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5E: Principles of Chemical Thermodynamics and Kinetics

Enzymes and their inhibitors, bioenergetics, the laws of thermodynamics, rate laws and reaction coordinates, and where equilibrium finally settles.

34 topics · 135 questions

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5E. Enzyme Classification by Reaction Type

  1. How it worksHow do the six enzyme classes carve every reaction a cell runs into separate categories?
  2. Worked exampleFind the class of an enzyme that moves a phosphate off ATP and onto glucose.
  3. Worked exampleCompare a lyase with a hydrolase using one reaction from each and show where they part ways.
  4. Going furtherWhat changes about the classification when the same enzyme catalyzes the reverse direction too?
Your turneasy1 of 3
In an assay, hexokinase transfers a phosphate group from ATP onto glucose 639 times per second per enzyme molecule. Which of the six enzyme classes does that reaction place it in?

5E. Enzyme Specificity, the Active Site and Induced Fit

  1. How it worksHow does an active site close around its substrate instead of waiting rigidly like a lock?
  2. Common mistakeWhy isn't the lock-and-key picture enough to explain how an enzyme lowers a barrier?
  3. Worked exampleCompare hexokinase acting on glucose with hexokinase meeting water, and show what induced fit buys.
  4. Going furtherWhat happens to catalysis when an enzyme grips the transition state harder than the substrate?
Your turnmedium1 of 3
An enzyme accelerates its reaction by a factor of 7 x 106. Why is a rigid lock-and-key active site not enough to explain how it lowers the barrier?

5E. Cofactors, Coenzymes and Vitamins

  1. How it worksHow does NAD+ work as a shuttle that carries two electrons away from a substrate?
  2. Worked exampleFind which vitamin supplies the coenzyme for a decarboxylation and which one supplies a redox step.
  3. Common mistakeWhy isn't a coenzyme used up like a substrate, even though it clearly changes during the reaction?
Your turneasy1 of 3
A purified enzyme shows no measurable activity until 36 micromolar Mg2+ is added to the assay. What does that tell you about the protein?

5E. Michaelis-Menten Kinetics, Km and Vmax

  1. How it worksHow does the enzyme filling up with substrate bend the rate curve into a hyperbola?
  2. How it worksHow does Km turn out to be exactly the substrate concentration that gives half of Vmax?
  3. Worked exampleFind Km and Vmax for an enzyme hitting 60 micromoles per minute at saturation and 30 at 2 mM.
  4. Common mistakeWhy isn't a low Km a sign that the enzyme is a fast one?
  5. Going furtherWhat changes about the curve when you double the amount of enzyme instead of the substrate?
Your turneasy1 of 3
An enzyme obeying Michaelis-Menten kinetics has Vmax = 69 micromoles per minute and Km = 6 millimolar. Write the initial velocity v as a function of the substrate concentration S, in millimolar.

5E. Lineweaver-Burk Plots

  1. How it worksHow does taking the reciprocal of both axes straighten a hyperbola into a straight line?
  2. Worked exampleFind Km and Vmax from a double reciprocal line with y-intercept 0.020 and x-intercept -0.50.
  3. Common mistakeWhy doesn't the x-intercept hand you Km directly instead of negative one over Km?
  4. Going furtherWhat happens to tiny errors in the low-substrate points once you take their reciprocals?
Your turneasy1 of 3
A Lineweaver-Burk plot for an enzyme has a y-intercept of 1/69 minutes per micromole and an x-intercept of -1/7 per millimolar. Find the substrate concentration, in millimolar, at which the enzyme runs at half of Vmax.

5E. Competitive Inhibition

  1. How it worksHow does an inhibitor parked in the active site raise apparent Km while leaving Vmax untouched?
  2. Worked exampleFind which Lineweaver-Burk intercept moves under competitive inhibition and which one stays pinned.
  3. Common mistakeWhy doesn't a competitive inhibitor lower the maximum rate when it is blocking the enzyme outright?
  4. Going furtherWhat changes about the inhibition once substrate concentration is driven extremely high?
Your turneasy1 of 3
An enzyme has Km = 29 micromolar with no inhibitor present. A competitive inhibitor is then added at a concentration equal to 6 times its Ki. Find the apparent Km, in micromolar.

