)

c) Find the marginal density f_Y(y) and use it to determine E(Y) and V(Y)

d) Find the correlation ρ(X,Y)

e) Are X and Y independent? Why?

The density of sodium is 0.971 g/cm3 and it has an atomic weight of 22.9897 g/mol. Each sodium atom contributes one valence electron to the metal, so the number of electrons per unit volume, N/V, is equal to the number of sodium atoms per unit volume.

   a) Calculate the number density of atoms per unit volume, N/V.    b) Calculate the Fermi energy of sodium.    c) Calculate the Fermi temperature.   d) At room temperature (298 K), calculate the chemical potential.   e) Calculate the degeneracy pressure for the electron gas.

A 515-Hz tuning fork is struck and placed next to a tube with a movable piston, creating a tube with a variable length. The piston is slid down the pipe and resonance is reached when the piston is 112.5 cm from the open end. The next resonance is reached when the piston is 82.5 cm from the open end. Round all answers to one decimal place.

Hint (a)

1. What is the speed of sound in the tube?
   v=v=  m/s
2. How far from the open end will the piston cause the next mode of resonance?
   L=L=  cm

The following data was generated for an isolated mammalian dihydrofolate reductase.

[7,8-dihydrofolate] (mM)          V (mol/s)                V (mol/s) with methotrexate

                1.1                                  333                                      169

                2.0                                  444                                      265

                5.0                                  667                                      465

A.        Graph the data with and without methotrexate on a Lineweaver-Burk plot. Clearly label which line is which.

B.        Calculate K_m for the enzyme in the presence and absence of methotrexate. Is this a competitive or non-competitive inhibitor?

C.        Considering that deoxynucleotide concentrations are limiting in the cell, what effect will addition of methotrexate have on DNA replication? Explain your reasoning.

A 180-lb person jumps out of an airplane with initial upward velocity of 5 ft/s at a height of 3000 ft (assuming the air resistance is proportional to its falling speed). The air resists the body's motion with a force of 2 lb for each ft/s of speed. Assuming the constant gravity is 32 ft/s^2 (1) find its velocity v = v(t) (2) find its terminal velocity (3) find the distance of falling x = x(t) (4) find the duration in seconds until the body hits the ground