Question

A reaction will be spontaneous only at low temperatures if both ΔH and ΔS are negative. For a reaction in which ΔH = −320.1 kJ/mol and ΔS = −98.00 J/K · mol, determine the temperature (in °C) below which the reaction is spontaneous.

Answer 1

2993 °C

Step-by-step explanation:

A reaction is spontaneous if the free Gibbs energy (ΔG) is negative. ΔG is related to the enthalpy of the reaction (ΔH) and the entropy of the reaction (ΔS) through the following expression.

ΔG = ΔH - T . ΔS

For 1 mol, if ΔG < 0, then

ΔH - T . ΔS < 0

ΔH < T . ΔS

-320.1 × 10³ J < T . (-98.00 J/K)

T < 3266 K

To convert Kelvin to Celsius we use the following expression.

K = °C + 273.15

°C = K - 273.15 = 3266 - 273.15 = 2993 °C