An endothermic reaction has a positive internal energy change Δ E. In such a case, what is the minimum value that the activation energy can have?

Question

An endothermic reaction has a positive internal energy change Δ E. In such a case, what is the minimum value that the activation energy can have? (A)  Δ E  (B)  Δ E=Δ H+Δ ngRT  (C)  Δ E=Δ H-Δ ngRT  (D)  Δ E=Ea+RT

Tardigrade Admin · Accepted Answer

From first law of thermodynamics,
we have

Δ E = Q + W \dots

(i)
Here,

Δ E =

change in internal energy,

= Δ EQ =

heat of the reaction

= Δ H W =

work done

= - P Δ V (∵

Reaction is endothermic.

)

= Δ n_{g} RT

Thus, Eq. (i)
becomes

Δ E = Δ H - Δ n_{g} RT

Q. An endothermic reaction has a positive internal energy change $Δ E$ . In such a case, what is the minimum value that the activation energy can have?

$Δ E$

$Δ E = Δ H + Δ n_{g} RT$

$Δ E = Δ H - Δ n_{g} RT$

$Δ E = E_{a} + RT$

From first law of thermodynamics,
we have $Δ E = Q + W \dots$ (i)
Here, $Δ E =$ change in internal energy,
$= Δ EQ =$ heat of the reaction
$= Δ H W =$ work done
$= - P Δ V (∵$ Reaction is endothermic. $)$
$= Δ n_{g} RT$ Thus, Eq. (i)
becomes $Δ E = Δ H - Δ n_{g} RT$

Q. An endothermic reaction has a positive internal energy change ΔE. In such a case, what is the minimum value that the activation energy can have?

ΔE

ΔE=ΔH+Δng​RT

ΔE=ΔH−Δng​RT

ΔE=Ea​+RT