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Session Summaries by GMAT Tutors

Grayslake, IL GMAT tutoring
[COVERED]: We began with discussing the student's assigned reading and problems, with which she proclaimed no difficulty, especially having read those concepts through the lens of correct thinking about equilibria. So, we then began our focus for this session -- Acid/Base Chemistry. We began with a discussion of the three definitions of acids, showing how each was a superset of the older one, and giving examples of molecules that fit in each level. I then introduced acid dissociation reactions as very similar to the dissociation reactions for crystalline solids we covered last time, comparing K-a to K-sp. We introduced the concept of acid strength, and how to quantify it using K-a. We discussed how the reaction of an acid and its conjugate base can be summed to equal the autodissociation of water, how that reaction can be used to determine Kw, and how Ka, Kb, and Kw interrelate, with an example problem. We then went over a table of strong and weak acids and bases, highlighting trends in what makes each strong or weak. This required a brief discussion of how to calculate formal charge using Lewis structures. We also discussed how to calculate the pH from the hydronium ion concentration, defining the p(Anything) = -log(that thing). We walked through the derivation of the Henderson-Hasselbach equation, discussing the conditions under which pH = pKa. I illustrated a mathematical shortcut to connect the [H30+] and pH. I then tried to move on to a critical thinking question with a test-day trap concerned with integrating the common ion effect with recognizing orders of magnitude. At this point, it became evident that the student's difficulty in working through the concepts thus far had stemmed from her lack of understanding how exponents and scientific notation work -- this necessitated a fundamental review of the instrumental math. This review allowed us to return to and quickly work through the critical thinking question. The student began to make the intuitive leaps necessary to avoid the traps, so I was very pleased that this session allowed a personalized instruction path. At this point, we were running long (~3h), but had not finished discussing titrations. The student had read the material, but had not picked up on the fact that titrations were done with strong acids or bases; after reviewing this, she rapidly picked up all the remaining points. We discussed the concept of Normality vs. Molarity, and showed how the equivalence point is represented on a titration curve as a vertical slope, beginning with the titration of a strong acid. By comparing that to the curve for a weak acid, the student was able to see how the pH at the equivalence point is higher than 7 for the weak. We then discussed why the slope of the buffer region was horizontal, discussing how the ratio of weak acid and conjugate base is roughly 1:1 at this point. We then compared these two graphs to that of a diprotic species. The student then correctly inferred the shape of the curve for a triprotic species. We closed with a quick discussion of how indicators are weak acids, and how to choose an indicator that is useful for our chosen titration. [PROGRESS]: The student continues to do her homework, and she stated after the formal close of the session that she had picked up a basic understanding of voltaic cells. The biggest breakthrough this session was getting her to really understand the mathematics she had heretofore not understood. [CHALLENGES]: Initially, the student would give the answer in the wrong format and answer questions that should have been in scientific notation in pH terms instead, often with values that would be wrong even if I had asked for pH. I had already drawn the log curve on a graph, and referred to it now. I gave the student a useful definition of exponents and graphs, running her through some progressions to show how the definitions were true, including raising numbers to the zeroth power, and to negative powers by doing the inverse operation (multiplication/division). Despite the seemingly tortuous nature of this detour, at the end, she finally understood exponents, and seemed to feel relieved that this mathematical tool was no longer mysterious. [EXTRA PRACTICE]: I assigned the student a chapter on scientific notation and logarithm/exponent math in addition to studying up on voltaic cells. We decided that we would cover that and the results of her first full-length practice test in the next session.
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Grayslake, IL GMAT tutoring
Today we reviewed math problems involving number properties, linear algebra, profit and profit percentage, and finally a group of five data sufficiency problems.
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Grayslake, IL GMAT tutoring
The student completed his data sufficiency homework and did not have any questions. He is getting more comfortable with the process for data sufficiency but admittedly needs more practice. Today, we began discussing geometry. We covered angle measurements of intersecting lines and triangles. I am sending worksheets for homework.
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