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

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:

[tex]3Mg(OH)_2+2H_3PO_4\rightarrow Mg_3(PO_4)_2+6H_2O[/tex]

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

[tex]2M_{Mg(OH)_2}V_{Mg(OH)_2}=3M_{H_3PO_4}V_{H_3PO_4}[/tex]

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

[tex]M_{Mg(OH)_2}=\frac{3M_{H_3PO_4}V_{H_3PO_4}}{2V_{Mg(OH)_2}} \\\\M_{Mg(OH)_2}=\frac{3*0.20M*0.0300L}{2*0.050L}=0.18M[/tex]

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

[tex]Mg(OH)_2+2HCl\rightarrow MgCl_2+2H_2O[/tex]

[tex]2M_{Mg(OH)_2}V_{Mg(OH)_2}=M_{HCl}V_{HCl}[/tex]

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

[tex]M_{HCl}=\frac{2M_{Mg(OH)_2}V_{Mg(OH)_2}}{V_{HCl}} \\\\M_{HCl}=\frac{2*0.18M*0.078L}{0.025L}\\\\M_{HCl} = 1.12M[/tex]

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