Question

How can endothermic reactions be spontaneous?

Answer 1

Endothermic reaction can only be spontaneous when molar entropy is sufficient or more to make $\Delta \text{G}$ negative and to overcome the endothermicity. Endothermic reactions are reactions that need external energy far away from the reaction to start and proceed.

Complete step by step answer:
Spontaneous reactions are that reaction which place on their own. Or spontaneous reactions happen ‘’automatically’’ i.e. do not require an input of energy to occur.
Chemical reaction can only occur spontaneously when the total free energy of products is less than the reactants. i.e. Reactions are spontaneous only when $\Delta \text{G}$, the change in free energy is negative. The $\Delta \text{G}$ is depend on or express as
$\Delta \text{G}=\Delta \text{H}-\text{T}\Delta \text{S}$
$\Delta \text{G}=$Change in free energy
$\Delta \text{H}=$ change in ‘’enthalpy’’
$\text{T}=$ Temperature in kelvin
$\Delta \text{S}=$ Change in ‘’entropy’’
Enthalpy is defined as the total kinetic and potential energy of a system at a constant pressure.
Entropy is defined as the degree of randomness or disorder of a system.
Endothermic reaction have positive value of $\Delta \text{H}\text{.}\,\Delta \text{G}$ will be negative only if $\text{T}\Delta \text{S}$ is bigger than $\Delta \text{H}$. Hence these reactions are spontaneous only if the entropy increase is sufficient to overcome the unfavourable enthalpy change.
Endothermic reactions generally involve a change of state. Examples increase, hence endothermic reaction, as when ice melts into water when placed at room temperature.

Note:
There is a term which is called endothermic salvation, not reaction because reactant recovered unchanged and no new product formed. Where some salts dissolve in water, there is cooling effect as the entropy increases e.g. The ice pack use or treatment of injuries and sports injuries.