Answer:
Step-by-step explanation:
To solve this problem, we need to use the balanced chemical equation for the reaction between hydrobromic acid (HBr) and magnesium hydroxide (Mg(OH)2):
2HBr + Mg(OH)2 -> MgBr2 + 2H2O
From the equation, we can see that 2 moles of hydrobromic acid react with 1 mole of magnesium hydroxide.
We are given the volume of the hydrobromic acid as 5.0 mL, but we do not know the number of moles of hydrobromic acid present. However, we do know the concentration and volume of the magnesium hydroxide used for the titration. We can use this information to calculate the number of moles of magnesium hydroxide used in the titration:
Molarity of Mg(OH)2 = 1.50 M
Volume of Mg(OH)2 used = unknown (we don't know how much was added to reach the endpoint)
We can assume that the reaction between the two solutions goes to completion and that all the magnesium hydroxide reacts with the hydrobromic acid present. Therefore, we can set up the following equation using the stoichiometry of the reaction:
2 moles HBr = 1 mole Mg(OH)2
moles of HBr = (moles of Mg(OH)2) / 2
Using the equation for molarity (M = moles / liters), we can calculate the number of moles of magnesium hydroxide used in the titration:
Molarity of Mg(OH)2 = moles of Mg(OH)2 / volume of Mg(OH)2
moles of Mg(OH)2 = Molarity of Mg(OH)2 x volume of Mg(OH)2
We don't know the volume of Mg(OH)2 used, but we can use the volume of hydrobromic acid and the balanced chemical equation to determine it. Since 2 moles of HBr react with 1 mole of Mg(OH)2, we can say that:
moles of Mg(OH)2 = (moles of HBr) / 2
Using the equation for molarity and the given volume of hydrobromic acid (5.0 mL or 0.005 L), we can calculate the number of moles of hydrobromic acid present:
Molarity of HBr = moles of HBr / volume of HBr
moles of HBr = Molarity of HBr x volume of HBr
Now we can combine the equations to solve for the unknown volume of magnesium hydroxide used in the titration:
moles of Mg(OH)2 = (Molarity of Mg(OH)2) x (volume of Mg(OH)2)
moles of HBr = 0.5 x moles of Mg(OH)2 (since 2 moles of HBr react with 1 mole of Mg(OH)2)
moles of HBr = (Molarity of HBr) x (volume of HBr)
Since the moles of HBr are the same in both equations, we can set them equal to each other:
(Molarity of HBr) x (volume of HBr) = 0.5 x (Molarity of Mg(OH)2) x (volume of Mg(OH)2)
Solving for the unknown variable, we get:
(Molarity of HBr) = (0.5 x (Molarity of Mg(OH)2) x (volume of Mg(OH)2)) / (volume of HBr)
(Molarity of HBr) = (0