5E. Noncompetitive and Mixed Inhibition

  1. How it worksHow does binding at a distant site drag Vmax down while leaving substrate affinity alone?
  2. Common mistakeWhy isn't noncompetitive inhibition reversed by flooding the system with more substrate?
  3. Worked exampleFind where the double reciprocal lines cross under pure noncompetitive inhibition.
  4. Going furtherWhat changes about the plot when the inhibitor slightly prefers the enzyme-substrate complex?
Your turneasy1 of 3
An enzyme has Vmax = 74 micromoles per minute with no inhibitor present. A pure noncompetitive inhibitor is added at a concentration equal to 4 times its Ki. Find the apparent Vmax, in micromoles per minute.

5E. Uncompetitive Inhibition

  1. How it worksHow does locking up the enzyme-substrate complex pull Km and Vmax down by the same factor?
  2. Worked exampleFind why an uncompetitive inhibitor makes the double reciprocal lines come out parallel.
  3. Common mistakeWhy isn't a falling Km automatically good news for how the enzyme performs?
  4. Ties togetherHow do all four inhibition types sort out when you group them by which intercept the line pivots around?
Your turneasy1 of 3
An enzyme has Km = 70 micromolar and Vmax = 59 micromoles per minute. An uncompetitive inhibitor is added that lowers both constants by the same factor of 6. Find the apparent Km, in micromolar.

5E. Cooperativity and the Sigmoidal Curve

  1. How it worksHow does one subunit binding oxygen make the other three suddenly eager to bind it too?
  2. Worked exampleCompare hemoglobin at 100 torr in the lung with 20 torr in muscle and find the oxygen unloaded.
  3. Common mistakeWhy isn't a Hill coefficient above one a measure of how tightly the protein binds?
  4. Going furtherWhat happens to the sigmoid curve when rising CO2 and falling pH push it to the right?
Your turneasy1 of 3
Hemoglobin leaves the lungs 97 percent saturated and returns from exercising muscle 36 percent saturated. On average, how many oxygen molecules did each hemoglobin tetramer deliver?

5E. Allosteric and Covalent Regulation of Enzymes

  1. How it worksHow does an effector binding far from the active site reshape that site from a distance?
  2. How it worksHow does hanging a phosphate on one serine flip an enzyme between its on and off states?
  3. Worked exampleWalk me through feedback inhibition shutting down a four-step pathway as the end product piles up.
  4. Going furtherWhat changes about the speed of regulation when the switch is covalent rather than reversible binding?
Your turnmedium1 of 3
A 6-step biosynthetic pathway is switched off by its own end product. Which step does the end product inhibit, and why that one?

5E. How pH and Temperature Set Enzyme Activity

  1. How it worksHow does pH changing the charge on two active-site residues switch catalysis on and off?
  2. Worked exampleCompare pepsin working at pH 2 with trypsin at pH 8 and account for the gap between them.
  3. Common mistakeWhy isn't a heat-denatured enzyme just a slow one that would recover on cooling?
  4. Going furtherWhat changes about the optimum for an enzyme from a bacterium living in a hot spring?
Your turnmedium1 of 3
An enzyme held at 86 degrees C loses all activity, and cooling the sample back to 37 degrees does not bring any of it back. What happened?

5E. Free Energy, Keq and the Principles of Bioenergetics

  1. How it worksHow does actual free energy change depend on real concentrations rather than standard ones?
  2. Worked exampleFind which way a reaction runs when its standard free energy is +2 kJ per mole but products are scarce.
  3. Common mistakeWhy isn't a positive standard free energy change proof that a reaction cannot happen?
  4. Going furtherWhat changes about a whole pathway when the cell holds one step far away from equilibrium?
Your turnhard1 of 3
Take 2.3RT to be 5.7 kJ per mole. A reaction has a standard free energy change of +9 kJ per mole, and the cell holds its mass-action ratio Q at 10−3. Find the actual free energy change, in kJ per mole.

5E. ATP Hydrolysis and Phosphoryl Group Transfer

  1. How it worksHow do charge repulsion, resonance and solvation together make ATP hydrolysis so favorable?
  2. Worked exampleFind how coupling a +13 kJ reaction to ATP hydrolysis at -30 kJ makes the pair spontaneous.
  3. Common mistakeWhy isn't the terminal phosphate bond of ATP a high-energy bond in the ordinary sense?
  4. Going furtherWhat changes when phosphoenolpyruvate, with a higher transfer potential, hands its phosphate to ADP?
  5. Ties togetherHow does ranking molecules by transfer potential predict which one can phosphorylate which?
Your turneasy1 of 3
A biosynthetic step needs +20 kJ per mole. It is coupled through a shared intermediate to ATP hydrolysis, which supplies -42 kJ per mole. Find the free energy change of the coupled pair, in kJ per mole.

