To determine the initial concentration of sulfuric acid (H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex]) that is neutralized by sodium hydroxide (NaOH), we need to follow a step-by-step process.
1. Write the balanced chemical equation for the reaction:
[tex]\[
H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + 2H_2O
\][/tex]
This equation shows that one mole of sulfuric acid reacts with two moles of sodium hydroxide.
2. Calculate the moles of NaOH used in the reaction:
We are given:
- Volume of NaOH solution = 60.0 mL
- Concentration of NaOH solution = 1.50 M (mol/L)
First, convert the volume from milliliters to liters:
[tex]\[
\text{Volume}_{\text{NaOH}} = 60.0 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.060 \, \text{L}
\][/tex]
Now, calculate the moles of NaOH:
[tex]\[
\text{Moles}_{\text{NaOH}} = \text{Volume}_{\text{NaOH}} \times \text{Concentration}_{\text{NaOH}} = 0.060 \, \text{L} \times 1.50 \, \text{mol/L} = 0.09 \, \text{mol}
\][/tex]
3. Determine the moles of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] that react with NaOH:
According to the balanced chemical equation, one mole of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] reacts with two moles of NaOH. Therefore, the moles of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] that reacted can be calculated by dividing the moles of NaOH by 2:
[tex]\[
\text{Moles}_{\text{H}_2\text{SO}_4} = \frac{\text{Moles}_{\text{NaOH}}}{2} = \frac{0.09 \, \text{mol}}{2} = 0.045 \, \text{mol}
\][/tex]
4. Calculate the initial concentration of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex]:
We are given:
- Volume of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] solution = 358 mL
First, convert the volume from milliliters to liters:
[tex]\[
\text{Volume}_{\text{H}_2\text{SO}_4} = 358 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.358 \, \text{L}
\][/tex]
Now, calculate the initial concentration of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex]:
[tex]\[
\text{Concentration}_{\text{H}_2\text{SO}_4} = \frac{\text{Moles}_{\text{H}_2\text{SO}_4}}{\text{Volume}_{\text{H}_2\text{SO}_4}} = \frac{0.045 \, \text{mol}}{0.358 \, \text{L}} = 0.12569832402234637 \, \text{M}
\][/tex]
Therefore, the initial concentration of the sulfuric acid solution is approximately 0.126 M.
