Question

Concentrated nitric acid is sold as a \(70.4 \%\) by mass solution. If this solution has a density of \(1.42 \mathrm{g} / \mathrm{mL}\) what mass of \(\mathrm{HNO}_{3}\) is contained in \(1.00 \mathrm{L}\) of the solution?

Short answer

The mass of HNO3 in 1.00 L of the concentrated nitric acid solution can be calculated by first finding the total mass of the solution using the density and volume, which is 1420 g, and then multiplying it by the concentration (0.704). This gives us a mass of HNO3 equal to \(1000 \: \text{g}\).

Step-by-step solution

Calculate the Total Mass of the Solution

Given the density and volume of the solution, we can calculate the total mass using the following formula: Total Mass = Density * Volume The density is given in grams per milliliter (g/mL) and the volume is given in Liters. So, we need to convert the volume into milliliters. Since 1 L = 1000 mL, we have: Volume = 1.00 L * (1000 mL / 1 L) = 1000 mL Now, we have the volume in the same unit as the density, so we can calculate the total mass: Total Mass = 1.42 g/mL * 1000 mL = 1420 g

Calculate the Mass of HNO3

Now that we have the total mass of the solution, we'll find the mass of HNO3 using the given percentage of concentration. Mass of HNO3 = Total Mass * Concentration First, convert the concentration to decimal form: Concentration = 70.4% = 0.704 Now, we can calculate the mass of HNO3: Mass of HNO3 = 1420 g * 0.704 = 1000 g So, there are 1000 g of HNO3 in 1.00 L of the concentrated nitric acid solution.

Key concepts

Mass Percentage

Mass percentage, also called mass percent or percent by mass, is a way of expressing a concentration of a component in a mixture or a solution. It's defined as the mass of the solute divided by the total mass of the solution, multiplied by 100 to get a percentage. Knowing the mass percentage helps in determining how concentrated a solution is.
For example, in the original exercise, the solution of nitric acid has a mass percentage of 70.4%. This means that in every 100 grams of the solution, 70.4 grams are nitric acid. It provides an understanding of how much of the solute is present in the entire solution.
To calculate mass percentage, use the formula:

• Mass Percentage = (Mass of Solute / Mass of Solution) × 100

This concept is extremely useful in chemical preparation and analysis since it gives a clear picture of the ratio between the solution's different components. It helps to compare concentrations of solutions regardless of their total weights.

Density

Density is a fundamental concept used in chemistry and physics to explain how much mass is packed into a given volume. It is expressed as mass per unit volume, commonly in units of grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). In our exercise, density is crucial to find the total mass of the solution when we know its volume.
Given the density and the volume, you can calculate mass using the simple formula:

• Total Mass = Density × Volume

Densities of liquids can give insight into their composition and concentration. For instance, the concentrated nitric acid has a density of 1.42 g/mL, meaning that every milliliter of solution has a mass of 1.42 grams. This information allows us to calculate that a full liter (1.00 L) of this solution weighs 1420 grams, giving the necessary foundation for further calculations of component concentrations.

Volume Conversion

Volume conversion is a simple yet essential skill that allows you to adjust volumes from one unit of measurement to another. Most commonly, in chemistry, we need to convert between liters and milliliters due to their frequent use. One liter is equivalent to 1000 milliliters, which is a crucial conversion factor.
In problems involving density, converting liters to milliliters ensures that the units are consistent, allowing for accurate computations involving mass and concentration. For the problem described, converting 1.00 L into 1000 mL was necessary to match the volume units with those of the density (given in g/mL).
Understanding how to properly convert between volume units is vital for conducting precise experiments and calculations. Always double-check to ensure all quantities are in the proper units before proceeding with any mathematical operation.