Problem 10
Question
For a chemical reaction with \(K<1\), is \(\Delta G^{\circ}\) positive or negative?
Step-by-Step Solution
Verified Answer
For a chemical reaction with \(K<1\), \(\Delta G^{\circ}\) is positive.
1Step 1: Understanding the Gibbs Energy Change
The Gibbs Free Energy Change (\(\Delta G^{\circ}\)) is a thermodynamic quantity that measures the maximum reversible work a system can perform at constant temperature and pressure. It's given by the equation \(\Delta G^{\circ} = -RT \ln K\), where R is the universal gas constant, T is the temperature in Kelvin, and K is the Reaction Quotient.
2Step 2: Interpreting the Reaction Quotient
If \(K<1\), it indicates that the system hasn't reached equilibrium yet and the reactants are favored over the products. In other words, the forward reaction is not spontaneous.
3Step 3: Relating \(\Delta G^{\circ}\) and K
Substitute \(K<1\) into the Gibbs equation. Since the natural logarithm of a number less than 1 is negative, and that negative result is then multiplied by negative RT (as in the above equation), \(\Delta G^{\circ}\) must be positive. This indicates that the forward reaction is not spontaneous at standard conditions and energy must be added for it to proceed.
4Step 4: Drawing Conclusions
Therefore, for a chemical reaction with \(K<1\), \(\Delta G^{\circ}\) is positive. This shows that the reaction is not spontaneous under standard conditions, and instead require an input of energy.