Phosphoric Acid is usually obtained at an 85% phosphoric acid solution, by mass. If this solution is 15 M, what is the density of the solution? Express your answer in g/ml
What is the molality of the solution in the phorphoric acid solution
Take the M of the solution times .85 to find the M of the phosphoric acid:
15 M x .85 = 12.75 M
If you assume 1L solution, that would mean there are 12.75 mol H3PO4 (Since M = mol solute/L solvent).
12.75 mol H3PO4 time the molecular weight of H3PO4 (98g/mol) gives you 1249.5 grams in 1 Liter of solution
So 1.2495g in 1mL of solution. Round the significant figures and the answer is 1.2 g/ml.
15 M = 15 mol / L. In 1 L of solution there are 15 mol of H3PO4. molar mass of H3PO4 = 97.995 g / mol.
Then 15 mol x 97.995 g / mol = 1,469.9 g of H3PO4 which is the 85% of total mass of solution.
Total mass = 1,469.9 g / 0.85 = 1,729 g of solution in 1 L
Density solution = 1,469.9 g/ 1,000.0 mL = 1,729 g / mL
This is slightly high for a 85% H3PO4. The real value is 1.685 g / mL at 25 oC. This is due to the fact that the Molarity of 85% H3PO4 is 14.7 M not 15 M.
To determine the density of the solution, we need to know the mass and volume of the solution.
Let's assume we have 100 g of the 85% phosphoric acid solution. This means that there is 85 g of phosphoric acid in this solution.
To calculate the volume, we need to use the molarity (M) and the molecular weight (MW) of phosphoric acid.
The molecular weight of phosphoric acid (H3PO4) can be calculated as follows:
1 atom of phosphorus (P) weighs 30.97 g/mol
3 atoms of oxygen (O) weigh 3 * 16.00 g/mol = 48.00 g/mol
4 atoms of hydrogen (H) weigh 4 * 1.01 g/mol = 4.04 g/mol
Therefore, the molecular weight of phosphoric acid is 30.97 + 48.00 + 4.04 = 83.01 g/mol.
Given that the solution is 15 M, which means there are 15 moles of phosphoric acid in 1 liter of solution (1 L = 1000 mL), we can calculate the volume using the following formula:
Volume (mL) = mass (g) / (Molarity (mol/L) × Molecular weight (g/mol))
Plugging in the values, we get:
Volume (mL) = 100 g / (15 mol/L × 83.01 g/mol)
Volume (mL) = 100 g / 1245.15 g/L
Volume (mL) ≈ 0.0802 L or 80.2 mL
Now that we know the mass (100 g) and volume (80.2 mL) of the solution, we can calculate the density using the following formula:
Density (g/mL) = Mass (g) / Volume (mL)
Density (g/mL) = 100 g / 80.2 mL ≈ 1.247 g/mL
Therefore, the density of the 85% phosphoric acid solution is approximately 1.247 g/mL.