To determine the mass of magnesium (Mg) required to react completely with the given amount of hydrochloric acid (HCl), we can follow these steps:
### Step 1: Determine the Moles of HCl
From the problem statement, it is given that 0.25 moles of HCl are to react.
### Step 2: Use the Balanced Chemical Equation
The balanced chemical equation for the reaction is:
[tex]\[ 2 \, \text{HCl} (aq) + \text{Mg} (s) \rightarrow \text{MgCl}_2 (aq) + \text{H}_2 (g) \][/tex]
From this equation, we see that 2 moles of HCl react with 1 mole of Mg. Therefore, the mole ratio of HCl to Mg is 2:1.
### Step 3: Calculate the Moles of Mg Required
Using the mole ratio (2 moles HCl : 1 mole Mg), we can calculate the moles of Mg needed:
[tex]\[ \text{moles of Mg} = \text{moles of HCl} \times \left(\frac{1 \, \text{mole Mg}}{2 \, \text{moles HCl}}\right) \][/tex]
Plugging in the given moles of HCl:
[tex]\[ \text{moles of Mg} = 0.25 \, \text{moles HCl} \times \left(\frac{1}{2}\right) \][/tex]
[tex]\[ \text{moles of Mg} = 0.125 \, \text{moles of Mg} \][/tex]
### Step 4: Calculate the Mass of Mg Required
The mass of a substance can be calculated using the formula:
[tex]\[ \text{mass} = \text{moles} \times \text{molar mass} \][/tex]
From the problem, the molar mass of Mg is provided as [tex]\( 24.31 \, \text{g/mol} \)[/tex].
[tex]\[ \text{mass of Mg} = 0.125 \, \text{moles} \times 24.31 \, \text{g/mol} \][/tex]
[tex]\[ \text{mass of Mg} = 3.03875 \, \text{g} \][/tex]
### Conclusion
Therefore, the mass of Mg required to react completely with 250 mL of 1.0 M HCl is [tex]\( 3.03875 \, \text{grams} \)[/tex].