5E. Biological Oxidation-Reduction and Electron Carriers

  1. How it worksHow does splitting a redox reaction into two half-reactions let you simply add their potentials?
  2. Worked exampleFind the overall potential and the free energy released when NADH passes electrons to oxygen.
  3. Common mistakeWhy isn't a more positive reduction potential a sign of a stronger reducing agent?
  4. Going furtherWhat changes about a flavoprotein's behavior when it can accept a single electron at a time?
Your turneasy1 of 3
The NAD+/NADH couple has a standard reduction potential of -304 millivolts and the half-oxygen/water couple one of +830 millivolts. Find the standard potential of the overall reaction, in volts, when NADH reduces oxygen.

5E. State Functions, the Zeroth Law and the First Law

  1. How it worksHow does conservation of energy split any change into heat exchanged plus work done?
  2. Common mistakeWhy isn't heat a state function when temperature so obviously is one?
  3. Worked exampleFind the change in internal energy when a system absorbs 500 J of heat and does 200 J of work.
  4. Going furtherWhat changes about the bookkeeping when a reaction runs in a sealed rigid vessel instead of a beaker?
Your turneasy1 of 3
A gas absorbs 687 joules of heat from its surroundings and does 277 joules of work pushing back the atmosphere. Find the change in its internal energy, in joules.

5E. Enthalpy, Heats of Formation and Bond Energies

  1. How it worksHow does breaking bonds cost energy while making them pays it back, netting out to enthalpy?
  2. Worked exampleFind the enthalpy of burning methane from bond energies of 413, 498, 799 and 463 kJ per mole.
  3. Worked exampleFind the standard enthalpy of a reaction from tabulated heats of formation of products and reactants.
  4. Common mistakeWhy isn't an exothermic reaction automatically a spontaneous one?
Your turnhard1 of 3
A reaction breaks 3 moles of bonds whose average bond energy is 430 kJ per mole and forms 4 moles of bonds whose average bond energy is 356 kJ per mole. Find the enthalpy change, in kJ.

5E. Hess's Law of Heat Summation

  1. How it worksHow does enthalpy being a state function let you flip and scale reactions and still add them up?
  2. Worked exampleFind the enthalpy of forming CO from carbon and oxygen by subtracting two measurable combustions.
  3. Going furtherWhat changes about the arithmetic when one reaction has to be reversed and doubled first?
Your turnhard1 of 3
Burning graphite to CO2 releases 408 kJ per mole, and burning CO to CO2 releases 283 kJ per mole. Find the enthalpy of formation of CO from graphite and oxygen, in kJ per mole.

5E. Calorimetry, Heat Capacity and Specific Heat

  1. How it worksHow does a bomb calorimeter turn a small temperature rise into the heat a reaction released?
  2. Worked exampleFind the heat absorbed when 250 g of water warms from 20 to 45 degrees C at 4.18 J per gram per degree.
  3. Worked exampleFind the specific heat of a metal when 50 g of it cools 40 degrees and gives up 460 J.
  4. Common mistakeWhy isn't heat capacity the same thing as temperature when both rise as you add energy?
Your turneasy1 of 3
A calorimeter holds 380 grams of water, whose specific heat is 4.2 joules per gram per degree. The water warms from 21 to 87 degrees C. Find the heat absorbed, in joules.

5E. Heats of Fusion and Vaporization and the Phase Diagram

  1. How it worksHow does a heating curve trade sloped temperature ramps for flat plateaus at each phase change?
  2. Worked exampleFind the total heat needed to take 100 g of ice at -10 degrees C all the way to steam at 110.
  3. Going furtherWhat happens to the boiling point when you climb a mountain and the outside pressure drops?
  4. Ties togetherHow does the flat plateau of a phase change rest on the same entropy argument that sets a boiling point?
Your turnhard1 of 3
Take the heat of fusion of ice as 334 joules per gram and the specific heat of liquid water as 4.2 joules per gram per degree. Find the heat, in joules, needed to melt 290 grams of ice at 0 degrees C and then warm the meltwater to 42 degrees C.

5E. Entropy and the Second Law

  1. How it worksHow does counting the arrangements a system can occupy turn disorder into an actual number?
  2. Worked exampleCompare the entropy change of melting ice, dissolving salt and compressing a gas and sign each one.
  3. Common mistakeWhy isn't a living organism building itself a violation of the second law?
  4. Going furtherWhat changes about the entropy of the surroundings when an exothermic reaction dumps heat into them?
Your turneasy1 of 3
A reaction releases 90 kJ per mole of heat into surroundings held at 315 kelvin. Find the entropy change of the surroundings, in joules per mole per kelvin.

