To determine the molarity of a solution, you use the formula:
[tex]\[ \text{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \][/tex]
Given:
- Moles of [tex]\( \text{FeBr}_3 \)[/tex] = 3 moles
- Volume of the solution = [tex]\( \frac{1}{2} \)[/tex] L (0.5 L)
First, we substitute the given values into the molarity formula:
[tex]\[ M = \frac{3 \text{ moles}}{0.5 \text{ L}} \][/tex]
Upon performing the division:
[tex]\[ M = 6.0 \text{ mol/L} \][/tex]
Thus, the molarity of the solution is [tex]\( 6.0 \text{ mol/L} \)[/tex].
Next, we compare this result to the given options:
A. [tex]\( \frac{3 \text{ mol}}{2 \text{ L}} \)[/tex]:
[tex]\[ \frac{3}{2} = 1.5 \ \text{mol/L} \][/tex]
B. [tex]\( \frac{3 \text{ mol}}{0.5 \text{ L}} \)[/tex]:
[tex]\[ \frac{3}{0.5} = 6.0 \ \text{mol/L} \][/tex]
C. [tex]\( \frac{0.5 \text{ L}}{3 \text{ mol}} \)[/tex]:
[tex]\[ \frac{0.5}{3} \approx 0.167 \ \text{mol/L} \][/tex]
D. [tex]\( \frac{2 \text{ L}}{3 \text{ mol}} \)[/tex]:
[tex]\[ \frac{2}{3} \approx 0.667 \ \text{mol/L} \][/tex]
From these calculations, it’s clear that:
- Option A results in [tex]\( 1.5 \ \text{mol/L} \)[/tex]
- Option B results in [tex]\( 6.0 \ \text{mol/L} \)[/tex]
- Option C results in [tex]\( 0.167 \ \text{mol/L} \)[/tex]
- Option D results in [tex]\( 0.667 \ \text{mol/L} \)[/tex]
The correct answer is therefore:
[tex]\[ B. \frac{3 \text{ mol}}{0.5 \text{ L}} = 6.0 \ \text{mol/L} \][/tex]
