The production of fruit juice at a free energy change of -345KJ/mol and equilibrium constant of 3.66x10^12 occurred at a temperature
(Gas constant=8.314KJ/mol)
To determine the temperature at which the production of fruit juice occurs, we can use the equation:
ΔG = -RTln(K)
Where:
ΔG is the free energy change (-345 KJ/mol)
R is the gas constant (8.314 KJ/mol)
T is the temperature (in Kelvin)
ln denotes the natural logarithm
K is the equilibrium constant (3.66x10^12)
First, let's convert the free energy change from KJ/mol to J/mol:
ΔG = -345 KJ/mol = -345,000 J/mol
Now, rearranging the equation to solve for T:
T = -ΔG / (R * ln(K))
Substituting the given values:
T = -(-345,000 J/mol) / (8.314 KJ/mol * ln(3.66x10^12))
Note: Since the gas constant, R, is given in KJ/mol, we need to convert the free energy change from J/mol back to KJ/mol.
T = 345,000 J/mol / (8.314 KJ/mol * ln(3.66x10^12))
Now, we can use a scientific calculator to evaluate ln(3.66x10^12) and perform the calculation:
T ≈ 345,000 J/mol / (8.314 KJ/mol * 27.491)
Simplifying further:
T ≈ 1655.17 K
Therefore, the temperature at which the production of fruit juice occurs is approximately 1655.17 Kelvin.
Options
A.273K
B.288K
C.200K
D.373K?