5E. Gibbs Free Energy and the Sign Rules

  1. How it worksHow does subtracting the entropy term from the enthalpy term decide a reaction's direction?
  2. Worked exampleFind the temperature above which a reaction with enthalpy +40 kJ and entropy +120 J per K turns spontaneous.
  3. Worked exampleFind the sign of free energy for all four combinations of enthalpy and entropy signs at 300 K.
  4. Common mistakeWhy isn't a spontaneous reaction one that actually happens quickly?
  5. Ties togetherHow does the same free energy sign rule that governs a beaker also govern a protein folding up?
Your turneasy1 of 3
A reaction has an enthalpy change of +62 kJ per mole and an entropy change of +147 joules per mole per kelvin. Find the temperature, in kelvin, above which it becomes spontaneous.

5E. Spontaneity Versus Rate

  1. How it worksHow does a tall activation barrier stall a reaction that thermodynamics says should already be over?
  2. Worked exampleCompare the free energy change and the activation energy for burning paper at room temperature.
  3. Common mistakeWhy doesn't a larger negative free energy change make a reaction go any faster?
Your turnmedium1 of 3
Converting diamond to graphite has a free energy change of -5 kJ per mole at 298 K, and yet a diamond survives for millions of years. What does that show?

5E. Rate Laws and Reaction Order

  1. How it worksHow does a rate law encode which reactants actually show up in the slow step?
  2. Common mistakeWhy isn't the exponent in a rate law the same as the coefficient in the balanced equation?
  3. Worked exampleFind the overall order and the units of k for a rate law first order in A and second order in B.
  4. Going furtherWhat changes about the half-life as you move from zero to first to second order?
Your turneasy1 of 3
A reaction is order 2 in A and order 1 in B, with a rate constant of 9. Write the rate as a function of the concentrations A and B.

5E. Determining Reaction Order From Data

  1. How it worksHow does comparing two trials where only one concentration moved isolate that reactant's order?
  2. Worked exampleFind the rate law when doubling A doubles the rate and tripling B multiplies the rate by nine.
  3. Worked exampleFind the rate constant from a trial where 0.10 M A and 0.20 M B give 0.0040 M per second.
  4. Going furtherWhat changes about the analysis when one reactant is in such excess that its concentration never moves?
Your turnmedium1 of 3
Holding [B] fixed, doubling [A] multiplies the rate by 23. By what factor does the rate change if [A] is tripled instead?

5E. The Rate-Determining Step

  1. How it worksHow does a multistep mechanism's slowest step end up writing the rate law for the whole thing?
  2. Worked exampleFind the rate law for a two-step mechanism whose slow first step consumes one A and one B.
  3. Common mistakeWhy isn't the rate law obvious when the slow step comes second, behind a fast equilibrium?
  4. Going furtherWhat changes about the rate law when a catalyst makes the old slow step faster than another one?
Your turnmedium1 of 3
A two-step mechanism begins with a slow step that consumes 3 molecules of A and one molecule of B, with rate constant 7. Write the predicted rate law as a function of the concentrations A and B.

5E. Activation Energy and the Transition State

  1. How it worksHow does a collision need both enough energy and the right orientation before anything happens?
  2. Worked exampleFind the fraction of molecules clearing a 50 kJ barrier at 300 K compared with 310 K.
  3. Common mistakeWhy isn't the transition state an intermediate you could ever scoop out of the flask?
  4. Going furtherWhat changes about the barrier in a solvent that happens to stabilize the transition state?
Your turnhard1 of 3
Two reactants undergo 7 x 106 collisions per second. A fraction 10−7 of those collisions carry enough energy, and 47 percent of the energetic ones are correctly oriented. Find how many collisions per second yield product.

5E. Reaction Coordinate Diagrams

  1. How it worksHow does the height of the hill set the rate while the drop across it sets the equilibrium?
  2. Worked exampleDraw the profile of a two-step reaction with an intermediate and mark the rate-determining step.
  3. Worked exampleFind the reverse activation energy when the forward barrier is 80 kJ and the reaction releases 30 kJ.
  4. Going furtherWhat changes about the picture once a catalyst opens a completely different pathway?
Your turneasy1 of 3
A reaction has a forward activation energy of 123 kJ per mole and releases 42 kJ per mole overall. Find the activation energy of the reverse reaction, in kJ per mole.

