A reaction has a standard free-energy change of -11.80 kJ/mol (-2.820 kcal/mol). Calculate the equilibrium constant for the reaction at 25 degrees C.
Please help!
DGo = -RTlnK.
To calculate the equilibrium constant (K) for a reaction, you need the standard free-energy change (ΔG°) and the temperature (T). The equation that relates these values is:
ΔG° = -RT ln(K)
Where:
ΔG° is the standard free-energy change
R is the gas constant (8.314 J/(mol·K) or 1.987 cal/(mol·K))
T is the temperature in Kelvin
ln is the natural logarithm
In this case, we have the ΔG° value (-11.80 kJ/mol or -2.820 kcal/mol), but we need to convert it to the SI unit of Joules/mol before using it in the equation.
To convert kJ/mol to J/mol:
ΔG° (in J/mol) = ΔG° (in kJ/mol) × 1000
So, ΔG° = -11.80 kJ/mol × 1000 = -11,800 J/mol
Next, we convert from J/mol to cal/mol, assuming 1 cal = 4.184 J:
ΔG° (in cal/mol) = ΔG° (in J/mol) / 4.184
Therefore, ΔG° (in cal/mol) = -11,800 J/mol / 4.184 ≈ -2,819.7 cal/mol ≈ -2,820 cal/mol
Now, we can rearrange the equation to solve for K:
ln(K) = -ΔG° / (RT)
To get the equilibrium constant (K), we need to exponentiate both sides of the equation using the base e (the exponential constant).
K = e^(-ΔG° / (RT))
Finally, we can plug in the known values:
ΔG° = -2,820 cal/mol
R = 1.987 cal/(mol·K)
T = 25 °C = 298 K
K = e^(-(-2820) / (1.987 × 298))
To calculate this, you can use a scientific calculator or an online calculator that has an exponential function (e^x).
Using this equation, you can determine the equilibrium constant (K) for the given reaction at 25 °C.