Answer:
[tex]V_{HCl}=0.208L=208mL[/tex]
Explanation:
Hello,
In this case, since the chemical reaction is:
[tex]2HCl+Mg(OH)_2\rightarrow MgCl_2+2H_2O[/tex]
We can see that hydrochloric acid and magnesium hydroxide are in a 2:1 mole ratio, which means that the neutralization point, we can write:
[tex]n_{HCl}=2*n_{Mg(OH)_2}[/tex]
In such a way, the moles of magnesium hydroxide (molar mass 58.3 g/mol) in 500 mg are:
[tex]n_{Mg(OH)_2}=500mg*\frac{1g}{1000mg}*\frac{1mol}{58.3g} =0.00858mol[/tex]
Next, since the pH of hydrochloric acid is 1.25, the concentration of H⁺ as well as the acid (strong acid) is:
[tex][H^+]=[HCl]=10^{-pH}=10^{-1.25}=0.0562M[/tex]
Then, since the concentration and the volume define the moles, we can write:
[tex][HCl]*V_{HCl}=2*n_{Mg(OH)_2}[/tex]
Therefore, the neutralized volume turns out:
[tex]V_{HCl}=\frac{2*0.00858mol}{0.0562\frac{mol}{L} }\\ \\V_{HCl}=0.208L=208mL[/tex]
Best regards.
