The following are quality control data for a manufacturing process at Kensprt Chemical Company. The data show the temperature in degrees centigrade at five points in time during the manufacturing cycle. The company is interested in using quality control charts in monitoring the temperature of its manufacturing cycle. Construct an X bar and R chart and indicate what its tells you about the process.

Sample      X bar      R

     1            95.72    1.0

     2            95.24      .9

     3            95.38      .8

     4            95.44      .4

     5            95.46      .5

     6            95.38    1.1

     7            95.40      .9

     8            95.44      .3

     9            95.08      .2

    10           95.50      .6

    11           95.80      .6

    12          95.22      .2

    13           95.56    1.3

    14           95.22      .5

    15           95.74      .8

    16          95.72     1.1

    17          94.82       .6

    18          95.46       .5

    19          95.60       .4

    20          95.64       .6

Problem 1. Consider a crystal with HCP structure, having an ideal c/a ratio. Complete parts (a)-(c) below.

(a) (1.0 pt max) Demonstrate that the ideal c/a ratio equals 2 6/3.

(b)(0.5 pt max) Find the volume of one unit cell for a given a value.

(c) (0.5 pt max) Demonstrate that the atomic packing factor for this crystal structure is  2/6.

Hints: (a) The c/a ratio is considered ideal when the distance from some atom to its nearest neighbors within the same hexagonally-packed layer equals the distance to its nearest neighbors belonging to a different layer.

(b) The volume of a prism is the product of the area of its base face and the height. Use the c/a ratio found in part (a).

(c) Find the relationship between the lattice constant a and the atomic radius R to calculate the APF value. Use the unit cell volume found in part (b)

If 15.0 mL of a 1.5M HCl solution at 21.50C is mixed with 25.0mL of a 1.5M NaOH solution at 21.50C that is in a calorimeter, and the final mixed solution temperature rises to28.50C, what is the ΔHrxnfor this process?Assume that Ccalorimeter= 35.5J/0C.

a.What is the balanced equation for the reaction?

b.What is the source of the heat that is causing the increase in temperature?

c.Calculate the amount of heat absorbed or lost for the HCl/NaOH solution. Assume aqueous conditions.(Cwater= 4.18 J/g·0C, d =1.0 g/mL)

d.Calculate the amount of heat absorbed or lost by the calorimeter. The calorimeter’s initial temperature is the same as the solution that is initially inside it.

e.Determine the amount of heat absorbed or lost during this reaction.

f.Which of the reactants is the limiting reagent? Determine the moles of the limiting reagent.

g.Determine the amount of heat given off per mole of limiting reagent(ΔHrxn).Make sure to include an appropriate sign indicating whether it is an endothermic (+) or exothermic (-) process. Provide your answer in units of kJ/mol.

Part A

Escherichia coli (E. coli) can under optimal conditions double every 20.0 minutes. How long would it take a single cell to saturate a 5.0 L culture assuming that optimal growth conditions prevaled and that no cells died? The maximum cell denisty in a saturated culture is 10¹⁰ cells mL^-1. Enter your answer to the nearest tenth of an hour.

Part B

Consider the information in Part A and decide how long it would take for the 5.0 L culture to attain 1.0% saturation? Again, enter your answer to the nearest tenth of an hour.

Part C

Imagine that just after the culture described above became saturated a researcher poured the culture into 15.0 L of fresh growth media. How long would it take for this 20.0 L (total volume) cuture to become saturated, again, assuming that optimal conditions prevailed and that no cells died. Enter your answer to the nearest minute.

A grit chamber is designed to treat an average wastewater flow of 1 m³/sec at an overflow rate of 4752 m³/m² –d to capture sand with the following particle size distribution:

         % by wt.                        Diameter (mm)

               30                                         1.0

               30                                         0.5

               30                                         0.2

               10                                         0.1

The design overflow rate is such that 100% removal of the 0.5 mm diameter particles will be achieved. The operating temperature is 20°C and the specific gravity of the sand particles is 2.65. Assume that the stickiness coefficient (k) for sand is 0.04 and the Darcy-Weisbach friction factor (f) is 0.03.

a. Determine the surface area and vertical cross-sectional area of the grit chamber if only the 0.1 mm diameter particles will be scoured away

b. Calculate the removal efficiency assuming that only the 0.1 mm diameter particles will be

     scoured away.

c. If the ratio of peak to average flow is 1.4, calculate the overall removal efficiency at the      peak flow.

Two 10-cm-diameter electrodes 0.52 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 20 Vbattery.

1--------

What are a) the charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes while the capacitor is attached to the battery?

2---------

What are a) the charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes after insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? The electrodes remain connected to the battery during this process.

3----------

What are a) the charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes after the original electrodes (not the modified electrodes of parts D-F) are expanded until they are 20 cm in diameter while remaining connected to the battery?

Consider a 2-acre detention basin with vertical walls. The triangular inflow hydrograph increases linearly from zero to a peak of 60 cfs at 60 min and then decreases linearly to a zero discharge at 180 min. Route the inflow hydrograph through the detention basin using the head discharge curve for the 5-ft pipe spillway in table below. The pipe is located at the bottom of the basin. Assuming the basin is initially empty, use the level pool routing procedure with 10-min time interval to determine the maximum depth in the detention basin.

Elevation Discharge

(ft) (cfs)

0.0    0

0.5    3

1.0    8

1.5 17

2.0 30

2.5 43

3.0 60

3.5 78

4.0 97

4.5 117

5.0 137

5.5 156

6.0 173

6.5 190

7.0 205

7.5 218

8.0 231

8.5 242

9.0 253

9.5 264

10.0 275

Explain the difference between a four firm concentration ratio, a Herfindahl-Hirschman Index, a Lerner index, and a Rothschild index.

Based on the information given below, indicate for each of the following, whether the industry is best characterized by the model of perfect competition, monopoly, monopolistic competition, or oligopoly.

a) Industry A has a four-firm concentration ratio of 0.005% and an HHI of 75. A representative firm has a Lerner index of 0.45 and a Rothschild index of 0.34.

b) Industry B has a four-firm concentration ratio of 0.0001% and an HHI of 55. A representative firm has a Lerner index of 0.0034 and a Rothschild index of 0.00023.

c) Industry C has a four-firm concentration ratio of 100 % and an HHI of 10,000. A representative firm has a Lerner index of 0.4 and a Rothschild index of 1.0.

d) Industry D has a four-firm concentration ratio of 100% and an HHI of 5,573. A representative firm has a Lerner index of 0.43 and a Rothschild index of 0.76.

For the elementary gas phase reaction H+C₂H₄ ®C₂H₅, the second-order rate constant

varies with temperature in the following way:

T / K                                       198      298      400      511      604

10¹² k/(cm³molecule^-1s^-1)       0.20     1.13     2.83     4.27     7.69

a) Use the data to calculate the activation energy, Ea, and the pre-exponential factor, A, for the reaction.

b) The simple collision theory of bimolecular reactions yields the following expression for the rate constant:

k = (8kT/p m)^1/2 sexp^(-Ea/RT)

where mis the reduced mass of the reactants and s is the reaction cross section.

i) Interpret the role of the three factors in this expression.

ii) Use the answer to part a) to estimate s for the reaction at 400K.

iii) Compare the value obtained with an estimate of 4.0x10^-19 m² for the collision cross section.

[Take the atomic masses of H and C to be 1.0 amu and 12 amu, respectively.]