To determine the molarity of a solution, we need to follow these steps:
1. Calculate the number of moles of BaBr₂:
- First, determine the molar mass of BaBr₂. The atomic masses are as follows:
- Barium (Ba): 137.33 g/mol
- Bromine (Br): 79.904 g/mol (since there are two bromine atoms in BaBr₂, double this value)
- Molar mass of BaBr₂ = 137.33 g/mol + 2 * 79.904 g/mol = 297.14 g/mol
- Next, determine the number of moles of BaBr₂ by using the formula:
[tex]\[
\text{Moles of BaBr₂} = \frac{\text{Mass of BaBr₂}}{\text{Molar mass of BaBr₂}}
\][/tex]
Given the mass of BaBr₂ is 285 g and its molar mass is 297.14 g/mol:
[tex]\[
\text{Moles of BaBr₂} = \frac{285 \ \text{g}}{297.14 \ \text{g/mol}} \approx 0.959
\][/tex]
(using significant figures, this value has 3 significant figures because 285 has 3 significant figures)
2. Calculate the molarity of the solution:
- Molarity (M) is defined as the number of moles of solute per liter of solution.
- Using the formula for molarity:
[tex]\[
\text{Molarity} = \frac{\text{Moles of BaBr₂}}{\text{Volume of solution in liters}}
\][/tex]
Given the volume of the solution is 3.25 L:
[tex]\[
\text{Molarity} = \frac{0.959 \ \text{mol}}{3.25 \ \text{L}} \approx 0.295 \ \text{M}
\][/tex]
(Considering significant figures: 0.959 has 3 significant figures and 3.25 has 3 significant figures, so the result should also have 3 significant figures)
Therefore, the molarity of the solution is [tex]\(0.295 \ \text{M}\)[/tex].
