# Difference Between Delta G And Delta G Prime

We define ΔG0(pronounced “Delta G zero dash”) as the change in free energy of a reaction under “standard conditions”, as defined below: All reactants and products have an initial concentration of 1.0 M. Thermodynamics.

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The prime usually denotes a standard free energy that corresponds to an apparent equilibrium constant where the concentration (or activity) of one or more constituents is held constant.

For example, for $ce{HA <=>A- + H+}$ the equilibrium constant is $K=frac{[ce{A-}][ce{H+}]}{[ce{HA}]}$ and the corresponding standard free energy change is $Delta G^circ=-RT ln(K)$. If you know the value of $K$ and the start concentration of $ce{HA}$ then you can compute the equilibrium concentrations of $ce{HA}$, $ce{A-}$, and $ce{H+}$.

However, if the pH is held constant then $[ce{H+}]$ is no longer a free variable and the apparent equilibrium constant is $K=frac{[ce{A-}]}{[ce{HA}]}$ and the corresponding standard free energy change is $Delta G^circ=-RT ln(K)$. So $Delta G^circ=-RT ln(K/[ce{H+}])=Delta G^circ+RTln[ce{H+}]$

In biochemistry there is often several important constituents in addition to $ce{H+}$ that are held constant such as $ce{Mg++}$, phosphate, etc.

One form of the fundamental equation of thermodynamics is:

$$dU = TdS – P dV + sum_{i}mu_i dN_i$$

In this equation, the total internal energy has canonical variables $V$, $S$, and $dN_i$, where $S$ is the total entropy (in units of $frac{mathrm J}{mathrm K}$), $V$ is the total volume, and $N_i$ is the number of moles of each molecular species present. $T$ is temperature; $P$ is pressure, and $mu_i$ is the chemical potential of species $i$. The equation implies that if we were to know an equation that gave $U$ as a function of $S$, $V$, and all the $N_i$ we would know everything about the system. However, this is inconvenient for two reasons. First, $S$ and $V$ are extensive variables. Make the system bigger without changing its composition, and $S$ and $V$ increase. Second and more importantly, it is often difficult to hold $S$ constant when doing experiments. The same is true of $V$. (We live in a constant pressure atmosphere.)

Taking the Legendre transform of $U$ with respect to variables $S$ and $V$ gives a new fundamental equation:

$$dG = -S dT + V dP + sum_{i}mu_i dN_i$$

This equation means that if we knew a function that gave the Gibbs free energy as a function of $T$, $P$, and all the $N_i$, we could easily compute all thermodynamic properties of the system.

Say were interested in the thermodynamics of ATP hydrolysis:

$ce{ATP + H2O <=> ADP + Pi}$

This equation is really better written as

$ce{A-P3O10H3 + H2O -> A-P2O7H2 + H3PO4}$

But of course in a buffer at pH 7, the conditions where many biochemical reactions occur, there really wont be $ce{H3PO4}$ etc., there will be dissociation of protons $ce{H+}$ and formation of anions like $ce{H2PO4-}$ etc. So now all those reactions will have to be tracked too. The number of protons released by ATP is not the same as released by inorganic phosphate, and this is generally true. During a reaction, it is difficult to hold the number $N_{ce{H+}}$ of protons constant, but through judicious choice of buffers etc. it is possible to hold the chemical potential of protons constant (i.e. do experiments at constant pH). Under such conditions, it makes sense to continue the Legendre transformations one step further:

$$dG^prime = -S dT + V dP – N_{ce{H+}} dmu_{ce{H+}} + sum_{i eq ce{H+}}mu_i dN_i$$

$Delta G^{circ prime}$ is a Legendre transform of $Delta G^{circ}$ with respect to the number of protons in the system.

Robert Albertys paper from 1994 is a good place for further reading.

The prime has nothing to do with whether a concentration is held constant. The prime is used to indicate that some species, typically protons or ions such as Mg, are being set to a value other than the standard 1M concentration for use in a reference free energy. Although the prime has been adopted by some in the biochemical community and was endorsed in 1994 by IUPAC, the prime is not used in other communities for good reason – it is much better to explicitly state what concentrations are being used for the reference free energy. When using a reference free energy other than the standard free energy, concentrations can vary or be held fixed. In most biochemical situations, it is useful to keep the pH fixed since buffers are used. But this is a separate issue.

The biochemistry convention does not assume all solutions are 1 M. If you did this then you would have [H+] = 1 M. This simply never happens in biochemical reactions. Instead, we assume pH = 7. We also assume that water has an activity of 1 even though its concentration is 55 M.

Delta G naught means that the reaction is under standard conditions (25 celsius, 1 M concentraion of all reactants, and 1 atm pressure). Delta G naught prime means that the pH is 7 (physiologic conditions) everything else is the same. The concentration of [H+] now isnt 1 molar because 1 molar concentration would be an extremely low pH (0). Delta G naught prime is just like Delta G naught but for biology.

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The universe must always conserve energy and move toward increased entropy. Chemical reactions must move towards lower energy states, releasing energy and causing an increase in disorder. Thermodynamics can easily tell us whether a reaction is possible and will occur spontaneously; it is more difficult to tell how quickly the reaction will occur.

Gibbs free energy, denoted G and measured in J/mol, is a measurement of a system’s usable energy content. A reaction will occur spontaneously if ΔG < 0.

H20 has a tetrahedral shape with two H and two lone pairs of electrons as the four prongs. O is much more electronegative than H, making water quite polar. Each H can donate a hydrogen bond and each lone pair can accept one. In ice, every H2O molecule forms 4 hydrogen bonds; in water, ~3.4, and in steam, 0. Above 0°C, T is high enough to make the increase in entropy due to melting outweigh the decrease in enthalpy due to breaking the favorable hydrogen bonds, such that ΔH – TΔS < 0.

It has been determined empirically through conductivity experiments that in water, [H+][OH-] = 1e-14, always. For water, Keq = [H+][OH-]/[H2O]. We rearrange this to say Keq[H2O] = [H+][OH-] and then we define the left half of the equation as Kw such that Kw = [H+][OH-] = 1e-14.

At equilibrium a reaction is proceeding at equal rates in both directions, such that the concentrations of reactants and products are not changing. It doesn’t mean the concentrations are equal. For a reaction A+B ↔ C+D, we define the equilibrium constant Keq =([C]eq[D]eq)/([A]eq[B]eq). Keq > 1 means C and D are more abundant at equilibrium, Keq < 1 means A and B are more abundant at equilibrium, and K == 1 means the two products are equal.

## What does naught mean in Delta H?

just deltaH can make reference to the enthalpy of anything, unspecified reaction, temperature, pressure, etc. Naught means standard conditions (1 atm 298 K)

## FAQ

What is Delta G Prime mean?

We define ΔG0‘ (pronounced “delta G naught prime”) as the free energy change of a reaction under “standard conditions” which are defined as: All reactants and products are at an initial concentration of 1.0M. Pressure of 1.0 atm. Temperature is 25°C.

What is the relationship between ∆ G and ∆ G?

A negative ∆G means that the reactants, or initial state, have more free energy than the products, or final state. Exergonic reactions are also called spontaneous reactions, because they can occur without the addition of energy.

How do you find Delta G from Delta G prime?

A negative ∆G means that the reactants, or initial state, have more free energy than the products, or final state. Exergonic reactions are also called spontaneous reactions, because they can occur without the addition of energy.

What does negative delta G Prime mean?

A negative ∆G means that the reactants, or initial state, have more free energy than the products, or final state. Exergonic reactions are also called spontaneous reactions, because they can occur without the addition of energy.