A student titrates 20.0 \(\mathrm{mL}\) of 1.0 \(M \mathrm{NaOH}\) with 2.0 \(\mathrm{M}\), \(\mathrm{HCO}_{2} \mathrm{H}\left(K_{\mathrm{a}}=1.8 \times 10^{-4}\right) .\) Formic acid is a monoprotic acid. How much formic acid is necessary to reach the equivalence point? (A) 10.0 mL (B) 20.0 mL (C) 30.0 mL (D) 40.0 mL

Short Answer

Expert verified
A) 10.0 mL

Step by step solution

01

Calculate moles of NaOH

First, the total moles of NaOH in the initial solution need to be calculated. The molarity (M) of a solution is defined as the moles of solute per liter of solution (mol/L). Thus, moles of NaOH can be calculated using the formula:Moles = Molarity x VolumeMolarity of NaOH = 1M and the volume is 20mL or 0.02L. Replacement of these values into the formula gives:Moles of NaOH = 1M x 0.02L = 0.02mol
02

Use stoichiometry of reaction

From the stoichiometry of the reaction (since formic acid is a monoprotic acid, it donates one proton) there will always be a 1:1 molar ratio between NaOH and HCO2H. So, moles of HCO2H needed to react with all NaOH = moles of NaOH = 0.02mol
03

Calculate volume of formic acid

Finally, the volume of 2M HCO2H needed to react with all the NaOH can be calculated. We already know the moles of HCO2H required and the molarity of the HCO2H solution, so we can use the formula:Volume = Moles ÷ MolarityVolume of HCO2H = 0.02mol ÷ 2M = 0.01L or 10 mL

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