Calculation of Molality, Molarity, and Mole Fraction of 30% HNO3 Solution

1. Understanding the problem
We are given a 30% HNO3 solution and we need to calculate its molality, molarity, and mole fraction. The density of the solution is also provided as 1.50 g/L.

2. Definitions
Before we proceed with the calculations, let's understand the definitions of molality, molarity, and mole fraction:

- Molality (m): It is defined as the number of moles of solute per kilogram of solvent. It is expressed in mol/kg.
- Molarity (M): It is defined as the number of moles of solute per liter of solution. It is expressed in mol/L.
- Mole Fraction (X): It is defined as the ratio of the number of moles of a component to the total number of moles in the solution. It is a dimensionless quantity.

3. Calculation of Molality
To calculate the molality, we need to know the mass of the solute (HNO3) and the mass of the solvent (water). Since the solution is given as 30% HNO3, it means that 30 g of HNO3 is present in 100 g of the solution.

Assuming the density of the solution remains constant at 1.50 g/mL, we can calculate the mass of the solution as follows:

Mass of the solution = Volume of the solution x Density of the solution
= 100 mL x 1.50 g/mL
= 150 g

Now, we can calculate the mass of the solute (HNO3) as 30% of the mass of the solution:

Mass of HNO3 = 30% of Mass of the solution
= 0.30 x 150 g
= 45 g

The molality (m) is calculated as the number of moles of solute (HNO3) divided by the mass of the solvent (water) in kg. The molar mass of HNO3 is 63 g/mol.

Moles of HNO3 = Mass of HNO3 / Molar mass of HNO3
= 45 g / 63 g/mol
= 0.714 mol

Molality (m) = Moles of HNO3 / Mass of solvent (water)
= 0.714 mol / 0.100 kg
= 7.14 mol/kg

Therefore, the molality of the 30% HNO3 solution is 7.14 mol/kg.

4. Calculation of Molarity
To calculate the molarity, we need to know the volume of the solution and the number of moles of solute (HNO3). The volume of the solution is given as 100 mL.

Molarity (M) is calculated as the number of moles of solute (HNO3) divided by the volume of the solution in liters.

Moles of HNO3 = Mass of HNO3 / Molar mass of HNO3
= 45 g / 63 g/mol
= 0.714 mol

Molarity (M