To determine the molarity of the [tex]\(\text{H}_2\text{SO}_4\)[/tex] solution, let's go through the problem step-by-step:
Step 1: Convert volumes from mL to L
First, we need to convert the volumes of both NaOH and [tex]\(\text{H}_2\text{SO}_4\)[/tex] solutions from milliliters (mL) to liters (L):
[tex]\[
\text{Volume of } \text{H}_2\text{SO}_4 = 22.55 \text{ mL} = 22.55 \div 1000 = 0.02255 \text{ L}
\][/tex]
[tex]\[
\text{Volume of } \text{NaOH} = 14.85 \text{ mL} = 14.85 \div 1000 = 0.01485 \text{ L}
\][/tex]
Step 2: Calculate the moles of NaOH used
We know the volume of the NaOH solution and its molarity. The molarity (M) is defined as the number of moles of solute per liter of solution. So, we can find the moles of NaOH:
[tex]\[
\text{Moles of NaOH} = \text{Molarity} \times \text{Volume in liters} = 0.146 \text{ M} \times 0.01485 \text{ L} = 0.0021681 \text{ moles}
\][/tex]
Step 3: Use the mole ratio to find moles of [tex]\(\text{H}_2\text{SO}_4\)[/tex]
From the balanced equation:
[tex]\[
2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O}
\][/tex]
We see that 2 moles of NaOH react with 1 mole of [tex]\(\text{H}_2\text{SO}_4\)[/tex]. Therefore, the mole ratio of NaOH to [tex]\(\text{H}_2\text{SO}_4\)[/tex] is 2:1.
[tex]\[
\text{Moles of } \text{H}_2\text{SO}_4 = \frac{\text{Moles of NaOH}}{2} = \frac{0.0021681}{2} = 0.00108405 \text{ moles}
\][/tex]
Step 4: Calculate the molarity of the [tex]\(\text{H}_2\text{SO}_4\)[/tex] solution
Finally, to find the molarity of the [tex]\(\text{H}_2\text{SO}_4\)[/tex] solution, we need to divide the moles of [tex]\(\text{H}_2\text{SO}_4\)[/tex] by the volume of the [tex]\(\text{H}_2\text{SO}_4\)[/tex] solution in liters:
[tex]\[
\text{Molarity of } \text{H}_2\text{SO}_4 = \frac{\text{Moles of } \text{H}_2\text{SO}_4}{\text{Volume of } \text{H}_2\text{SO}_4\text{ in liters}} = \frac{0.00108405}{0.02255} = 0.04807317073170732 \text{ M}
\][/tex]
So, the molarity of the [tex]\(\text{H}_2\text{SO}_4\)[/tex] solution is approximately [tex]\(0.0481 \text{ M}\)[/tex].
