To determine the molarity of the HBr solution, we will follow a step-by-step approach:
1. Convert Volumes to Liters:
- We need to convert the given volumes of the HBr solution and the LiOH solution from milliliters to liters.
[tex]\[
\text{Volume of HBr} = 47.0 \ \text{mL} = \frac{47.0}{1000} \ \text{L} = 0.047 \ \text{L}
\][/tex]
[tex]\[
\text{Volume of LiOH} = 37.5 \ \text{mL} = \frac{37.5}{1000} \ \text{L} = 0.0375 \ \text{L}
\][/tex]
2. Calculate the Moles of LiOH:
- Using the volume and molarity of the LiOH solution, we find the number of moles of LiOH.
[tex]\[
\text{Moles of LiOH} = \text{Molarity of LiOH} \times \text{Volume of LiOH (in liters)}
\][/tex]
[tex]\[
\text{Moles of LiOH} = 0.215 \ \text{M} \times 0.0375 \ \text{L} = 0.0080625 \ \text{moles}
\][/tex]
3. Determine the Moles of HBr:
- The reaction between HBr and LiOH proceeds in a 1:1 molar ratio as given by the equation:
[tex]\[ \text{HBr} + \text{LiOH} \rightarrow \text{LiBr} + \text{H}_2\text{O} \][/tex]
- Therefore, the moles of HBr will be equal to the moles of LiOH.
[tex]\[
\text{Moles of HBr} = \text{Moles of LiOH} = 0.0080625 \ \text{moles}
\][/tex]
4. Calculate the Molarity of HBr:
- Molarity is defined as the number of moles of solute divided by the volume of the solution in liters.
[tex]\[
\text{Molarity of HBr} = \frac{\text{Moles of HBr}}{\text{Volume of HBr solution (in liters)}}
\][/tex]
[tex]\[
\text{Molarity of HBr} = \frac{0.0080625 \ \text{moles}}{0.047 \ \text{L}} \approx 0.1715 \ \text{M}
\][/tex]
Therefore, the molarity of the HBr solution is approximately [tex]\(0.1715 \ \text{M}\)[/tex].
