Determining Spontaneity of Chemical Reactions at Different Temperatures

What factors determine the spontaneity of a chemical reaction at different temperatures?

Based on the data provided, how can we determine if a reaction is spontaneous at various temperature ranges?

Answer:

To determine the spontaneity of a chemical reaction at different temperatures, we need to consider the standard enthalpy change (ΔH) and the standard entropy change (ΔS). These factors play a crucial role in determining whether a reaction will be spontaneous or non-spontaneous under given temperature conditions.

In the given data, a reaction has a standard enthalpy change of 54.5 kJ and a standard entropy change of -124.5 J/K. The spontaneity of this reaction at different temperatures can be determined using the Gibbs free energy equation: ΔG = ΔH - TΔS

Where ΔG represents the Gibbs free energy change, ΔH is the standard enthalpy change, ΔS is the standard entropy change, and T is the temperature in Kelvin.

At no temperature (T = 0 K), the entropy change becomes irrelevant, and the reaction will be spontaneous if ΔH is negative. However, this scenario is not realistic as temperature is always greater than zero. Therefore, we need to consider the reaction at all temperatures.

The sign of ΔG at all temperatures depends on the relation between TΔS and ΔH. If TΔS is greater than ΔH, the reaction will be spontaneous, indicated by a negative ΔG. If TΔS is less than ΔH, the reaction will be non-spontaneous, with a positive ΔG value. When TΔS equals ΔH, the reaction will be at equilibrium, resulting in a ΔG of zero.

By calculating the temperature at which TΔS equals ΔH, we can determine the spontaneity of the reaction. In this case, T = 438 K, indicating that at temperatures below 438 K (T < 438 K), the reaction is non-spontaneous. Conversely, at temperatures above 438 K (T > 438 K), the reaction becomes spontaneous.

Therefore, the standard enthalpy change and standard entropy change of a reaction play a crucial role in determining its spontaneity at different temperatures. Utilizing the Gibbs free energy equation allows us to calculate the temperature at which the reaction transitions between being spontaneous and non-spontaneous.