Question

A reaction occurs spontaneously if:

• A. T\(\triangle\)S < \(\triangle\)H and both \(\triangle\)H and \(\triangle\)S are +ve
• B. T\(\triangle\)S > \(\triangle\)H and both \(\triangle\)H and \(\triangle\)S are +ve
• C. T\(\triangle\)S = \(\triangle\)H and both \(\triangle\)H and \(\triangle\)S are +ve
• D. T\(\triangle\)S >\(\triangle\)H and \(\triangle\)H is +ve and \(\triangle\)S is -ve

Answer 1

The Correct Option is B

To determine when a reaction occurs spontaneously, we need to consider the Gibbs free energy change (\(\Delta G\)) of the reaction. The formula for Gibbs free energy is:

\(\Delta G = \Delta H - T\Delta S\)

Where:

• \(\Delta G\) is the change in Gibbs free energy. 
• \(\Delta H\) is the change in enthalpy.
• \(\Delta S\) is the change in entropy.
• \(T\) is the temperature in Kelvin.

A reaction is spontaneous if \(\Delta G\) is negative (\(\Delta G < 0\)). This can happen under the following conditions:

1. \(\Delta H\) is negative, \(\Delta S\) is positive: This will always result in \(\Delta G < 0\), regardless of the temperature.
2. \(\Delta H\) is negative, \(\Delta S\) is negative: The reaction is spontaneous at low temperatures.
3. \(\Delta H\) is positive, \(\Delta S\) is positive: The reaction is spontaneous at high temperatures.
4. \(\Delta H\) is positive, \(\Delta S\) is negative: The reaction is never spontaneous.

Given the options, we have to find when both \(\Delta H\) and \(\Delta S\) are positive and the reaction is spontaneous. For this scenario:

If T\(\Delta S\) > \(\Delta H\), then \(\Delta G\) will be negative, indicating a spontaneous reaction.

Therefore, the correct answer is: T\(\Delta S\) > \(\Delta H\) and both \(\Delta H\) and \(\Delta S\) are positive.