Final answer:
To calculate the mole fraction of HNO₃ in a commercial nitric acid solution, we first determine the total moles of HNO3 and water in the solution and then divide the moles of HNO₃ by the total moles in the solution. After the calculation, we find that the mole fraction of HNO₃ is approximately 0.412. The correct answer is option: a) 0.412
Step-by-step explanation:
To find the mole fraction of HNO₃ in the solution, we first need to calculate the number of moles of HNO₃ in 1 liter (L) of the solution. The mole fraction (X) of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components of the solution.
Using the density of the solution (1.42 g/mL), we can determine the mass of 1 L of the solution (since 1 L = 1000 mL). The mass of 1L of solution is 1.42 g/mL × 1000 mL = 1420 g.
To find the moles of HNO₃, we will use the molality (m) which is given as 16.0 m, meaning there are 16.0 moles of HNO₃per kilogram of water.
Since the molarity (M) is not provided, we assume that the molality and molarity are approximately equal given the high concentration of the solution. So we calculate moles of HNO₃ as 16.0 moles per kilogram (1000 g) of water.
However, we need to correct for the presence of HNO₃ in the mass of the solution. We will assume that the majority of the mass is water, given HNO₃'s relatively low molar mass (63.018 g/mol).
Mass of HNO₃ in solution = 16.0 moles × 63.018 g/mol
= 1008.288 g.
Moles of HNO₃= 1008.288 g / 63.018 g/mol
= 16.0 moles.
The total mass of the solution is the mass of the water plus the mass of HNO3, so total mass = 1420 g - 1008.288 g
= 411.712 g of H₂O.
Moles of water = 411.712 g / 18.015 g/mol (molar mass of H₂O) = 22.85 moles (approximately).
The total moles in the solution = 16.0 moles of HNO₃+ 22.85 moles of H₂O= 38.85 moles (approximately).
The mole fraction of HNO₃= moles of HNO₃/ total moles = 16.0 / 38.85 = 0.412 (approximately), which corresponds to answer (a).