The equilibrium constant K for the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate is 1.66X10^5 at 37 degrees celcius, and Standard Delta H is -20.1 kJ/mol. Calculate Standard Delta S for the hydrolysis at 37 degrees celcius. On the assumption that Standard Delta H and Standard Delta S are temperature independent, calculate K at 25 degree celcius.
To calculate the standard delta S for the hydrolysis of ATP at 37 degrees Celsius, you can use the equation:
ΔG = ΔH - TΔS
Where:
ΔG is the standard Gibbs free energy change
ΔH is the standard enthalpy change
ΔS is the standard entropy change
T is the temperature in Kelvin
First, convert the temperature from Celsius to Kelvin:
37 degrees Celsius + 273.15 = 310.15 K
Now, rearrange the equation to isolate ΔS:
ΔS = (ΔH - ΔG)/T
We already have the value for ΔH (-20.1 kJ/mol), so we need to calculate ΔG. Use the relationship:
ΔG = -RT ln K
Where:
R is the gas constant (8.314 J/mol·K)
T is the temperature in Kelvin
ln K is the natural logarithm of the equilibrium constant at the given temperature
Substitute the values:
ΔG = - (8.314 J/mol·K) * (310.15 K) * ln (1.66x10^5)
Calculate ΔG, then substitute the values into the equation for ΔS to find the value at 37 degrees Celsius.
To calculate K at 25 degrees Celsius, you can use the equation:
ln(K2/K1) = ΔS/R * (1/T1 - 1/T2)
Where:
K1 is the equilibrium constant at T1 (37 degrees Celsius)
K2 is the equilibrium constant at T2 (25 degrees Celsius)
ΔS is the standard entropy change
R is the gas constant (8.314 J/mol·K)
T1 and T2 are the temperatures in Kelvin
Rearrange the equation to solve for K2:
K2 = K1 * e^(ΔS/R * (1/T1 - 1/T2))
Substitute the known values into the equation (K1 is the calculated value at 37 degrees Celsius, ΔS is the value obtained earlier, R is the gas constant, T1 is 37 degrees Celsius converted to Kelvin, and T2 is 25 degrees Celsius converted to Kelvin). Calculate K2 using these values.