Translational motion test, #2

I don't understand why if the frictional force of air resistance is proportional to an object's cross sectional area, and not velocity, it would never reach terminal velocity. If the frictional force of air resistance is much smaller than the weight of the falling object, wouldn't it never reach terminal velocity anyways?
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If the frictional force is proportion to cross-sectional area, then the frictional force will always have the same value as an object falls (it's area isn't changing, right?).  Thus, if the air resistance is smaller than the weight of the object, we will never reach translational equilibrium; the weight will always be larger than the drag force.

In real life, this isn't the case.  Drag starts off at a very small value (smaller than the weight), but increases with the velocity of the falling object.  Eventually, the drag force is equal to the weight, and that's when the object is in translational equilibrium -- at terminal velocity.

Translational motion test, #5

Is there an easier way to do this problem than what is written as the explanation?  The explanation is rather difficult to understand.
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This is one of the most asked about questions in the whole Kaplan curriculum.  Here’s my explanation:

This question reads:  “Cells can only absorb nutrients through their surfaces.  In order for a cell to absorb nutrients most efficiently, it will grow to a maximum size and then divide.  If the total volume remains constant when a cell divides, then the ratio of the total surface area of the daughter cells to that of the original cell is:”

Let’s start with defining a few variables here.  According to our passage, “each animal has a characteristic length L…its area is proportional to L²…and its volume is proportional to L³.”

Let’s also define the subscript “1” to mean the cell before it’s divided, and “2” to represent each cell after it’s divided.

The total volume here is constant – the one cell before division has the same volume as adding together the two cells after division.  This gives us the equation that L₁³=2L₂³.  Let’s take the cube-root of both sides.  Well, the cube root is the same as taking each side to the 1/3 power.  So we would have:

(L₁³)^1/3=(2L₂³)^1/3.  When you have an exponent raised to an exponent, we multiply their values.  This means that this simplifies out to L₁=2^1/3L₂.  The 2^1/3 is because we have to distribute the exponent to both values in the parentheses.

From here, we can figure out the answer to our question.  It asks us to find the total surface area of the daughter cells, as compared to the area of the original cell, or

2L₂²:L₁².  Remember that there are TWO daughter cells, so that’s why we have the two here.  Well, we know how L₁ and L₂ are related, so we can say that

2L₂²:L₁² can be represented as 2L₂²:(2^1/3L₂)² – we just substituted in our value for L₁ from that volume calculation before.  Distributing our exponent on the right-hand side, we have 2L₂²:2^2/3L₂².  Let’s divide both sides by L₂².  That gives use 2:2^2/3.  But… that doesn’t quite look like any of the answers here.  Since most of the answers have 1 on the right-hand side, let’s divide both sides by 2^2/3.  That gives us:

[2/2^2/3]:[2^2/3/2^2/3].  When we divide two items that have the same root and different exponents, we simply subtract the exponents.  That means that we have [2^1-2/3]:1, or 2^1/3:1.  That corresponds to answer choice (C).  If you’re having difficulty with exponents, I encourage you to go on to Google and type in “Exponent Practice.”  You want to be able to work with exponents very easily on the MCAT.  The four big rules are:

(X^A)(X^B) = X^A+B

(X^A)/(X^B) = X^A-B

(X^A)^B = X^AB

nth root of X = X^1/n

Re-Cap of Verbal II

Hey everyone,

Congratulations on being done with half of the MCAT class!  Please be on the lookout for a survey arriving in the next week or two from Kaplan, asking you to rate me and the Kaplan program in general.  PLEASE fill this out -- it's one of the best ways I can get feedback from you all, and it's completely anonymous.  You'll also note that there's a space for comments; these are often even more helpful to me than the categorical ratings.  And again, it's anonymous.  The only information I will see besides the ratings and comments is our class code (MCHV10702).

Your Required Homework before Organic Chemistry II is as follows:

• Organic Chemistry Review Notes Chapters 6-10 & 13 (Aromatic Compounds, Alcohols & Ethers, Aldehydes & Ketones, Carboxylic Acids, Carboxylic Acid Derivatives, Spectroscopy)
• Addition & Elimination Online Workshop & Quiz
• Spectroscopy Online Workshop & Quiz
• Comments: The spectroscopy workshop is the best and most useful organic chemistry workshop we have, so please make sure to complete that one before our class.  The assigned reading in the Review Notes covers a tremendous amount of material, but in your first read through just keep an eye on understanding the primary general mechanism of carbonyl reactivity.  That is what we will emphasize in class for that is the emphasis on the MCAT.

