A 6.50-g sample of a diprotic acid requires 137.5 mL of a 0.750 M NaOH solution for complete neutralization. Determine the molar mass of the acid.

Short Answer

Expert verified
The molar mass of the diprotic acid can be calculated by first determining the moles of NaOH (0.1031 mol) used in the reaction, then finding the moles of the diprotic acid (0.05155 mol) based on the stoichiometry of the balanced equation. Finally, dividing the mass of the diprotic acid (6.50 g) by the moles of the acid results in a molar mass of 126.0 g/mol for the diprotic acid.

Step by step solution

01

Write the balanced chemical equation for the reaction.

The general formula for the reaction between a diprotic acid (H2A) and sodium hydroxide (NaOH) is: H2A + 2NaOH -> 2H2O + Na2A (This equation represents the complete neutralization of the diprotic acid and the formation of water and the sodium salt of the acid.)
02

Find the moles of NaOH.

We are given the volume and the concentration of the NaOH solution. To find the moles of NaOH, we will use the formula: moles of NaOH = volume (in liters) × concentration moles of NaOH = (137.5 mL × (1 L / 1000 mL)) × 0.750 M moles of NaOH = 0.1031 mol
03

Determine the moles of the diprotic acid.

Using the stoichiometry from the balanced chemical equation, we can determine the moles of the diprotic acid (H2A): 1 moles of H2A react with 2 moles of NaOH So, for the moles of NaOH calculated in Step 2, we can find the moles of H2A by dividing the moles of NaOH by 2: moles of H2A = moles of NaOH / 2 moles of H2A = 0.1031 mol / 2 moles of H2A = 0.05155 mol
04

Calculate the molar mass of the diprotic acid.

Now that we have the moles of the diprotic acid, we can calculate its molar mass using the formula: molar mass = mass of the acid / moles of the acid We are given the mass of the diprotic acid as 6.50 g. So: molar mass = 6.50 g / 0.05155 mol molar mass = 126.0 g/mol The molar mass of the diprotic acid is 126.0 g/mol.

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