Question

A 0.0250L solution of HCl is neutralized by 0.0780L of an unknown Mg(OH)2 solution. Also 0.050L of this Mg(OH)2 solution is neutralized by 0.0300L of a 0.20 M H3(PO3) solution. What is the concentration of the HCl solution

Answer 1

`M_(HCl) = 1.12M`

Step-by-step explanation:

Hello!

In this case, for the first reaction we need to focus on, the neutralization of magnesium hydroxide by phosphoric acid, we can write up the following equation:

`3Mg(OH)_2+2H_3PO_4\rightarrow Mg_3(PO_4)_2+6H_2O`

Whereas the acid and base react in a 3:2 mole ratio; thus, we can write:

`2M_(Mg(OH)_2)V_(Mg(OH)_2)=3M_(H_3PO_4)V_(H_3PO_4)`

Now, solving for the concentration of the magnesium hydroxide solution we get:

`M_(Mg(OH)_2)=(3M_(H_3PO_4)V_(H_3PO_4))/(2V_(Mg(OH)_2)) \\\\M_(Mg(OH)_2)=(3*0.20M*0.0300L)/(2*0.050L)=0.18M`

Now, for the reaction between hydrochloric acid and magnesium hydroxide we have:

`Mg(OH)_2+2HCl\rightarrow MgCl_2+2H_2O`

`2M_(Mg(OH)_2)V_(Mg(OH)_2)=M_(HCl)V_(HCl)`

Therefore, solving for the concentration of the hydrochloric acid solution we get:

`M_(HCl)=(2M_(Mg(OH)_2)V_(Mg(OH)_2))/(V_(HCl)) \\\\M_(HCl)=(2*0.18M*0.078L)/(0.025L)\\\\M_(HCl) = 1.12M`

Best regards!