To reinforce what we have covered in Verbal Reasoning II, complete the following:

• Take Test 2 in Verbal Reasoning Strategy & Practice Book
• Argument Dissection Basics Workshop & Quiz
• Writing Sample:  Advanced Workshop
• Revisit the email I sent out after Verbal Reasoning I for a refresher on the Verbal Reasoning strategies and my comments on the Writing Sample section.

Helpful Hints:

• Even as you are practicing STPM, don’t let up on your mapping.  By now, you should be fairly comfortable with the strategy, but if you are not, be sure to map every passage in the Verbal Reasoning Section Tests assigned until it starts to feel natural.  Don’t give in to the temptation to allow highlighting on the computer screen to take the place of mapping.  It is a poor substitute.  Rather, use highlighting sparingly for numbers, names, technical terms or definitions.
• Now that you’ve learned about the different question types that will appear in the Verbal Reasoning section on Test Day, practice recognizing them by identifying each question that you practice.  Pay attention to the words and phrases that clue you in to the question type.
• Understanding argumentation is very important for success in the VR section.  Evidence and conclusions will be stated directly in the passage.  Assumptions and inferences will not.  Remember that an assumption is the unstated piece of an argument that links the evidence to the conclusion; inferences are unstated conclusions.  On the MCAT, the only correct inference is the one that MUST be true, not simply MIGHT be true.  Remember this equation:  E (+ A) = C (+ I).

See you next time!

dispersion forces

How do dispersion forces cause noble gases to liquefy at low temps?
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Dispersion forces -- like any intermolecular force -- cause gas particles to be drawn close to each other.  Once the particles are brought close enough to each other, they become a liquid.  Liquids and gases are both fluids (contain to their container and can flow), but, in liquids, the particles are "rolling over" on each other; they're much closer than in gases.  Remember that it is these intermolecular forces that must be overcome for a liquid to boil. 

Re-Cap of Gen Chem II

Hey everyone,

Per usual, this email will focus on General Chemistry II, but first, your homework for Verbal Reasoning II.

Your Required Homework before Verbal Reasoning II is as follows:

• Verbal Reasoning Review Notes:  Chapters 4-5
• Writing Sample Review Notes:  Chapters 2-5

For those of you who would like some additional Verbal Reasoning review before class, I recommend the following:

• Verbal Reasoning Foundation Review Unit 2

General Chemistry II Helpful Hints:

• The Kaplan Question Strategy – “Stop, Think, Predict, Match” – is a simple but elegant way to make sure that you systematically solve every problem and answer every question in the most efficient and effective way.  Sure, you could arrive at the answer in a number of ways, but why waste time with haphazard approaches?  Thinking and predicting are especially important in light of the fact that there are three wrong answers for every one correct and credited answer.
• Remember that while chemical kinetics and thermodynamics are very different studies (the one assesses rates of reactions while the other measures changes in energies), there are ways in which they “intersect.”  For example, K_eq = K_f/K_r  where K_f and K_r stand for the rate constants for the forward and reverse reactions, respectively.  At K_eq, the forward rate and the reverse rate are equal and thus rate_f/rate_r = 1.
• Conceptually, K_eq = K_sp = K_a = K_b; and Q = I.P.; all “K’s” are temperature-dependent, as is molar solubility.  The common ion effect reduces molar solubility (the value of “x” when you’re solving these questions), NOT K_sp.

