Q13.27 P - Chemistry: Molecular Nature Of Matter And Change

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? 

 

Step-by-Step Solution

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 1: 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.,

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

   
   

   
   

   
   

   
   

Step 2: The condition for &#916;H solution 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.