biophysical chemistry

Heat capacity equation

q = mcΔT

q

q = heat absorbed or released by the system

m

m = mass of the substance

c

c = specific heat capacity

ΔT

ΔT = Tf − Ti

Specific heat of water

c ≈ 4.184 J/(g·K)

Heat absorbed by a system

q > 0

Heat released by a system

q < 0

Heat during a phase change

q = nΔHphase

Heat required for melting

q = nΔHfus

Heat released during freezing

q = −nΔHfus

Heat required for vaporization

q = nΔHvap

Heat released during condensation

q = −nΔHvap

Moles from mass

n = m/M

First law of thermodynamics

ΔU = q + w

Internal energy change

ΔU = change in internal energy of the system

Work from expansion/compression

w = −PextΔV

Expansion

ΔV > 0, therefore w < 0

Compression

ΔV < 0, therefore w > 0

Work done ON the system

w > 0

Work done BY the system

w < 0

Enthalpy

H = U + PV

Enthalpy change

ΔH = ΔU + Δ(PV)

Heat at constant pressure

qp = ΔH

Ideal gas law

PV = nRT

Ideal gas constant for energy calculations

R = 8.314 J/(mol·K)

Ideal gas constant for L·bar

R = 0.08314 L·bar/(mol·K)

Temperature conversion

T(K) = T(°C) + 273.15

Ideal gas internal energy

ΔU = nCvΔT

Ideal gas enthalpy

ΔH = nCpΔT

Relationship between Cp and Cv

Cp = Cv + R

Constant-pressure ideal gas work

w = −nRΔT

Constant-pressure ideal gas heat

q = ΔH = nCpΔT

Gibbs free energy equation

ΔG = ΔH − TΔS

Standard Gibbs free energy equation

ΔG° = ΔH° − TΔS°

Meaning of ΔG < 0

Reaction is thermodynamically favorable in the written direction

Meaning of ΔG > 0

Reaction is thermodynamically unfavorable in the written direction

Meaning of ΔG = 0

System is at equilibrium

Standard Gibbs free energy and equilibrium constant

ΔG° = −RT ln K

Finding K from ΔG°

K = e^(−ΔG°/RT)

Finding ΔG° from K

ΔG° = −RT ln K

Finding ln K from ΔG°

ln K = −ΔG°/(RT)

If ΔG° < 0

K > 1; products are favored at equilibrium

If ΔG° > 0

K < 1; reactants are favored at equilibrium

If ΔG° = 0

K = 1

Nonstandard Gibbs free energy

ΔG = ΔG° + RT ln Q

Reaction quotient

Q = products raised to their stoichiometric coefficients divided by reactants raised to their stoichiometric coefficients

Reaction quotient for A + B → C + D

Q = [C][D]/[A][B]

At equilibrium

Q = K

At equilibrium ΔG

ΔG = 0

If Q < K

The reaction tends toward products

If Q > K

The reaction tends toward reactants

If Q = K

The system is at equilibrium

Adding reactions

Add the ΔG° values

Reversing a reaction

Change the sign of ΔG°

Multiplying a reaction by a coefficient

Multiply ΔG° by the same coefficient

Equilibrium constant when reactions are added

K overall = K1 × K2

Equilibrium constant when a reaction is reversed

K reverse = 1/K forward

Equilibrium constant when a reaction is multiplied by n

Knew = K^n

Reaction coupling

Two or more reactions are combined so their ΔG° values add to give the overall ΔG°

Overall ΔG° for coupled reactions

ΔG°overall = ΔG°1 + ΔG°2 + …

Biochemical reaction direction under cellular conditions

Use ΔG = ΔG° + RT ln Q rather than relying only on ΔG°

Mole fraction of a gas component

Xcomponent = moles component / total moles

Gas volume from ideal gas law

V = nRT/P

microscopy

technical field using a microscope to view samples and objects that cannot be seen with the unaided eye

spectroscopy

study of interaction between matter and radiated energy

energy

ability to do work

heat

(q) energy transferred due to temperature difference

work

energy transferred when a force causes movement or a system change in volume

enthalpy

(H) the heat/energy associated with a system

entropy

(S) measure of how spread out or disordered energy/matter in a system

ΔH<0

exothermic (release)

ΔH>0

endothermic (absorbs)

thermodynamics

study of the relationship between heat of other forms of energy

1st law

energy can be transferred from the system to the surroundings and vice versa

internal energy

a state function, depending on current state of system and is independent of how that state was prepared

state function

relates to system state quantities, does not depend on the path the system arrived at it’s equilibrium state

system

part of the world that we are interested in

surroundings

where we make our observations, separated by a boundary

work

how heat/energy is expressed

adiabatic wall

boundary that does not permit the transfer of energy even though there is a temperature difference between the system and the surrounding

Esystem =

w + q

if work and heat increase

internal energy is greater than 0

if heat increases and work stays the same

internal energy is greater than 0

if heat decreases and work stays the same

internal energy is greater than 0

conservation of energy

heat and work are equivalent ways or changing a system’s internal energy

ΔU means

energy passed through the boundary as heat or work [closed]

Chemical reaction system is

the actual reaction

Chemical reaction boundary is

the container

electrical work

chemically driven work

expansion work

change is volume

Pex

expansion against constant pressure

work / pressure / volume equation

w = -P(ΔV)

heat at constant temperature equation

q = nΔH

E,P, and V depend

solely on the current state of the system

constant pressure reaction equation

ΔH = ΔU + Δ(PV)

Hsys equation

Hsys = U + PV

constant volume reaction equation

ΔU = q_v (change in internal energy is equal to the heat exchanged at constant volume)

what happens if the internal energy (ΔU) and temperature decrease

system loses heat / does work on surroundings

what happens if the internal energy (ΔU) and temperature increase

system gains heat/ surroundings do work