A sample of nitric acid has a density of 1.42g/cm3 and contains 69.5% by weight of the pure acid.What is the molarity of the solution?
Things to keep in mind:
Molarity=Moles/Volume (L)
HNO3=63.01g/mol
69.5%=0.695
and
1cm^3=1mL=10^-3L
Convert Density from g/cm^3 to g/L:
1.42g/cm3*(1cm^3/10^-3L)=1420g/L
Calculate the amount of pure acid:
1.420g/L*(0.695)= mass of pure HNO3 in g/L
Since the molar mass of HNO3=63.01g/mol
Then,
mass of pure HNO3 in g/L*(mol/63.01g)= moles/L=Molarity
***Answer contains no more than 3-significant figures.
To find the molarity of the solution, we need to determine the number of moles of nitric acid present in the given sample.
First, let's calculate the mass of the pure nitric acid in the sample. Since the sample is 69.5% pure acid by weight, we can assume we have 69.5 grams of pure nitric acid in every 100 grams of the sample (by weight).
Given that the density of nitric acid is 1.42 g/cm³, we can calculate the volume of the sample using the formula: Volume = mass/density.
Using the given density of 1.42 g/cm³, the mass of the sample would be equal to the volume (in cm³), multiplied by the density.
Let's say we have a 100g sample of nitric acid solution, with a density of 1.42 g/cm³. Therefore, the volume of the sample would be:
Volume = mass/density = 100g / 1.42 g/cm³ = 70.42 cm³
Next, we need to convert the volume from cm³ to liters, as molarity is defined as the number of moles of solute per liter of solution. Since 1 L is equivalent to 1000 cm³, the volume in liters would be:
Volume = 70.42 cm³ * (1 L / 1000 cm³) = 0.07042 L
To find the number of moles of nitric acid in the solution, we need to multiply the mass of pure nitric acid by the mole fraction of nitric acid in the sample. The mole fraction can be calculated by dividing the mass of pure nitric acid by the molar mass of nitric acid:
Molar mass of HNO₃ (Nitric acid) = 1(1.01 g/mol) + 1(14.01 g/mol) + 3(16.00 g/mol) = 63.02 g/mol
Mole fraction of nitric acid = mass of pure nitric acid / molar mass of nitric acid
Mole fraction of nitric acid = 69.5 g / 63.02 g/mol = 1.103 mol
Finally, we can calculate the molarity of the solution by dividing the number of moles by the volume in liters:
Molarity (M) = Number of moles / Volume (in Liters)
Molarity = 1.103 mol / 0.07042 L ≈ 15.66 M
Therefore, the molarity of the nitric acid solution is approximately 15.66 M.