for a given solute the partition coefficient at room temperature 20c is 0.7 calculate the free energy and use this to estimate the temperature required to achieve 0.72 distribution ratio
To calculate the free energy, we need to use the equation:
ΔG = -RT ln(K)
Where:
ΔG is the change in Gibbs free energy
R is the ideal gas constant (approximately 8.314 J/mol·K)
T is the temperature in Kelvin (K)
ln(K) is the natural logarithm of the partition coefficient (K)
Given that the partition coefficient (K) is 0.7, we can calculate the free energy. However, we need to convert the temperature to Kelvin first.
Let's convert the room temperature from Celsius to Kelvin:
T(K) = 20°C + 273.15
T(K) = 293.15 K
Now we can calculate the free energy:
ΔG = -(8.314 J/mol·K)(293.15 K) ln(0.7)
Using a calculator:
ΔG ≈ -8.314 J/mol·K * 293.15 K * ln(0.7)
ΔG ≈ -5891.00 J/mol
Now, to estimate the temperature required to achieve a distribution ratio of 0.72, we rearrange the equation to solve for temperature:
ΔG = -RT ln(K)
Rearranging:
T = -ΔG / (R ln(K))
Given that ΔG = -5891.00 J/mol, R = 8.314 J/mol·K, and K = 0.72, we can plug in these values to estimate the temperature:
T = -( -5891.00 J/mol ) / ( 8.314 J/mol·K * ln(0.72) )
Using a calculator:
T ≈ 326.67 K
Therefore, the estimated temperature required to achieve a distribution ratio of 0.72 is approximately 326.67 Kelvin.