Here are some other key takeaways from our General Chemistry II lesson:

• Chemical Kinetics
• This has been a topic that traditionally is tested often because of the many different types of questions that can be asked.  The OWQ, our coverage of this topic in Passage I, and the associated topical test does a nice job of covering the wide range of ways it can be tested.  To break it down further, here’s a review of the basic concepts:
• Distinguish and identify catalysts and intermediates.
• Rate Law expression (rate = k[A]^x[B]^y):  the rate of a reaction depends upon the bottleneck – that is, the slowest step in the mechanism.  The reactants in the slowest step will appear in the rate law, thus if the rate law is experimentally determined we can use that information to derive a plausible reaction mechanism (as the student did in the last paragraph of Passage I).
• Be able to determine the rate law expression from experimental data; to make sure you’ve got this skill down determine the rate law for given the following data below:

[A]	[B]	Rate of product formation
2	2	10
2	4	20
4	6	120

• Determination of the limiting reagent:  we did not formally review stoichiometry concepts in General Chemistry I or II, but you are expected to be quite familiar with how to balance a chemical reaction and answer questions related to yields (i.e. percent yield, theoretical yield, etc).  If you want more practice, check out the Stoichiometry topical test!

• Thermochemistry
• The application of thermodynamics to chemical reactions is called thermochemistry.  Thermodynamics is primarily concerned with heat transfer into or out of a system (recall the first law equation ΔU = Q - W).  Heat transfer can result from a chemical or physical process.  Calorimetry is how we measure heat transfer, thus allowing us to determine enthalpy and energy changes (more on calorimetry below).
• Understand difference between state functions (enthalpy, entropy, Gibbs free energy, internal energy) and process/path functions (work & heat).  Note that Hess’ Law can be applied to any state function since all are path-independent.
• Enthalpy:  know the relevant terminology (endothermic, exothermic, heat of formation, bond enthalpy) and look at diagram on page 204 to understand Hess’ Law and how it re-affirms that enthalpy is a state function.
• Entropy:  the second law of thermodynamics has many interpretations, but the main point is that the entropy of the universe continually increases, for while reversible process have a net change in entropy of zero, irreversible process have a positive net change in entropy.
• Reversible processes:  freezing of a puddle of water.  Freezing decreases the entropy of the water, but the heat energy given off by that process increases the entropy of the environment, thus net change in entropy of universe is zero.
• Irreversible process:  drop a glass cup on floor and it shatters into many pieces.  Increase in entropy of the system does not occur at expense of environment.
• Gibbs Free Energy: best way to conceptually understand this formula is to look at question 10 (passage 2). 

• Equilibrium
• Understand difference between kinetics & equilibrium:
• Kinetics tells us about the rate of a reaction, while thermodynamics tells us what equilibrium will look like.  That said, keep in mind that the equilibrium expression is derived from the rate laws of the forward and reverse reactions of each step of the overall reaction.
• Remember that exponents of the concentrations of the reactants and products are equal to their stoichiometric coefficients in the equilibrium expression, not necessarily in the kinetic rate law.
• Understand the relationship between Q and K_eq.  The equations on page 209 are restatements of this concept.
• Remember that the degree sign means standard conditions, which means that T = 298 K, P = 1 atm, and concentrations are 1 M!
• Le Chatelier’s Principle:  know the three ways to stress a system out of equilibrium, and be able to predict how the system will respond to each type of stress.
• System #1 on page 211 introduced the problem solving approach for many questions related to equilibrium expressions.  Review our approach to this question: how did we define the variable x? Where did we assume it was negligible?  Why? 
• Solution Equilibria
• K_sp is not any different than K_eq – we use different terminology but the principles discussed above still apply.
• Know the terminology (ion product, unsaturated, saturated, supersaturated, molar solubility, common ion effect, solubility product constant).
• Understand the relationship between the common ion effect, molar solubility, ion product, and K_sp.
• Know how to use the K_sp expression to solve for molar solubility or solubility product constant.
• How do you modify the expression when a common ion is present?

• Dissociate vs. Dissolve
• On this page we discussed the dissociation of crystalline solids.  We didn’t use the word dissolve, because dissolving a solid in solution results in a breakdown of INTERmolecular forces between molecules.  The molecule remains intact as it dissolves into solution.  For example, when glucose is dissolved in water the atoms within a glucose molecule remain covalently bonded to each other.  In contrast, a molecule of NaCl will dissociate in solution because the ionic bonds that hold the atoms in a lattice structure will be solvated.  
• The factors that determine whether or not any given crystal salt will dissociate are its lattice energy (i.e. the electrostatic attractive forces holding the salt together), solvation energy (i.e. strength of attraction b/w solvent and dissociated ions), and entropy (solute form is more disordered that crystalline form).

