A solution that is 7.56% by mass NaNO3 (molar mass=85.0 g/mole) in water (molar mass=18.0 g/mole) has a density of 1.09 g/mL. What is its molarity?
The Correct Answer and Explanation is :
To determine the molarity of a solution, we need to calculate the number of moles of NaNO₃ per liter of solution. Molarity (M) is defined as:
[
M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
]
Given information:
- Mass percent of NaNO₃ = 7.56%
- Molar mass of NaNO₃ = 85.0 g/mol
- Molar mass of H₂O = 18.0 g/mol
- Density of the solution = 1.09 g/mL
Step 1: Determine the mass of NaNO₃ in the solution
A 7.56% mass percent means that in 100 g of solution, there are 7.56 g of NaNO₃.
Thus, for every 100 g of solution, we have:
[
\text{Mass of NaNO₃} = 7.56 \, \text{g}
]
[
\text{Mass of solution} = 100 \, \text{g}
]
Step 2: Find the volume of the solution
To find the volume of the solution, use the density equation:
[
\text{Density} = \frac{\text{Mass of solution}}{\text{Volume of solution}}
]
Rearrange this to find the volume of the solution:
[
\text{Volume of solution} = \frac{\text{Mass of solution}}{\text{Density}}
]
Substitute the values:
[
\text{Volume of solution} = \frac{100 \, \text{g}}{1.09 \, \text{g/mL}} = 91.74 \, \text{mL} = 0.09174 \, \text{L}
]
Step 3: Calculate the moles of NaNO₃
Using the molar mass of NaNO₃ (85.0 g/mol), calculate the moles of NaNO₃:
[
\text{Moles of NaNO₃} = \frac{\text{Mass of NaNO₃}}{\text{Molar mass of NaNO₃}} = \frac{7.56 \, \text{g}}{85.0 \, \text{g/mol}} = 0.08894 \, \text{mol}
]
Step 4: Calculate the molarity
Now, calculate the molarity (M) by dividing the moles of NaNO₃ by the volume of the solution in liters:
[
M = \frac{0.08894 \, \text{mol}}{0.09174 \, \text{L}} = 0.970 \, \text{M}
]
Thus, the molarity of the solution is approximately 0.970 M.
Explanation:
The solution’s molarity was determined by first calculating the mass of NaNO₃ and the volume of the solution. By using density, we converted mass to volume. Then, using the molar mass of NaNO₃, we found the number of moles in the solution. Finally, molarity was determined by dividing the moles of NaNO₃ by the volume of the solution in liters.