To find the molar concentration of the NaOH solution, we need to follow a series of steps based on stoichiometry and molarity concepts.
### Given Data:
1. Volume of [tex]\( H_2SO_4 \)[/tex] = 42.49 mL
2. Concentration of [tex]\( H_2SO_4 \)[/tex] = 0.219 M
3. Volume of [tex]\( NaOH \)[/tex] = 25.0 mL
### Step 1: Calculate the moles of [tex]\( H_2SO_4 \)[/tex] used in the reaction.
Using the formula:
[tex]\[ \text{Moles} = \text{Molarity} \times \text{Volume (in liters)} \][/tex]
First, convert volume of [tex]\( H_2SO_4 \)[/tex] from mL to L:
[tex]\[ 42.49 \, \text{mL} = 42.49 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.04249 \, \text{L} \][/tex]
Now calculate the moles of [tex]\( H_2SO_4 \)[/tex]:
[tex]\[ \text{Moles of } H_2SO_4 = 0.219 \, \text{M} \times 0.04249 \, \text{L} = 0.00930531 \, \text{moles} \][/tex]
### Step 2: Use stoichiometry to find the moles of [tex]\( NaOH \)[/tex] that reacted.
Given the balanced chemical equation:
[tex]\[ H_2SO_4(aq) + 2NaOH(aq) \rightarrow Na_2SO_4(aq) + 2H_2O(l) \][/tex]
From the equation, 1 mole of [tex]\( H_2SO_4 \)[/tex] reacts with 2 moles of [tex]\( NaOH \)[/tex].
So, moles of [tex]\( NaOH \)[/tex]:
[tex]\[ \text{Moles of } NaOH = 2 \times \text{Moles of } H_2SO_4 \][/tex]
[tex]\[ \text{Moles of } NaOH = 2 \times 0.00930531 = 0.01861062 \, \text{moles} \][/tex]
### Step 3: Calculate the molarity of the [tex]\( NaOH \)[/tex] solution.
[tex]\[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution (in liters)}} \][/tex]
Convert volume of [tex]\( NaOH \)[/tex] from mL to L:
[tex]\[ 25.0 \, \text{mL} = 25.0 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.025 \, \text{L} \][/tex]
Now calculate the molarity of [tex]\( NaOH \)[/tex]:
[tex]\[ \text{Molarity of } NaOH = \frac{0.01861062 \, \text{moles}}{0.025 \, \text{L}} = 0.7444248 \, \text{M} \][/tex]
### Conclusion
The molar concentration of the NaOH solution is approximately [tex]\( 0.744 \, \text{M} \)[/tex].
So the correct answer is:
[tex]\[ \boxed{0.744 \, \text{M}} \][/tex]
