• Standard states

for pure solids and liquids, the pure substance

for gases, the gas at a pressure of 1 atm

for solutions, a concentration of 1 mol/L

• For the rxn,

R is the gas constant 8.314 J mol-1 K-1; T is temperature in K.

G˚ is the standard free energy change, a constant for a rxn at a given temperature.

aA + bB cC + dD

Free Energy Change of a Reaction Under Nonstandard Conditions

1.12 Life and ThermodynamicsAdditional Review of Thermodynamics

The sign of ΔG determines the direction of rxn spontaneity.

Free Energy Change of a Reaction Under Biochemical Conditions:

0 = ΔG°’ + RT lnK at equilibrium, ΔG = 0

ΔG°’ = – RT lnK

The sign of ΔG°’ indicates whether the products or reactants are favored

when rxn is at equilibrium.

A negative sign favors product formation;

1.12 Life and ThermodynamicsStandard States for Biochemical Reactions

• Standard free energy change, G°, assumes a concentration of 1 M

– if [H+] = 1 M, then pH = 0

– but the pH in most cells is near the neutral range

• For biochemical rxns, we define a modified standard state for the [H+]

– standard state for [H+] = 10-7 M, pH = 7.0

– this modified standard state is given the symbol G°’

We can use the relative concentrations of reactants and products for a rxn at pH 7 & 25oC, to calculate the equilibrium constant K and the standard free energy Go’

The hydrolysis of ATP at pH7, yielding ADP, HPO42- ion, and H+:

Ka = = 2.23 x 105 at pH 7, 25oC[ATP]

[ADP][HPO42-][H+]

Go’ = – RT lnK = – 8.314 J Mol-1 K-1 x 298K ln (2.23 x 105)

= – 30.5 kJ/mol = – 7.09 kcal/mol spontaneous

1.12 Life and ThermodynamicsStandard States for Biochemical Reactions

Under the modified standard biochemical state, the hydrolysis of ATP to

Coupling of Production and Use of Energy

• The coupling of energy-producing and energy-requiring reactions is a central theme in the metabolism of all organisms.

• “High Energy” bonds- bonds that require or release convenient amounts of energy (depending on the direction of the reaction).

• ATP is an essential high energy bond-containing compound.

• Phosphorylation of ADP to ATP requires energy.

• Hydrolysis of ATP to ADP releases energy.

Biochemical rxns often are coupled together so that an endergonic rxnoccurs using the energy released by a couple exergonic reaction.

E.g., the phosphorylation of glucose is coupled to the hydrolysis of one phosphate group of ATP, in which the enzyme transfers the phosphate group from ATP to glucose.

Separating the rxn into two steps: 1) hydrolysis of ATP; 2) phosphorylation of glucose.

The sum of the two parts of the rxn gives the overall rxn; it is exergonic overall.

intake = internal heat produced + work + stored chemical energy

1.12 Life and ThermodynamicsStandard States for Biochemical Reactions

In the cell, ATP turn over is rapid. An average ATP molecule is hydrolyzed within minutes of its synthesis.

ATP hydrolysis is accompanied by relief of the electrostatic repulsion between the negative charges on ATP by charge separation.

The resulting phosphate anion is stabilized by resonance.

Adenosine-5’-Triphosphate (ATP) Coupling of Production and Use of Energy

Organophosphates Important in Producing Energy

High energy bonds are found in many organophosphate compounds which play roles in metabolism; The Go’ of hydrolysis of some of these compounds is higher than that of ATP. However, the most important one is ATP.

When 1 molecule of glucose is completely oxidized to CO2 and H2O, up to 32 molecules of ATP can be produced.

The exergonic rxn for complete oxidation of a glucose molecule is:

glucose + 6O2 6 CO2 + 6 H2O Go’ = - 2867 kJ/mol

32 ADP + 32 Pi 32 ATP Go’ = + 976 kJ

The endergonic rxn for phosphorylating ADP to ATP is:

glucose + 6O2 + 32 ADP + 32 Pi 6 CO2 + 6 H2O + 32 ATP

Go’ = - 2867 kJ/mol + 976 kJ/mol = - 1891 kJ/mol

The overall rxn is:

The efficiency of energy use: 976/2867 x 100% = 34%

Coupling of Production and Use of EnergyEnergy Efficiency

Due to common ion effect, the addition of an acid (H+) to a buffer shifts the acid ionization equilibrium to the left, converting some of the A- to the HA form (Le Chatellier’s principle):

2.5 Buffers

The addition of a base (OH-) leads the conversion of some the acid form (HA) to the A- Form:

HA + OH- → H2O + A−

Variation in the [A-]/[HA] ratio results in only minor changes in pH

How could a buffer minimize changes in pH?

2.5 Buffers

pH = pKa + log [A-]

[HA]

Consider a buffer soln has 0.063 M [HPO42-] and 0.1 M H2PO4

- at pH 7. If 1.0 mL of 0.10 M HCl is added to 99.0 mL of the buffer, what is the pH of the resulting solution?

pH = 7.20 + log 0.062

0.101

pH = 6.99

Henderson-Hasselbalch Equation

HPO42- + H+ H2PO4

-

[H+] = 1.023 x 10-7 M

pKa = 7.20

2.5 Buffers

pH = pKa + log [A-]

[HA]

Calculate the pH if you add 3 mL of 0.1 M HCl to 100 mL of a buffer solution that contains 0.10 M H2PO4

- and 0.063 M [HPO42-] at pH 7.0. pKa = 7.20

pH = 7.20 + log 0.0060

0.0103

pH = 6.97

Henderson-Hasselbalch Equation

HPO42- + H+ H2PO4

-

[H+] = 1.07 x 10-7 M

HPO42-

molH+

molH2PO4

-

mol

Before addition of HCl 0.0063 1.0 x 10-8 0.01

Addition of HCl (no rxn yet) 0.0063 3.0 x 10-4 0.01

After HCl reacts with HPO42- 0.0060 ? 0.0103

Ionic Strength2.5 Buffers

Ionic strength (I) is a measure of the concentration of all ions in a soln.

where ci is the molarity of ion i, zi is the charge number of ion i.

I = ½ Ci Zi2

n

i =1

The ionic strength for a 0.5 M NaCl solution:

I = ½ (0.5 x 12 + 0.5 x 12) = 0.5 (a unitless quantity)

The ionic strength for a 0.5 molar CaCl2 solution:

I = ½ (0.5 x 22 + 0.5 x 2 x 12) = 1.5

A good buffer should not significantly change the ionic strength (I) of thereaction system because the ionic strength of a solution can affect importantproperties such as substrate binding and catalytic activities of an enzyme.