For a particular reaction, δh∘=20.1 kj/mol and δ∘=45.9 j/(mol⋅k). assuming these values change very little with temperature, at what temperature does the reaction change from nonspontaneous to spontaneous in the forward direction? t= k is the reaction in the forward direction spontaneous at temperatures greater than or less than the calculated temperature?

The temperature should be higher than 437.9 Kelvin (or 164.75 °C) to be spontaneous

Explanation:

Step 1: Data given

ΔH∘=20.1 kJ/mol

ΔS is 45.9 J/K

Step 2: When is the reaction spontaneous

Consider temperature and pressure = constant.

The conditions for spontaneous reactions are:

ΔH <0

ΔS  > 0

ΔG <0  The reaction is spontaneous at all temperatures

ΔH <0

ΔS  <0

ΔG <0 The reaction is spontaneous at low temperatures ( ΔH - T*ΔS <0)

ΔH >0

ΔS  >0

ΔG <0 The reaction is spontaneous at high temperatures ( ΔH - T*ΔS <0)

Step 3: Calculate the temperature

ΔG <0 = ΔH - T*ΔS

T*ΔS > ΔH

T > ΔH/ΔS

In this situation:

T > (20100 J)/(45.9 J/K)

T > 437.9 K

T > 164.75 °C

The temperature should be higher than 437.9 Kelvin (or 164.75 °C) to be spontaneous