A compound has four pKa values (3.5, 5.8, 9, and 12). Calculate the pH of the solution when 500 ml of 0.50 M of tetrasodium X is mixed with 650 ml of 1.0 M HCl. Include chemical equations in the answer.
To calculate the pH of the solution after mixing tetrasodium X and HCl, we need to consider the reactions that occur.
First, write the balanced equation for the reaction between tetrasodium X and HCl:
X4Na + 4HCl → 4NaCl + XH
Since tetrasodium X has four acidic hydrogens, it will react with four equivalents of HCl, producing four equivalents of sodium chloride (NaCl) and one equivalent of XH (the compound with the acidic hydrogens).
Next, determine the moles of tetrasodium X and HCl used:
For tetrasodium X:
moles of X = concentration of tetrasodium X × volume of tetrasodium X solution
= 0.50 M × 0.500 L
= 0.250 moles
For HCl:
moles of HCl = concentration of HCl × volume of HCl solution
= 1.0 M × 0.650 L
= 0.650 moles
Since tetrasodium X reacts with four equivalents of HCl, the limiting reagent is HCl. Therefore, we will use the moles of HCl in further calculations.
Now, calculate the number of moles of XH formed:
moles of XH = moles of HCl × (1 mole XH / 4 moles HCl)
= 0.650 moles × (1 mole XH / 4 moles HCl)
= 0.1625 moles XH
Given the pKa values of XH (3.5, 5.8, 9, and 12), we can determine which acidic group is deprotonated based on the pH. Deprotonation occurs when the pH is higher than the pKa value.
Since we are mixing tetrasodium X (a strong base) with HCl (a strong acid), we can assume the pH of the solution will be highly acidic. Therefore, all the acidic groups of XH will be protonated (pH < pKa). As a result, the pH will essentially be the pH of the HCl solution, which is about 0.
Therefore, the pH of the solution after mixing will be around 0.