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13 September, 16:27

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?

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  1. 13 September, 18:15
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    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
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