• Electrolytes and Conductivity (we didn’t have time for this in class, but you’re expected to know this info):
• In aqueous solutions, electrical conductivity depends upon the presence of ions in solution.  The movement of these ions in response to an electric field is what makes up current.  Note that pure water does not conduct an electrical current well since the concentrations of OH^- and H₃O⁺ are very low.
• A strong electrolyte is a solute that dissociates completely into its constituent ions (e.g. NaCl, KI, HCl) in solution.  A weak electrolyte hydrolyzes incompletely in solution (e.g. acetic acid, ammonia, etc.).  Non-electrolytes do not ionize at all (e.g. O₂, N₂,noble gases, sugar, etc.).

• Solubility rules
• Direct questions are rare, but knowledge of these rules can help you understand passages.  In other words, memorizing these rules will not really help you.  Knowing the general trends can help.  At the least know that all salts of alkali metals, nitrates, and ammonium ions are water soluble.

• Heat & Phase Changes
• Heat v Temperature
• Getting sloppy with terminology can lead to misinterpretations and lead you down the wrong path, and these two often get confused so let’s try to clarify the difference between these two.
• Heat = amount of kinetic energy transferred from one object to another as the result of a temperature difference between them.  Rapidly moving molecules in hotter object collide with more slowly moving molecules in colder object, resulting in transfer of KE to slower-moving object causing it to speed up, i.e. think of it as a microscopic transfer of energy.
• Temperature = macroscopic property of a system that is proportional to the average kinetic energy of all the molecules in that system. 
• Temperature is a property of a system, but heat is a process function that tells the energy transfer that occurs into or out of a system.  In other words, a system does not contain heat.  A system contains energy (proportional to temperature) and heat is energy in transit.
• Types of Heat Transfer
• Conduction:  transfer of heat through direct contact via collisions with neighboring molecules
• Convection:  movement of heat through a fluid (liquid or gas) medium. 
• Think of a cold object (raw steak) and hot object (electric coils of convection oven).  The medium is air.  Air particles collide with the surface of the hot object (electric coils), result in the transfer of heat from the coils to the air particles.  The air particles rise up and collide with the cold object (raw steak), transferring heat energy to the food.  The air particles that collide with the steak get cooled back down.  At the end of the day, we’ve transferred heat energy from the electric coils to the steak via air.  Yay, cooked steak!  Boo, raw steak (easy ticket to food poisoning!).
• By the way, note that via Charles’ Law we know that the volume of the air particle will drop, and since the mass remains constant that means their density increases, which means they will sink back to the bottom where they’ll get re-heated by the electric coils.  In other words, the concept of hot air rising is a bit of a misnomer because hot air doesn’t really “rise”: what happens is that hot air has lower density than cold air so the cold air sinks down this making it look like hot air rises.  Next time you want to get your super nerd face on make sure to point that out to someone.
• Radiation: transfer of energy by electromagnetic waves. 
• No medium required because electromagnetic waves can propagate through a vacuum (ex:  Sun warming Earth!)
• Calorimetry (measuring heat transfer)
• There are two types of calorimeters: constant-pressure and constant-volume.
• Constant-pressure calorimeter: in this case, Q = ΔH
• Constant-volume calorimeter: in this case, Q = ΔH = ΔU (think of 1^st law of thermodynamics, ΔU = Q – W)
• Review the example provided in the Review Notes of a constant-volume bomb calorimeter to understand how it can be applied to problems
• Phase Changes & Phase Equilibria: Know both equations for Q and understand heating curves
• Vapor Pressure & Boiling Point
• Key relationship to know:  boiling point of a solution occurs when the temperature of the solution has raised the vapor pressure above the solution to be equal to the atmospheric pressure. 
• Vapor pressure of a solution depends upon the temperature of the solution (proportional relationship, i.e. higher temperature means higher vapor pressure) and its heat of vaporization (inverse relationship, i.e. higher heat of vaporization means lower vapor pressure).
• Vapor pressure is independent of the shape and volume of a container (pressure is force per unit area), but the rate of vaporization does increase with surface area because molecules can only escape from the surface.  In other words, if we put the same solution in two different containers the one with the greater surface area will evaporate quicker but the vapor pressure above both will be the same.
• Phase Diagrams:
• The most popular phase diagram is a Pressure vs. Temperature curve; be familiar with understanding how to read this curve.
• Know the terminology (triple point, critical point, freezing, melting/fusion, evaporation, condensation, sublimation, deposition).
• How is the phase diagram for water different?  Why?  Is this the meaning of life?
• Raoult’s Law uses another type of phase diagram (see your Review Notes) so be ready for other types of phase diagrams.

