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Question 6 of 10

What is the molarity of a solution of 3 moles (mol) of [tex]FeBr_3[/tex] in [tex]\frac{1}{2} L[/tex] water?

A. [tex]\frac{3 \, \text{mol}}{2 \, \text{L}}[/tex]

B. [tex]\frac{3 \, \text{mol}}{0.5 \, \text{L}}[/tex]

C. [tex]\frac{0.5 \, \text{L}}{3 \, \text{mol}}[/tex]

D. [tex]\frac{2 \, \text{L}}{3 \, \text{mol}}[/tex]



Answer :

GinnyAnswer
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]

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