Cola drinks have a phosphoric acid content that is described as `from 0.057% to 0.084% of 75% phosphoric acid, by mass." Estimate the pH range of cola drinks corresponding to this average range of H3PO4 content.
I am having trouble with the wording of this question, I know I need to find the mass first, then the analytical concentration of H3PO4, but I have no idea how.
I agree it is a little confusing as to exactly what they want. In particular the pH range of the average range is confusing but I would go with the average percent or (0.057+0.084)/2 = about 0.0705%. I would start with 100 mL of solution and that will contain 100 x 0.000705 = 0.0705g of H3PO4. Since that is only 75% pure, then g actual H3PO4 is
0.0705 x 0.75 = g H3PO4.
Convert that to mols, then M = mols/0.1L = ?
To estimate the pH range of cola drinks corresponding to the given average range of H3PO4 content, we first need to calculate the concentration of H3PO4 in the cola drinks.
Given that the phosphoric acid content is described as ranging from 0.057% to 0.084% of 75% phosphoric acid by mass, we can calculate the mass of H3PO4 in cola drinks using the following steps:
1. Assume we have a 100g sample of cola drink (this is just an arbitrary value to make calculations easier).
2. Calculate the range of mass of H3PO4 in the cola drink:
- Lower mass limit: 0.057% of 75g (75% phosphoric acid) = 0.057g
- Upper mass limit: 0.084% of 75g (75% phosphoric acid) = 0.084g
Now that we have the mass of H3PO4, we can calculate the molar concentration of phosphoric acid using the following steps:
3. Find the molar mass of H3PO4:
- H (hydrogen) atomic mass = 1g/mol
- P (phosphorus) atomic mass = 31 g/mol
- O (oxygen) atomic mass = 16 g/mol (x 4 since there are 4 oxygen atoms in H3PO4) = 64 g/mol
- Total molar mass of H3PO4 = 3(1) + 31 + 4(16) = 98g/mol
4. Calculate the molar concentration:
- Lower concentration limit: (0.057g / 98g/mol) = 0.00058 mol/L
- Upper concentration limit: (0.084g / 98g/mol) = 0.00086 mol/L
Finally, to estimate the pH range, we need to take into account the ionization of phosphoric acid in water. Phosphoric acid is a triprotic acid, meaning it can donate three hydrogen ions (H+). Each ionization step is accompanied by a change in the pH.
However, since we're dealing with an average range, let's assume that only one H+ is ionized per H3PO4 molecule. This gives us the average molar concentration of H+ ions:
Average H+ concentration = (0.00058 + 0.00086) mol/L / 2 = 0.00072 mol/L
To estimate the pH range, we can use the formula for the pH of a strong acid:
pH = -log[H+]
Using this formula, we can calculate the pH range:
Lower pH limit: -log(0.00072) ≈ 3.14
Upper pH limit: -log(0.00072) ≈ 3.14
Therefore, the estimated pH range of cola drinks corresponding to the average range of H3PO4 content is approximately 3.14.