Calculate the molarity of 10 % HNO3 (w/w) solution if its density is 2.0 g/cc at 25° C.
To calculate the molarity (M) of a solution, we need to know the number of moles of solute (HNO3 in this case) and the volume of the solvent (water, in most cases). However, in this question, we are given the percentage concentration (w/w) and the density of the solution.
To start, we need to convert the percentage concentration (w/w) to mass concentration. The given 10% HNO3 (w/w) solution means that 10 g of HNO3 is present in 100 g of the solution.
Next, we need to calculate the moles of HNO3. To do this, we'll need the molar mass of HNO3. The molar mass of HNO3 is calculated by adding up the atomic masses of its constituent elements, which are hydrogen (H), nitrogen (N), and oxygen (O). The atomic mass of hydrogen is approximately 1 g/mol, nitrogen is 14 g/mol, and oxygen is 16 g/mol. Therefore, the molar mass of HNO3 is 1 + 14 + (3 × 16) g/mol = 63 g/mol.
Now, with the moles of HNO3 and the volume of the solution, we can calculate the molarity.
Step 1: Convert the given density to mass of the solution (1000 cc = 1 L):
Density = mass / volume
mass = density × volume
mass = 2.0 g/cc × 1000 cc = 2000 g
Step 2: Calculate the mass of HNO3 in the solution:
mass of HNO3 = (10% / 100%) × mass of the solution
mass of HNO3 = (10/100) × 2000 g = 200 g
Step 3: Calculate the moles of HNO3:
moles of HNO3 = mass of HNO3 / molar mass of HNO3
moles of HNO3 = 200 g / 63 g/mol ≈ 3.175 mol
Step 4: Calculate the volume of the solution:
volume of the solution = mass of the solution / density
volume of the solution = 2000 g / 2.0 g/cc = 1000 cc = 1 L
Step 5: Calculate the molarity:
Molarity (M) = moles of HNO3 / volume of solution
Molarity (M) = 3.175 mol / 1 L = 3.175 M
Therefore, the molarity of the 10% HNO3 (w/w) solution with a density of 2.0 g/cc at 25°C is approximately 3.175 M.