A solution contains 6.00% (by mass) or (mass/mass) NaBr (sodium bromide) (molar mass = 102.89 g/mol). The density of the solution is 1.046 g/cm. What is the molarity of the NaBr solution?
a. 0.610
b. 0.305
c. 0.583
d. 0.280
e. 0.105
The correct answer and explanation is :
To determine the molarity of the NaBr solution, we follow these steps:
Step 1: Define Given Information
- Mass percent of NaBr = 6.00% (which means 6.00 g NaBr in 100 g of solution)
- Density of solution = 1.046 g/cm³
- Molar mass of NaBr = 102.89 g/mol
Step 2: Convert Mass of Solution to Volume
We assume 100 g of solution. Using density:
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \text{ g}}{1.046 \text{ g/cm}^3}
]
[
= 95.60 \text{ cm}^3 = 95.60 \text{ mL} = 0.09560 \text{ L}
]
Step 3: Calculate Moles of NaBr
Since 6.00 g of NaBr is present in 100 g of solution:
[
\text{Moles of NaBr} = \frac{6.00 \text{ g}}{102.89 \text{ g/mol}}
]
[
= 0.0583 \text{ moles}
]
Step 4: Calculate Molarity
Molarity (M) is defined as:
[
M = \frac{\text{moles of solute}}{\text{liters of solution}}
]
[
M = \frac{0.0583}{0.09560}
]
[
= 0.610 \text{ M}
]
Final Answer:
[
\mathbf{0.610 \text{ M} \Rightarrow \text{Option (a)}}
]
Explanation
Molarity is the number of moles of solute per liter of solution. We calculated the moles of NaBr from the given mass and molar mass. Then, using density, we found the volume of the solution. Finally, dividing moles by volume gave the correct molarity.
