Alright, let's tackle this problem step by step. The question involves a chemical reaction between magnesium hydroxide ([tex]\( Mg(OH)_2 \)[/tex]) and hydrochloric acid ([tex]\( HCl \)[/tex]). The balanced chemical equation for this reaction is:
[tex]\[ Mg(OH)_2(aq) + 2HCl(aq) \rightarrow 2H_2O(l) + MgCl_2(aq) \][/tex]
Given:
- The moles of hydrochloric acid ([tex]\( HCl \)[/tex]) are 0.321 moles.
- We need to find out how many moles of magnesium hydroxide ([tex]\( Mg(OH)_2 \)[/tex]) are required to react with the given amount of hydrochloric acid.
From the balanced equation, we see that 1 mole of [tex]\( Mg(OH)_2 \)[/tex] reacts with 2 moles of [tex]\( HCl \)[/tex]. This gives us a stoichiometric ratio:
[tex]\[ \frac{1 \text{ mole of } Mg(OH)_2}{2 \text{ moles of } HCl} \][/tex]
To find the required moles of [tex]\( Mg(OH)_2 \)[/tex], we can set up the following proportion:
[tex]\[ \text{Required moles of } Mg(OH)_2 = \frac{\text{Given moles of } HCl}{\text{Stoichiometric ratio}} \][/tex]
Substitute the given values and the ratio:
[tex]\[ \text{Required moles of } Mg(OH)_2 = \frac{0.321 \text{ moles of } HCl}{2} \][/tex]
Simplify the fraction:
[tex]\[ \text{Required moles of } Mg(OH)_2 = 0.1605 \text{ moles} \][/tex]
Therefore, 0.1605 moles of magnesium hydroxide are required to react with 0.321 moles of hydrochloric acid.