To reinforce all the content we covered in General Chemistry II, complete the following topical tests:

• Stoichiometry Test 1
• Comments:  These questions do a nice job of testing your stoichiometric abilities.  Granted, many of these questions involve a ton of math, and the AAMC is unlikely to test you directly on stoichiometry the way this test does…but some of the passages and questions may indirectly test your ability to determine stoichiometrically balanced reactions.  Once you get through this test, you should be able to handle any stoichiometry question.
• Kinetics & Equilibrium Test 1
• Comments:  Passage I is just as likely to show up in the Biological Sciences section, and you’ll probably find its question set refreshingly straightforward.  On the other hand, passage II has a lot of icky math and it directly tests your ability to apply log rules.  This passage is a throwback to the way the MCAT used to be written, but it is worth your time to see if you can understand all of the concepts.  In other words, after reading the question stem, are you at a complete loss as to how to solve the question, or do you understand how to get started? 
• Thermodynamics & Thermochemistry Test 1
• Comments:  Many of the questions here directly test your math skills, but there’s enough conceptual questions in both passages to make it worth your while; furthermore, the AAMC hasn’t sworn off mathematical questions.  As always, focus on the concept behind each question.

That’s all for now.  See you at Verbal II!

Weak Subject Strategies

Hello Alex,

I was wondering, what was the most difficult subject (physics, chem, orgo, bio, verbal) for you when you took the MCAT? What did you do to force yourself to study it and become stronger in that subject? And if you have time, what would you suggest as a strategy for people with a weakness in a particular subject (i.e. if you're weak at physics do XYZ, if your verbal is low do ABC, etc.). Thanks!
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I'd have to say that my weakest section was Verbal while I was studying the MCAT.  I think the biggest piece of advice I can give you in this department is essentially what I said in the Biology I re-cap email -- you just have to start getting invested, and it gets easier to keep doing work on that section.  Procrastination will not beget motivation; only starting the process will beget motivation.  For Verbal in general, it's really just key to do passages.  Find ones that interest you!  Use these to practice the strategies we've discussed in class, and later in your studying process, you'll be able to tackle some of those harder (not as interesting passages).


In the sciences, it's really the same thing.  You just gotta jump in to get the motivation going!


I would strongly recommend looking at the High-Yield Problem Solving Guide (in the back of the Review Notes) and QBank (available online) to help with these weak areas.  They'll help hone your thinking on the topics, not just the content itself.

Re-Cap of Physics II

Hey everyone,

Let’s briefly discuss the preview assignments for Gen Chem II:

• General Chemistry Review Notes: read chapters 4-6 and 8-9
• These chapters cover the following topics: Compounds & Stoichiometry, Kinetics & Equilibrium, Thermochemistry, Phase & Phase Changes, and Solutions! 
• That is quite a load.  If your time is extremely limited, prioritize the three online workshops first.  Each one of them is excellent and provides a wealth of high-yield information. 
• Chemical Kinetics OWQ
• If you only have time for one OWQ right now, please complete this one. The very first passage of the lesson will test you on how to determine the rate law from trial data.  This OWQ does a nice job in showing you how to work through the math.  Don’t just look at the slide and nod your head along.  Test yourself, and learn how to determine the rate law quickly.
• Properties of Solutions OWQ
• Although direct questions regarding the properties of solutions are rare, problems that integrate your knowledge of solutions into other problems are common.  Memorizing all of the solubility rules is a bit of overkill…the more important slides in this workshop are the slides that review units of concentration.  Definitions and examples of percent composition by mass, mole fraction, molarity, molality, normality and dilutions are thoroughly reviewed here.  Finally it concludes with a thorough discussion of colligative properties (notice that osmotic pressure is listed there!  This maps well to the examples of osmosis we discussed in Biology I). 
• Reaction Types OWQ
• This OWQ reviews all reaction types, but we will not cover redox reactions until Gen Chem III.

