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 range of H3PO4 content.
pH range lower limit:
pH range upper limit:
For the lower limit I would multiply 0.00057*75 which gives g/100 and multiply by 10 to convert to g/L. Then g/molar mass H3PO4 = moles/L = M
Look up k1 for H3PO4, solve for H^+ and convert to pH.
The upper limit would be similar.
2.33*10^-3
To estimate the pH range corresponding to the given range of phosphoric acid content in cola drinks, we need to consider the dissociation of phosphoric acid (H3PO4) in water.
Phosphoric acid dissociates into three hydrogen ions (H+) and one phosphate ion (PO43-) in a stepwise manner. Each stage of dissociation has its own equilibrium constant (Ka) and contributes to the overall acidity of the solution. The three dissociation reactions of H3PO4 are as follows:
1st dissociation: H3PO4 ⇌ H+ + H2PO4-
2nd dissociation: H2PO4- ⇌ H+ + HPO42-
3rd dissociation: HPO42- ⇌ H+ + PO43-
The overall acidity of the solution, represented by the pH, depends on the concentration of hydrogen ions (H+) in the solution. Mathematically, the pH is defined as the negative logarithm of the hydrogen ion concentration.
To estimate the pH range, we can consider the upper and lower limits of the phosphoric acid content mentioned in the question.
1. Lower limit: 0.057% of 75% phosphoric acid, by mass
This corresponds to a concentration of phosphoric acid in cola drinks of 0.057 / 100 * 0.75 = 0.0004275 moles per liter (mol/L).
2. Upper limit: 0.084% of 75% phosphoric acid, by mass
This corresponds to a concentration of phosphoric acid in cola drinks of 0.084 / 100 * 0.75 = 0.00063 moles per liter (mol/L).
Now, we can use these concentrations of phosphoric acid to calculate the pH range:
1. Lower limit:
Using the dissociation constant (Ka) for the 1st dissociation reaction: H3PO4 ⇌ H+ + H2PO4-, which is approximately 7.5 × 10^-3 mol/L, we can estimate the concentration of hydrogen ions (H+) at equilibrium. However, to calculate the pH, we need to account for the three stages of dissociation.
As a rough estimate, assuming equal contribution from each stage of dissociation, we can consider the concentration of H+ ions as one-third of the concentration of the 1st stage (H3PO4): 0.0004275 / 3 mol/L = 0.0001425 mol/L.
Taking the negative logarithm of this concentration, we get the estimated pH lower limit.
2. Upper limit:
Using the same approach as above but with the concentration of H3PO4 at the upper limit (0.00063 mol/L), we can calculate the estimated pH upper limit.
Please note that this estimation assumes ideal conditions and equal contribution from each stage of dissociation. In reality, the actual pH may vary due to other factors in the drink, such as carbonation, additional acidity from other ingredients, etc.
So, in conclusion:
pH range lower limit: Estimated value from the calculation above.
pH range upper limit: Estimated value from the calculation above.