For the reaction to generate 2‐phosphoglycerate (2PG) from 3‐phosphoglycerate (3PG, ΔG = 0.83 kJ/mol; ΔGo’ = 4.4 kJ/mol. (R = 8.31 x 10‐3 kJ•K‐1•mol‐1)
a)What is the ratio of 3PG:2PG in cells at 37C?
b)Considering your result, is the reaction under cellular conditions favoring the formation of 3PG or
the formation of 2PG?
To answer these questions, we need to utilize the Gibbs-Helmholtz equation, which relates the change in Gibbs free energy (ΔG) to temperature (T) and the standard Gibbs free energy change (ΔGo'):
ΔG = ΔGo' + RTln(Q)
Where:
ΔG is the actual Gibbs free energy change
ΔGo' is the standard Gibbs free energy change
R is the gas constant (8.31 x 10^(-3) kJ•K^(-1)•mol^(-1))
T is the temperature in Kelvin
Q is the reaction quotient
Now let's answer each question step by step:
a) To find the ratio of 3PG to 2PG in cells at 37°C, we need to use the equation:
ΔG = ΔGo' + RTln(Q)
Since we want to find the ratio, we can assume that the reaction is at equilibrium (ΔG = 0), so the equation becomes:
0 = ΔGo' + RTln(Q)
Rearranging the equation, we can solve for the ratio (Q):
Q = exp(-ΔGo' / RT)
Plugging in the given values:
ΔGo' = 4.4 kJ/mol
R = 8.31 x 10^(-3) kJ•K^(-1)•mol^(-1)
T = 37°C = 310 K
Q = exp(-4.4 / (8.31 x 10^(-3) * 310))
Calculating Q will give us the ratio of 3PG to 2PG in cells at 37°C.
b) Once we have the ratio of 3PG to 2PG (from part a), we can determine whether the reaction under cellular conditions is favoring the formation of 3PG or 2PG.
If the ratio of 3PG to 2PG is greater than 1, it means there is more 3PG than 2PG, indicating that the reaction is favoring the formation of 3PG. On the other hand, if the ratio is less than 1, it means there is more 2PG than 3PG, indicating that the reaction is favoring the formation of 2PG.
So, by comparing the calculated ratio from part a to 1, we can determine which product is favored under cellular conditions.
To calculate the ratio of 3PG:2PG in cells at 37°C, we can use the formula for the calculation of equilibrium constant (K) at a given temperature:
ΔGo' = -R * T * ln(K)
Where:
ΔGo' = standard free energy change
R = gas constant (8.31 x 10^-3 kJ•K^-1•mol^-1)
T = temperature in Kelvin
Rearranging the equation gives us:
K = e^(-ΔGo' / (R * T))
Let's substitute the given values and calculate the equilibrium constant (K) first:
K = e^(-4.4 kJ/mol / (8.31 x 10^-3 kJ•K^-1•mol^-1 * (37°C + 273.15 K)))
K ≈ e^(-4.4 / (8.31 * 310.15))
K ≈ e^(-4.4 / 2575.9865)
K ≈ e^-0.001708
K ≈ 0.99829482
Now, we can determine the ratio of 3PG:2PG using the equilibrium constant (K). Let's assume the initial concentration of 3PG is x (mol) and the initial concentration of 2PG is y (mol). At equilibrium, the concentrations can be calculated as follows:
3PG: y / x + y = K
2PG: x / x + y = 1 - K
To simplify:
3PG: y / (x + y) = K
2PG: x / (x + y) = 1 - K
Substituting the value for K:
3PG: y / (x + y) = 0.99829482
2PG: x / (x + y) = 1 - 0.99829482
Simplifying further will give us the ratio of 3PG:2PG.