Determine the pH (to two decimal places) of the solution that is produced by mixing 30.3 mL of 1.00×10-4 M HBr with 829 mL of 5.77×10-4 M Ca(OH)2.
To determine the pH of the solution produced by mixing HBr and Ca(OH)2, we need to consider the acid-base reaction that occurs between them.
HBr (hydrobromic acid) is a strong acid, and Ca(OH)2 (calcium hydroxide) is a strong base. Therefore, they will react to form water (H2O) and an ionic compound called calcium bromide (CaBr2).
The balanced chemical equation for the reaction is:
2HBr + Ca(OH)2 -> 2H2O + CaBr2
From the balanced equation, we can see that 2 moles of HBr react with 1 mole of Ca(OH)2 to produce 2 moles of H2O and 1 mole of CaBr2.
Now, let's calculate the number of moles of HBr and Ca(OH)2 in the given volumes.
For HBr:
Volume of HBr = 30.3 mL
Concentration of HBr = 1.00×10^(-4) M
Number of moles of HBr = Concentration × Volume
= 1.00×10^(-4) M × 0.0303 L
= 3.03×10^(-6) moles
For Ca(OH)2:
Volume of Ca(OH)2 = 829 mL
Concentration of Ca(OH)2 = 5.77×10^(-4) M
Number of moles of Ca(OH)2 = Concentration × Volume
= 5.77×10^(-4) M × 0.829 L
= 4.77×10^(-4) moles
Based on the reaction stoichiometry, we can see that 2 moles of HBr react with 1 mole of Ca(OH)2. Therefore, the limiting reactant is Ca(OH)2 because there are fewer moles available for the reaction.
Since all the Ca(OH)2 will react, we can find the number of moles of HBr that react by using the stoichiometry of the balanced equation.
Using the ratio:
2 moles HBr react with 1 mole Ca(OH)2
Number of moles of HBr reacted = (Number of moles of Ca(OH)2) × (2 moles HBr / 1 mole Ca(OH)2)
= 4.77×10^(-4) moles × (2 / 1)
= 9.54×10^(-4) moles
Now that we know the number of moles of HBr that reacted, we can calculate the new concentration of HBr in the solution.
Total volume of the solution = Volume of HBr + Volume of Ca(OH)2
= 30.3 mL + 829 mL
= 859.3 mL
Concentration of HBr in the solution = (Number of moles of HBr reacted) / (Total volume of the solution in liters)
= (9.54×10^(-4) moles) / (0.8593 L)
= 1.110×10^(-3) M
Now, to determine the pH of the solution, we need to find the concentration of H+ ions. Since HBr is a strong acid, it dissociates completely in water to produce H+ ions. Therefore, the concentration of H+ ions is equal to the concentration of HBr.
Concentration of H+ ions = 1.110×10^(-3) M
Finally, we can calculate the pH using the formula:
pH = -log(H+ concentration)
pH = -log(1.110×10^(-3))
pH ≈ 2.953
Therefore, the pH of the solution produced by mixing 30.3 mL of 1.00×10^(-4) M HBr with 829 mL of 5.77×10^(-4) M Ca(OH)2 is approximately 2.95.