CHEM 114 ‐ Lab Experiment 8 Equilibrium II – Le Chatelier’s Principle

1. There are safety hazards in this lab experiment.  Specifically, what are the safety hazards associated with the experimental procedure?  Be sure to clearly identify and explain why these are hazards.

The successful interpretation of Young’s double slit experiment is dependent on a complete understanding of Huygen’s principle. Explain what Huygen’s principle tells us about a wave and how it is used to demonstrate that the double slit experiment shows that light is a wave.

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. Use the Tech Help button for further assistance. n=9, p=0.2, x < 4

If I want to design an experiment related to kinetic friction, can the following proposal meet the requirement?
By varying the weight of an object and measure the stopping distance of that object.
Is this related to kinetic friction? If not, how should I change my experiment?

3. Let P be an nxn projection matrix (which means that it satisfies P²=P and P^T=P). The goal of this problem is to show that P as a linear transformation is the orthogonal projection onto the range of P.

(a) Show that if v is in the range of P, then Pv=v.

(b) Show that if v is orthogonal to the range of P then Pv=0. (Hint: PPv lies in the range of P, hence is orthogonal to v. Study the dot product of v with PPv.)

(c) The previous parts show that P and the projection map act the same way on vectors that lie either in the range of P or the orthogonal complement of it. Why does this imply that P and the projection map agree on all vectors?

An absorption column operates at 1 atm to separate compound A from air using pure water as solvent. If the concentration of A in the inlet air stream is 900 ppm and the Henry's law constant for A in water is 1000 atm/ppm:

a) What is the equilibrium line equation? (** draw on chart and label)

If the desired outlet air is to contain 200 ppm compound A:

b) What is (L/V)min? (** draw on chart and label)

c) If the actual operating (L/V) is 1.285(L/V), what is the operating equation? (** draw on chart and label)

d) If the actual operating (L/V) is 1.285(L/V), what is the required number of ideal stages? (** draw on chart)

Consider a thin flat rectangular region that of size 4 x 2 m2 and it is electrically insulated at its four corners. (A)Solve Laplace’s equation  2 V(x,y) = 0 in the rectangular region 0 < x < 4 m and 0 < y < 2 m using the separation of variable technique subject to the following boundary conditions:
V(0,y) = 0
V(4,y) = q(y) = 50 sin (3π y / 2)
V(x,0) = 0
V(x,2) = f(x) =100 sin (π x / 4)
(B) Use the result of part (A) to find the corresponding electric field inside the region.

You have just isolated a new strain of Gram negative bacteria that can catabolize the sugar aspartame. Genome comparisons to all other strains don't provide any insight into the identity of this pathway. 1) Describe an experiment to identify the pathway coding for aspartame catabolism 2) Describe an experiment to move this pathway into E. coli 3) Given what we learned in class, describe how this pathway is likely positively regulated and where promoter sequence would be 4) Describe an experiment to phenotypically confirm how this pathway is regulated using a SCREEN involving styrene catabolism 5) Describe an experiment to phenotypically confirm how this pathway is regulated using a SELECTION involving LacZ

Please list relevant strain/plasmid names, or draw/describe your own custom plasmids for these experiments

A researcher has used a complex design to study the effects of caffeine (caffeinated and decaffeinated) and problem difficulty (easy and hard) on subjects’ memories. The researcher tested a total of eighty subjects, with twenty subjects randomly assigned to each of the four groups resulting from the factorial combination of the two independent variables. The data presented in the table represent the percentage words that subjects recalled correctly in each of the four conditions.

1. Is there evidence of a possible interaction in this experiment?

2.What aspects of the results of this experiment would lead you to be hesitant to interpret an interaction, if one were present in this experiment?

3.How could the researcher modify the experiment so as to be able to interpret an interaction if it should occur?

Suppose you heard from a friend that only 75% of people pass Math 1044. In disbelief, you poll 50 randomly selected Math 1044 students and find that 43 of them passed. Answer the following questions with a significance threshold of α = 0.05. You may assume the success-failure conditions hold.

(a) What is the null hypothesis, H0, for this experiment?

(b) What are two valid alternative hypotheses, Ha for this experiment?

(c) Compute the p-value for this experiment using a one-tailed test.

(d) Would we accept or reject H0 using the one-tailed p-value? Justify.

(e) Compute the p-value for this experiment using a two-tailed test.

(f) Would we accept or reject H0 using the two-tailed p-value? Justify.