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Answer :
The molecular weight of the unknown weak acid is approximately 2.5 g/mol.
To determine the molecular weight of the unknown weak acid, we can use the concept of acid-base titration and the equation:
M1V1 = M2V2
Where:
M1 = Initial concentration of the acid (unknown)
V1 = Initial volume of the acid solution
M2 = Final concentration of the acid (after reaching the equivalence point)
V2 = Final volume of the acid solution
Given:
Mass of the unknown acid = 9.73 g
Volume of the acid solution = 125 mL
Volume of NaOH added = 50.0 mL
Concentration of NaOH = 1.00 M
First, we need to calculate the initial concentration of the unknown acid:
M1 = (mass of the unknown acid) / (volume of the acid solution)
= 9.73 g / 0.125 L (since 125 mL = 0.125 L)
= 77.84 M
Next, we can calculate the final concentration of the acid after reaching the equivalence point. At the equivalence point, the moles of NaOH added are equal to the moles of the weak acid initially present. Therefore, we can use the equation:
M1V1 = M2V2
(77.84 M) × (0.050 L) = M2 × (0.100 L) (since 50 mL = 0.050 L)
Solving for M2:
M2 = (77.84 M × 0.050 L) / 0.100 L
= 38.92 M
Finally, to find the molecular weight (molar mass) of the unknown weak acid, we can use the formula:
Molar mass = (mass of the unknown acid) / (moles of the unknown acid)
Moles of the unknown acid = (final concentration of the acid) * (final volume of the acid solution)
= 38.92 M × 0.100 L
= 3.892 moles
Molar mass = 9.73 g / 3.892 moles
= 2.5 g/mol
Therefore, the molecular weight of the unknown weak acid is approximately 2.5 g/mol.
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