✨ VIPSolutions

Let's solve the problem step by step: --- ### **Step 1: Calculate the mass of bromide ions (Br⁻) in the solution** **Molar mass of MgBr₂:** - Mg: 24.3 g/mol - Br: 79.9 g/mol (x2 for two Br) - Total: 24.3 + (2 × 79.9) = **184.1 g/mol** **Moles of MgBr₂:** - \( \text{Moles of MgBr}_2 = \frac{197.4 \text{ g}}{184.1 \text{ g/mol}} = 1.072 \text{ mol} \) **Each mole of MgBr₂ gives 2 moles of Br⁻:** - Moles of Br⁻ = 1.072 × 2 = **2.144 mol** **Mass of Br⁻:** - Molar mass of Br = **79.9 g/mol** - Mass of Br⁻ = 2.144 mol × 79.9 g/mol = **171.3 g** --- ### **Step 2: Find the total mass of the solution (assuming density ≈ 1 g/mL)** - Volume of water = **1.80 L** = **1800 g** (since 1 mL water ≈ 1 g) - Adding MgBr₂: **197.4 g** - Total mass ≈ 1800 g + 197.4 g = **1997.4 g** --- ### **Step 3: Calculate ppm of Br⁻** \[ \text{ppm} = \frac{\text{mass of Br}^-}{\text{total mass of solution}} \times 10^6 \] \[ \text{ppm} = \frac{171.3}{1997.4} \times 10^6 = 85,800 \] --- ## **Final Answer** \[ \boxed{85,800 \ \text{ppm of Br}} \]

The concept used involves converting the given mass of magnesium bromide (MgBr₂) into the total mass of bromide ions (Br⁻) by calculating the molar amount and using the stoichiometric ratio. Then, the mass of bromide ions is related to the total solution mass to determine the concentration in ppm, which expresses the mass of solute per million parts of solution.

The approach to solving this problem primarily relies on principles of stoichiometry and concentration calculations. First, we determine the molar mass of magnesium bromide (MgBr₂) to convert the given mass into moles. Using the chemical formula, we identify that each mole of MgBr₂ contains two moles of bromide ions (Br⁻). By multiplying the moles of MgBr₂ by 2, we find the total moles of bromide ions present in the solution. Next, we convert these moles into mass by multiplying by the molar mass of bromide (79.9 g/mol). After obtaining the total bromide mass, we consider the total mass of the solution, which includes the water and the dissolved magnesium bromide. Assuming the density of water is approximately 1 g/mL, we convert the volume into grams and add the mass of MgBr₂ to find the total solution mass. Finally, to express the concentration in ppm, we divide the mass of bromide ions by the total solution mass and multiply by one million, since ppm denotes parts per million. This method effectively combines stoichiometry with concentration unit conversions to determine the bromide concentration in the solution.