The Density Of A 3.539 M HNO3 Aqueous Solution Is 1.150 G/ml. At 20C. Calculate The Molality Of The Solution.
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Understanding the Problem
In this article, we will explore how to determine the molality of a nitric acid (HNO₃) aqueous solution given specific data points. The problem provides the molarity (3.539 M), the density of the solution (1.150 g/mL), and the temperature at which measurements are taken (20°C). Our goal is to calculate the molality, which is a measure of concentration expressing moles of solute per kilogram of solvent.
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Key Concepts and Definitions
Before delving into the calculation, it's important to understand some fundamental concepts:
What is Molarity (M)?
- Molarity is defined as the number of moles of solute (HNO₃) per liter of solution.
- Expressed as mol/L.
What is Density?
- Density (\(\rho\)) is mass per unit volume, typically expressed as g/mL or g/L.
- In this case, the density of the solution is 1.150 g/mL.
What is Molality (m)?
- Molality is the number of moles of solute per kilogram of solvent.
- Expressed as mol/kg.
Why is Molality Important?
- Molality is temperature-independent because it depends on mass, which doesn't change with temperature.
- Useful in colligative property calculations.
Step-by-Step Calculation of Molality
To find the molality, we need to determine:
- The mass of the solution per liter.
- The mass of HNO₃ in that liter.
- The mass of the solvent (water) in that liter.
- The number of moles of HNO₃.
Let's proceed step-by-step.
1. Calculate the mass of 1 liter of the solution
Given the density:
\[
\text{Mass of 1 L of solution} = \text{Density} \times \text{Volume}
\]
Since 1 L = 1000 mL:
\[
\text{Mass} = 1.150\, \text{g/mL} \times 1000\, \text{mL} = 1150\, \text{g}
\]
So, each liter of the solution weighs 1150 grams.
2. Determine the number of moles of HNO₃ in 1 liter
Given molarity:
\[
\text{Moles of HNO}_3 = 3.539\, \text{mol/L}
\]
This means in 1 liter of solution, there are 3.539 moles of HNO₃.
3. Calculate the mass of HNO₃ in 1 liter
The molar mass of HNO₃:
\[
\text{H} = 1.008\, \text{g/mol} \\
\text{N} = 14.007\, \text{g/mol} \\
\text{O}_3 = 3 \times 16.00\, \text{g/mol} = 48.00\, \text{g/mol}
\]
Total molar mass of HNO₃:
\[
1.008 + 14.007 + 48.00 = 63.015\, \text{g/mol}
\]
Mass of HNO₃ in 1 liter:
\[
\text{Mass} = 3.539\, \text{mol} \times 63.015\, \text{g/mol} \approx 223.2\, \text{g}
\]
4. Find the mass of water (solvent) in 1 liter
Total mass of solution:
\[
1150\, \text{g}
\]
Mass of HNO₃:
\[
223.2\, \text{g}
\]
Therefore, the mass of water:
\[
\text{Mass of water} = 1150\, \text{g} - 223.2\, \text{g} = 926.8\, \text{g}
\]
Convert this to kilograms:
\[
926.8\, \text{g} = 0.9268\, \text{kg}
\]
5. Calculate molality
Molality (\(m\)) is:
\[
m = \frac{\text{moles of solute}}{\text{kg of solvent}}
\]
Substituting the known values:
\[
m = \frac{3.539\, \text{mol}}{0.9268\, \text{kg}} \approx 3.82\, \text{mol/kg}
\]
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Final Answer
The molality of the 3.539 M HNO₃ aqueous solution at 20°C is approximately 3.82 mol/kg.
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Additional Insights and Applications
Understanding how to convert between different concentration units is vital in chemistry, especially when preparing solutions or analyzing experimental data. Here are some key applications:
1. Comparing Concentration Measures
- Molarity and molality are two common ways to express solution concentration.
- Molarity varies with temperature due to volume changes, whereas molality remains constant.
2. Practical Uses in Laboratory Settings
- Molality is often preferred when temperature stability is crucial, such as in colligative property measurements like boiling point elevation or freezing point depression.
3. Safety and Handling of Nitric Acid
- Nitric acid is a highly corrosive and reactive acid.
- Proper understanding of concentration helps in safe handling and accurate dilution procedures.
4. Calculations in Industrial Applications
- Precise concentration calculations are essential in manufacturing processes involving nitric acid, such as in fertilizers, explosives, and chemical syntheses.
Conclusion
Calculating the molality of a solution from molarity and density involves understanding the relationships between mass, volume, and moles. In our case, starting from the known molarity and density, we determined the total mass of solution, the mass of solute (HNO₃), and the mass of solvent (water). Ultimately, we found that the molality of the solution is approximately 3.82 mol/kg, a concentration measure critical for various scientific and industrial applications.
By mastering such calculations, chemists can accurately prepare solutions, interpret experimental data, and ensure safety and precision in laboratory and industrial processes.
