For a chemical reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ $\left(\Delta_{\mathrm{r}} \mathrm{H}^{\ominus}=80 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ the entropy change $\Delta_{\mathrm{r}} \mathrm{S}^{\ominus}$ depends on the temperature T (in K) as $\Delta_{\mathrm{r}} \mathrm{S}^{\ominus}=2 \mathrm{~T}\left(\mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$. Minimum temperature at which it will become spontaneous is ______ K. (Integer)

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Chemical Thermodynamics

For a chemical reaction

A + B ⇌ C + D

(Δ_{r} H^{⊖} = 80 kJ mol^{- 1})

the entropy change

Δ_{r} S^{⊖}

depends on the temperature T (in K) as

Δ_{r} S^{⊖} = 2 T (JK^{- 1} mol^{- 1})

.
Minimum temperature at which it will become spontaneous is ______ K. (Integer)

Answer: 200

The reaction runs of its own accord once

Δ_{r} G^{⊖}

turns negative. With

Δ_{r} H^{⊖} = 80 kJ mo l^{- 1} = 80000 J mo l^{- 1}

and

Δ_{r} S^{⊖} = 2 T J K^{- 1} mo l^{- 1}

Δ_{r} G^{⊖} = Δ_{r} H^{⊖} - T Δ_{r} S^{⊖} = 80000 - T (2 T) = 80000 - 2 T^{2}

This becomes negative when

2 T^{2} > 80000 \Rightarrow T^{2} > 40000 \Rightarrow T > 200

The minimum temperature at which the reaction becomes spontaneous is

200

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Integer answer