To determine the molarity of the HBr solution, we need to go through several steps:
### Step 1: Determine the Moles of LiOH
First, we need to calculate the number of moles of LiOH used in the titration. We are given the volume of the LiOH solution and its molarity.
- Volume of LiOH solution = 37.5 mL
- Molarity of LiOH solution (M) = 0.215 M
To find the number of moles, we use the formula:
[tex]\[ \text{Moles of LiOH} = \text{Molarity of LiOH} \times \left( \frac{\text{Volume of LiOH}}{1000} \right) \][/tex]
Converting the volume from mL to L:
[tex]\[ \text{Volume of LiOH (L)} = \frac{37.5 \, \text{mL}}{1000} = 0.0375 \, \text{L} \][/tex]
Now, calculating the moles:
[tex]\[ \text{Moles of LiOH} = 0.215 \, \text{M} \times 0.0375 \, \text{L} = 0.0080625 \, \text{moles} \][/tex]
### Step 2: Determine the Moles of HBr
From the balanced chemical equation:
[tex]\[ \text{HBr} + \text{LiOH} \rightarrow \text{LiBr} + \text{H}_2\text{O} \][/tex]
We see that the reaction occurs in a 1:1 mole ratio. This means that the moles of HBr will be equal to the moles of LiOH at the equivalence point.
- Moles of HBr = 0.0080625 moles
### Step 3: Calculate the Molarity of the HBr Solution
Next, we need to find the molarity of the HBr solution. We are given the volume of the HBr solution.
- Volume of HBr solution = 47.0 mL
To find the molarity, we use the formula:
[tex]\[ \text{Molarity (M)} = \frac{\text{Moles of HBr}}{\text{Volume of HBr in Liters}} \][/tex]
Converting the volume from mL to L:
[tex]\[ \text{Volume of HBr (L)} = \frac{47.0 \, \text{mL}}{1000} = 0.047 \, \text{L} \][/tex]
Now calculating the molarity:
[tex]\[ \text{Molarity of HBr} = \frac{0.0080625 \, \text{moles}}{0.047 \, \text{L}} = 0.17154255319148937 \, \text{M} \][/tex]
### Final Answer
The molarity of the HBr solution is approximately [tex]\( \boxed{0.1715 \, \text{M}} \)[/tex].
