A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of adenosine triphosphate, ATP, to adenosine diphosphate, ADP, as described by
ATP(aq) +H2O (l) --->ADP(aq) +HPO4^2-
for which ΔG°rxn = –30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of ΔGrxn in a biological cell in which [ATP] = 5.0 mM, [ADP] = 0.90 mM, and [HPO4^2–] = 5.0 mM.
dGrxn = dGo + RTln Q
To calculate the value of ΔGrxn in a biological cell, we can use the equation:
ΔGrxn = ΔG°rxn + RT ln(Q)
Where:
- ΔGrxn represents the change in Gibbs free energy of the reaction under specific conditions.
- ΔG°rxn is the standard Gibbs free energy change, given as -30.5 kJ/mol.
- R is the gas constant (8.314 J/(mol·K)).
- T is the temperature in Kelvin.
- Q is the reaction quotient.
First, we need to convert the temperatures from Celsius to Kelvin:
T(K) = 37.0 + 273.15
T(K) = 310.15 K
Next, we need to calculate the reaction quotient, Q:
Q = [ADP][HPO4^2–] / [ATP]
Q = (0.90 mM)(5.0 mM) / (5.0 mM)
Q = 0.90
Now we can substitute the values into the equation and calculate ΔGrxn:
ΔGrxn = -30.5 kJ/mol + (8.314 J/(mol·K))(310.15 K) ln(0.90)
ΔGrxn = -30.5 kJ/mol + (8.314 J/(mol·K))(310.15 K) ln(0.90)
Simplifying the equation will give you the value of ΔGrxn.