The balanced chemical equation for the reaction between acetic acid and barium hydroxide is:
2 HC₂H₂O₂ + Ba(OH)₂ → Ba(C₂H₂O₂)₂ + 2 H₂O
From the balanced equation, we can see that 2 moles of acetic acid react with 1 mole of barium hydroxide to produce 1 mole of barium acetate and 2 moles of water.
The number of moles of acetic acid used in the titration can be calculated as follows:
moles of HC₂H₂O₂ = Molarity × volume in liters
moles of HC₂H₂O₂ = 1.2 M × (55.00 mL / 1000 mL/ L)
moles of HC₂H₂O₂ = 0.066 moles
From the balanced equation, we know that 2 moles of acetic acid react with 1 mole of barium hydroxide. Therefore, the number of moles of barium hydroxide present in the titration can be calculated as:
moles of Ba(OH)₂ = 0.066 moles / 2
moles of Ba(OH)₂ = 0.033 moles
The molarity of the barium hydroxide solution can be calculated as:
Molarity = moles / volume in liters
We rearrange this equation to solve for the volume:
volume in liters = moles / Molarity
volume in liters = 0.033 moles / 0.67 M
volume in liters = 0.04925 L
Finally, we convert the volume to milliliters:
volume in mL = 0.04925 L × 1000 mL/L
volume in mL = 49.25 mL
Therefore, the volume of the sample of barium hydroxide used in the titration is 49.25 mL. The answer is blue.