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)+H20(l)-->ADP(aq)+HPO4^2-(aq) for which Delta G°rxn = –30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of Delta Grxn in a biological cell in which [ATP] = 5.0 mM, [ADP] = 0.60 mM, and [HPO42–] = 5.0 mM.

Question

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)+H20(l)-->ADP(aq)+HPO4^2-(aq) for which Delta G°rxn = –30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of Delta Grxn in a biological cell in which [ATP] = 5.0 mM, [ADP] = 0.60 mM, and [HPO42–] = 5.0 mM.

Answer 1

delta G rxn = dGo + RTlnQ where

Q = (ADP)(HPO4^2-)/(ATP)

Answer 2

Watch the units. dGo part in kJ and +RTlnK part in J

Answer 3

To calculate the value of ΔG°rxn in a biological cell, we need to use the equation:

ΔG°rxn = -RT ln(K)
where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and K is the equilibrium constant.

First, let's convert the temperature from Celsius to Kelvin by adding 273.15:

T = 37.0 + 273.15 = 310.15 K

Next, we need to calculate the equilibrium constant, K. We can use the concentrations of the reactants and products to find K:

K = ([ADP] * [HPO4^2-]) / ([ATP] * [H2O])

Substituting the given concentrations:

K = (0.60 mM * 5.0 mM) / (5.0 mM * 1.0 M)

K = 0.12

Now, we can calculate ΔG°rxn using the equation:

ΔG°rxn = -RT ln(K)

Substituting the values:

ΔG°rxn = -(8.314 J/(mol·K) * 310.15 K) * ln(0.12)

ΔG°rxn = -8070 J/mol

Finally, to convert ΔG°rxn from Joules to kilojoules:

ΔG°rxn = -8070 J/mol / 1000 J/kJ

ΔG°rxn = -8.07 kJ/mol

Therefore, the value of ΔG°rxn in the biological cell is approximately -8.07 kJ/mol.