The Comprehensive Guide to Nitric Acid Density: Unlocking the Secrets of Concentration, Temperature, and Calculations

Nitric acid, also known as HNO3, is a highly corrosive and toxic liquid with a range of uses in various industries, from chemical manufacturing to metal processing. Its density is a crucial physical property that varies depending on its concentration and temperature, making it essential for chemists, engineers, and researchers to understand its behavior.

Understanding the Relationship between Nitric Acid Concentration and Density

The density of nitric acid solutions is directly proportional to their concentration. This is because the higher the concentration of nitric acid, the more nitrogen dioxide it can dissolve, which in turn increases the overall density of the solution.

According to PubChem, the density of fuming nitric acid, which is concentrated nitric acid containing dissolved nitrogen dioxide, can be expressed using the following formula:

ρ = 1.5041 + 0.0108 × c

Where:
– ρ is the density of the nitric acid solution in g/mL
– c is the concentration of the nitric acid solution in wt%

This formula demonstrates that as the concentration of nitric acid increases, the density of the solution also increases linearly.

The Effect of Temperature on Nitric Acid Density

In addition to concentration, the temperature of the nitric acid solution also plays a significant role in its density. The Complete Aqueous Nitric Acid Solutions Density-Concentration Calculator provides a comprehensive table of density and concentration values for nitric acid solutions at different temperatures.

The data from this calculator shows that the density of a nitric acid solution decreases as the temperature increases, while the concentration of the solution increases with density. For example, a nitric acid solution with a density of 1.4 g/mL has a concentration of approximately 68.4% by weight at 20°C, but the concentration would be slightly lower at higher temperatures.

This relationship can be expressed using the following formula:

ρ = ρ₀ × (1 - α × (T - T₀))

Where:
– ρ is the density of the nitric acid solution at temperature T in g/mL
– ρ₀ is the density of the nitric acid solution at reference temperature T₀ in g/mL
– α is the thermal expansion coefficient of the nitric acid solution in °C⁻¹
– T is the temperature of the nitric acid solution in °C
– T₀ is the reference temperature in °C

By using this formula, you can calculate the density of a nitric acid solution at any given temperature, provided that you know the density at a reference temperature and the thermal expansion coefficient of the solution.

Calculating the Percentage of Nitric Acid in a Solution

Determining the percentage of nitric acid in a solution is crucial for many applications, and there are several methods to do so. One simple approach is to use the formula:

% Nitric Acid = 1.33 × v

Where v is the volume of the solution in milliliters. This formula is derived from the fact that 1 mL of 70% nitric acid by volume weighs 1.33 grams. Therefore, the percentage of nitric acid in a solution can be calculated by multiplying the volume of the solution by 1.33.

Another method to calculate the percent HNO3 by mass in a solution is to use the following formula:

% HNO3 by mass = (molarity × molar mass of HNO3 × density) / (1 + (molarity × molar mass of HNO3 × density)) × 100%

Where:
– molarity is the concentration of the nitric acid solution in moles per liter
– molar mass of HNO3 is approximately 63.01 g/mol
– density is the density of the nitric acid solution in g/mL

For example, if the density of a commercial aqueous nitric acid solution is 1.42 g/mL and the solution is 16 M, the percent HNO3 by mass can be calculated as follows:

% HNO3 by mass = (16 × 63.01 × 1.42) / (1 + (16 × 63.01 × 1.42)) × 100%
% HNO3 by mass ≈ 69.4%

Therefore, the commercial aqueous nitric acid solution is approximately 69.4% HNO3 by mass.

Nitric Acid Density Data and Numerical Examples

To further illustrate the relationship between nitric acid concentration, temperature, and density, here are some additional data points and numerical examples:

Nitric Acid Density-Concentration Table

Concentration (wt%)	Density at 20°C (g/mL)	Density at 40°C (g/mL)
50	1.3066	1.2958
60	1.3716	1.3595
70	1.4321	1.4187
80	1.4880	1.4732
90	1.5388	1.5226

Numerical Example 1

Calculate the density of a 75% nitric acid solution at 30°C.

Given:
– Concentration = 75% by weight
– Temperature = 30°C

Using the formula:
ρ = ρ₀ × (1 – α × (T – T₀))

Where:
– ρ₀ = 1.4321 g/mL (from the table, density at 20°C)
– α = 0.0005 °C⁻¹ (typical thermal expansion coefficient for nitric acid)
– T = 30°C
– T₀ = 20°C

Plugging in the values:
ρ = 1.4321 × (1 – 0.0005 × (30 – 20))
ρ = 1.4260 g/mL

Therefore, the density of a 75% nitric acid solution at 30°C is approximately 1.4260 g/mL.

Numerical Example 2

A nitric acid solution has a density of 1.38 g/mL. What is the concentration of the solution?

Using the formula:
ρ = 1.5041 + 0.0108 × c

Rearranging the formula to solve for concentration:
c = (ρ – 1.5041) / 0.0108

Plugging in the given density:
c = (1.38 – 1.5041) / 0.0108
c ≈ 60.1% by weight

Therefore, the concentration of the nitric acid solution with a density of 1.38 g/mL is approximately 60.1% by weight.

Conclusion

In summary, the density of nitric acid solutions is a crucial physical property that varies depending on the concentration and temperature of the solution. By understanding the relationships between these factors, as well as the formulas and data provided in this guide, you can accurately determine the density and concentration of nitric acid solutions for a wide range of applications.

Whether you’re a chemist, engineer, or researcher working with nitric acid, this comprehensive guide should serve as a valuable resource for all your nitric acid density-related needs.

References

• Nitric Acid | HNO3 | CID 944 – PubChem
• The Complete Aqueous Nitric Acid Solutions Density-Concentration Calculator
• Determine % Nitric Acid. Titration? Conversion factor? – Finishing.com
• Commercial aqueous nitric acid has a density of 1.42 g/mL and is 16 M. Calculate the percent HNO3 by mass in the solution. Verified Solution.