To reinforce what we have covered in Physics II, complete the following (please also see notes below):

• Physics Subject Tests 4 & 5
• Electrostatics & Electromagnetism Test 1
• Electric Circuits Test 1
• Sound Test 1
• Wave Characteristics & Periodic Motion Test 1

All of these items are available on your syllabus through www.kaptest.com

Before we jump into our review, one note:

• Physics II is a tough lesson; don’t be discouraged if you don’t understand everything right away.  If the concepts of simple harmonic motion, electrostatics or circuits aren’t clear to you now, spend some time with the Physics II Foundation Review.  And don’t forget that your Review Notes are also online in a “cafeteria menu” organization.  This means that you can revisit the review notes by topic rather than by chapter.  You can find the review notes in the “My Tools” tab on your kaptest.com homepage.  Also, make sure to check out the attached document that walks you through the example circuit we looked at in class.

When you review your notes from our Physics II session, focus on these key points:

• Thermodynamics
• Review each type of process from the Review Notes (isothermal, isobaric, isochoric, adiabatic) and test your understanding of each conceptually as well as quantitatively via the equation ΔU = Q – W_{by sys}.  Revisit Question 4 and see if you can explain why C is the correct answer without referring to the graph! 
• Simple Harmonic Motion (Springs + Pendulums)
• Understand what SHM means (curve of displacement versus time is a sinusoid)
• Know and understand all of the formulas we discussed:
• Restoring force (for springs + pendulums)
• Angular frequency, frequency, period (for springs + pendulums)
• Expression for the potential energy of a spring
• Expression for the total mechanical energy of a spring (energy is proportional to AMPLITUDE²!)
• Understand when a mass oscillating at SHM is at max KE and max PE; be able to identify the directions of acceleration, velocity and displacement
• Waves:
• Standing waves are created when a propagating wave reflects off of a boundary; the reflected wave interferes constructively and destructively with the waves that are propagating toward the boundary.  Standing waves are called such because they appear to be “standing still”; the only evident movement is an oscillation of amplitude.
• There are two types of boundaries which can help create standing waves: closed and open.  Closed boundaries include the attachments of guitar strings to the guitar or the end of the flag that is secured to the flag pole.  Open boundaries include the distal end of an oboe or the end of the flag that is flapping in the wind.
•  Be able to answer the following questions on waves:
• What is a wave? 
• What properties of a wave can we determine from a plot of the wave’s displacement versus time?  What properties can we determine from a plot of a wave’s displacement versus distance?
• What is the wave speed formula? 
• Recall that the velocity of a wave is dictated by its medium.  Within a given medium at a given temperature a wave’s velocity will not change.  The speed of a wave changes only if the wave moves into a new medium or if the temperature of the medium it is propagating through changes.
• What are the units of intensity? 
• What property of a wave is related to its intensity?  What is the relationship – linear or exponential?
• Did you notice that the relationship between the total energy of a spring and amplitude is exactly the same?  Cool, right?
• What is the difference between an electromagnetic wave and a pressure wave?  What is the difference between a transverse and longitudinal wave? 
• For an animation that diagrams the different types of wave motions visit this link: http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html
• Sound
• Decibel scale: know that an increase in 10 decibels is equivalent to increasing the intensity by a factor of 10.

Also, here are some comments about the topical tests associated with Physics II:

• Electrostatics & Electromagnetism Test 1
• Comment: this test has a lot of solid conceptual questions.  The 2^nd passage is tough, but that’s good because you’ll learn from it.
• Electric Circuits Test 1
• Comment: The first passage is a bit out there, but the 2^nd passage is fantastic.  RC circuits are not discussed anywhere else, and although you are not “officially” expected to be familiar with them it is in your best interest to understand how they work because of their applicability in many applications.
• Sound Test 1
• Comment: don’t allow yourself to get psyched out by the new info in either passage.
• Wave Characteristics & Periodic Motion Test 1
• Comment: three of the questions associated with the first passage are mathematical, but question #1 and #4 are good conceptual questions.  In general, many students find the first passage to be one of the most difficult physics passages in our entire library.  Some of you may find the second passage weird, but the questions there are a bit easier.

See you at Gen Chem II!