5E. The Arrhenius Equation

  1. How it worksHow does an exponential of activation energy over temperature convert heat into reaction speed?
  2. Worked exampleFind the activation energy when a rate constant triples between 300 K and 320 K.
  3. Common mistakeWhy isn't a catalyst's effect seen in the frequency factor rather than in the exponent?
Your turnhard1 of 3
A reaction has an activation energy of 76 kJ per mole. Taking R as 8.3 joules per mole per kelvin and 1/300 minus 1/320 as 2.1 x 10−4 per kelvin, find the natural logarithm of the ratio of rate constants at 320 K and at 300 K.

5E. Catalysis

  1. How it worksHow does a catalyst open a different route over the barrier without moving either endpoint?
  2. Worked exampleCompare the catalyzed and uncatalyzed barriers for a reaction sped up a millionfold at 300 K.
  3. Common mistakeWhy doesn't a catalyst push the position of equilibrium toward more product?
  4. Going furtherWhat changes about a catalytic cycle when a heavy metal poisons the surface it depends on?
Your turnhard1 of 3
A catalyst speeds a reaction by a factor of 106 at 300 K. Taking RT as 2.5 kJ per mole and ln 10 as 2.3, find how far the catalyst has lowered the activation energy, in kJ per mole.

5E. Kinetic Versus Thermodynamic Control

  1. How it worksHow does the low barrier win while it is cold and the deeper well win once everything is reversible?
  2. Worked exampleFind which product dominates when one has a 15 kJ barrier and the other a deeper well behind 25 kJ.
  3. Going furtherWhat changes about the outcome when a kinetically controlled mixture is left to warm up?
Your turnmedium1 of 3
Product K forms over a barrier of 17 kJ per mole into a shallow well; product T forms over a higher barrier of 35 kJ per mole into a deeper one. Which product dominates cold, and which after long heating?

5E. Keq and the Law of Mass Action

  1. How it worksHow does the forward rate falling and the reverse rate rising pin a system at equilibrium?
  2. Common mistakeWhy isn't equilibrium a state where the reaction has finally stopped?
  3. Worked exampleFind Keq for a reaction that ends with 0.40 M product and 0.20 M of each of two reactants.
  4. Going furtherWhat changes about the expression when a pure solid or a pure liquid is one of the species?
Your turnmedium1 of 3
A gas-phase reaction turns A and B into C, with a stoichiometric coefficient of 2 on A, 2 on B and 3 on C. Write the equilibrium constant in terms of the equilibrium concentrations A, B and C.

5E. The Reaction Quotient Q

  1. How it worksHow does holding Q up against Keq point the reaction forward or backward every time?
  2. Worked exampleFind which direction a reaction shifts when Q is 0.50 and Keq is 4.0.
  3. Common mistakeWhy isn't a Q larger than Keq a sign that the reaction is about to speed up?
Your turnhard1 of 3
For A + 2 B in equilibrium with C, a freshly mixed sample holds [A] = 4 x 10−1 M, [B] = 2 x 10−1 M and [C] = 8 x 10−1 M. Find the reaction quotient Q.

5E. Le Châtelier's Principle

  1. How it worksHow does a system at equilibrium answer a stress by consuming whatever you just added?
  2. Worked exampleFind which way ammonia synthesis shifts when you add pressure, add heat, then pull out ammonia.
  3. Worked exampleFind what happens to the blood carbonate equilibrium when someone hyperventilates and blows off CO2.
  4. Common mistakeWhy doesn't adding a catalyst count as a stress the equilibrium has to answer?
  5. Going furtherWhat changes about the shift when the number of gas moles is identical on both sides?
Your turnmedium1 of 3
Ammonia synthesis, N2 + 3 H2 in equilibrium with 2 NH3, is exothermic. A reactor at 224 atmospheres is compressed further, then heated, then has ammonia drawn off. Which set of shifts is right?

5E. The Relationship Between Standard Free Energy and K

  1. How it worksHow does a logarithm convert an equilibrium constant into a standard free energy change?
  2. Worked exampleFind Keq for a reaction whose standard free energy is -11.4 kJ per mole at 298 K.
  3. Worked exampleFind the standard free energy change for a reaction whose Keq is 100 at body temperature.
  4. Common mistakeWhy isn't a Keq of exactly 1 a sign that nothing at all is happening?
  5. Ties togetherHow does the link between free energy and K tie beaker thermodynamics to enzyme kinetics in a cell?
Your turnhard1 of 3
Two reactions are added to give an overall reaction. The first has an equilibrium constant of 101 and the second one of 101. Find the base-ten logarithm of the overall equilibrium constant.

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