To calculate \Delta G^\circ', we use the relationship between $\Delta G'$ and \Delta G^\circ':

\Delta G' = \Delta G^\circ' + RT \ln(Q)

where:

• $\Delta G'$ is the free energy change under experimental conditions, which is given as $-3.3 \, \text{kJ/mol}$.
• \Delta G^\circ' is the standard free energy change we want to find.
• $R$ is the universal gas constant, $8.314 \times 10^{-3} \, \text{kJ/(mol·K)}$.
• $T$ is the temperature in Kelvin (35°C = 308 K).
• $Q$ is the reaction quotient, which is the ratio of the concentrations of the unfolded and folded states.

Step 1: Calculate the reaction quotient $Q$.

The reaction quotient $Q$ is given by:

[ Q = \frac{[\text{unfolded}]}{[\text{folded}]} ]

In this experiment:

• $[\text{folded}] = 1 \, \mu M$
• $[\text{unfolded}] = 4 \, \mu M$

So:

$Q = \frac{4 \, \mu M}{1 \, \mu M} = 4$

Step 2: Substitute values into the equation.

-3.3 \, \text{kJ/mol} = \Delta G^\circ' + (8.314 \times 10^{-3} \, \text{kJ/(mol·K)})(308 \, \text{K}) \ln(4)

Calculate $RT \ln(4)$:

• $\ln(4) \approx 1.386$
• $RT \ln(4) = (8.314 \times 10^{-3})(308)(1.386)$

$RT \ln(4) \approx (2.561 \, \text{kJ/mol})$

Step 3: Solve for \Delta G^\circ'.

-3.3 \, \text{kJ/mol} = \Delta G^\circ' + 2.561 \, \text{kJ/mol}

\Delta G^\circ' = -3.3 \, \text{kJ/mol} - 2.561 \, \text{kJ/mol}

\Delta G^\circ' \approx -5.861 \, \text{kJ/mol}

So, the standard free energy change \Delta G^\circ' is approximately $-5.86 \, \text{kJ/mol}$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How does temperature affect the folding of a protein and its \Delta G^\circ'?
2. What does a negative \Delta G^\circ' indicate about a protein's folding stability?
3. How would the calculation change if the concentration of the folded and unfolded states were reversed?
4. What is the significance of the reaction quotient $Q$ in determining $\Delta G'$?
5. How do different values of \Delta G^\circ' relate to the equilibrium constant $K$ for protein folding?

Tip: Always check the units in thermodynamic calculations to ensure consistency, especially when working with temperatures and gas constants.