Question

For ${\mathbf{\Delta H}}_{\mathbf{solution}}$to be very small, what quantities must be nearly equal in magnitude? Will their signs be the same or opposite?

Short answer

The quantities that must be nearly equal in magnitude are

${\mathbf{\Delta H}}_{\mathbf{mix}}\mathbf{=}\mathbf{(}\mathbf{\Delta }{\mathbf{H}}_{\mathbf{solute}}\mathbf{+}{\mathbf{\Delta H}}_{\mathbf{solvent}}\mathbf{)}$

Their signs will be the opposite.

Step-by-step solution

To calculate the enthalpy of the solution.

1. Solute particles separate from one another.This process is endothermic because it involves the breaking of bonds between solute molecules so, requires energy.$\mathbf{Solute}\mathbf{}\left(\mathbf{aggregated}\right)\mathbf{+}\mathbf{heat}\mathbf{}\mathbf{solute}\mathbf{}\mathbf{\left(}\mathbf{separated}\mathbf{\right)}\mathbf{;}\mathbf{}\text{here,}{\mathbf{\Delta H}}_{\mathbf{solute}\mathbf{}}\mathbf{>}\mathbf{0}$

2. Solvent particles separate from one another.This process is also endothermic because it also requires energy in breaking bonds.$\mathbf{Solvent}\mathbf{}\left(\mathbf{aggregated}\right)\mathbf{}\mathbf{+}\mathbf{}\mathbf{heatsolvent}\mathbf{}\mathbf{\left(}\mathbf{separated}\mathbf{\right)}\mathbf{;}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\text{here,}{\mathbf{\Delta H}}_{\mathbf{solvent}}\mathbf{>}\mathbf{0}$

   
   

3. Solute and solvent particles mix together. This process is exothermic because here particles attract each other, so energy is released.$\mathbf{solute}\mathbf{}\left(\mathbf{separated}\right)\mathbf{}\mathbf{+}\mathbf{}\mathbf{solvent}\left(\mathbf{separated}\right)\mathbf{}\mathbf{solution}\mathbf{}\mathbf{+}\mathbf{}\mathbf{heat}\mathbf{;}\mathbf{}\mathbf{}\text{here,}\mathbf{\Delta }{{\mathbf{H}}_{\mathbf{mix}}}_{\mathbf{}}\mathbf{<}\mathbf{0}$

   
   

   The overall process is called the thermochemical solution cycle.

   Total enthalpy change is obtained by combining all the enthalpy changes during the complete process, i.e.,

   ${\mathbf{\Delta H}}_{\mathbf{solution}}\mathbf{=}{\mathbf{\Delta H}}_{\mathbf{solute}}\mathbf{+}{\mathbf{\Delta H}}_{\mathbf{solvent}}\mathbf{+}{\mathbf{\Delta H}}_{\mathbf{mix}}$
   

   
   

   
   

   
   

   
   

The condition for ΔHsolution to be very small.

For $\Delta H_{solution}$to be very small, the enthalpy change is because of the mixing of solute and solvent must be equal to the combined enthalpy change when the solute and solvent particles are separated.