Calculate the free energy of hydrolysis of ATP, ADP, Pi concentrations are 3.4, 1.3, and 4.8 mM respectively. (ATP hydrolysis has delta G= - kJ/mol)
To calculate the free energy of hydrolysis of ATP, we will use the formula:
ΔG = ΔG˚ + RTln([products]/[reactants])
Where:
ΔG is the free energy change of the reaction
ΔG˚ is the standard free energy change at standard conditions (usually at 1 M concentration)
R is the gas constant (8.314 J/mol·K or 0.008314 kJ/mol·K)
T is the temperature in Kelvin
ln is the natural logarithm
[products] and [reactants] are the concentrations of the products and reactants, respectively.
Given:
[ATP] = 3.4 mM
[ADP] = 1.3 mM
[Pi] = 4.8 mM
ΔG˚ = -kj/mol (assuming a specific value)
Before we begin, note that the concentrations provided are in millimoles per liter (mM), but we can convert them to moles per liter (M) by dividing by 1000.
First, we need to calculate the concentrations in M:
[ATP] = 3.4 mM = 3.4/1000 M = 0.0034 M
[ADP] = 1.3 mM = 1.3/1000 M = 0.0013 M
[Pi] = 4.8 mM = 4.8/1000 M = 0.0048 M
Now, let's substitute the values into the formula:
ΔG = ΔG˚ + RTln([products]/[reactants])
Assuming you have the specific value of ΔG˚, and a temperature value (in Kelvin), you can substitute those values into the equation to calculate ΔG.
To calculate the free energy of hydrolysis of ATP, we can use the equation:
ΔG = ΔG°' + RT ln(Q)
Where:
ΔG is the free energy of hydrolysis of ATP
ΔG°' is the standard free energy change (specifically for ATP hydrolysis, it is -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, which is the ratio of product concentrations to reactant concentrations.
In this case, we have the concentrations of ATP, ADP, and Pi as:
[ATP] = 3.4 mM
[ADP] = 1.3 mM
[Pi] = 4.8 mM
First, we need to convert the concentrations to mol/L:
[ATP] = 3.4 × 10^-3 mol/L
[ADP] = 1.3 × 10^-3 mol/L
[Pi] = 4.8 × 10^-3 mol/L
Assuming the reaction is:
ATP + H2O → ADP + Pi
The reaction quotient is given by:
Q = [ADP] × [Pi] / [ATP]
Substituting the values:
Q = (1.3 × 10^-3) × (4.8 × 10^-3) / (3.4 × 10^-3)
Now, we can calculate the free energy of hydrolysis using the equation mentioned earlier. Assuming room temperature (25°C or 298 K), we can calculate as follows:
ΔG = -30.5 kJ/mol + (8.314 J/(mol·K) × 298 K) × ln(Q)
Plug in the calculated value of Q into the equation and solve for ΔG.