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Chapter 6: Problem 80

The concentration of a certain sodium hydroxide solution was determined by using the solution to titrate a sample of potassium hydrogen phthalate (abbreviated as KHP). KHP is an acid with one acidic hydrogen and a molar mass of \(204.22 \mathrm{g} / \mathrm{mol}\). In the titration, \(34.67 \mathrm{mL}\) of the sodium hydroxide solution was required to react with 0.1082 g KHP. Calculate the molarity of the sodium hydroxide.

Short Answer

Expert verified
The molarity of the sodium hydroxide solution is 0.0153 M.

Step by step solution

01

1. Write the balanced equation for the reaction between NaOH and KHP

The reaction between sodium hydroxide (NaOH) and potassium hydrogen phthalate (KHP) can be written as follows: \(NaOH + KHC_8H_4O_4 \rightarrow NaKC_8H_4O_4 + H_2O\) This balanced equation shows that one mole of NaOH reacts with one mole of KHP.
02

2. Calculate the moles of KHP

We are given the mass of KHP, 0.1082 g, and its molar mass, 204.22 g/mol. We can calculate the moles of KHP in the sample using the following formula: Moles of KHP = (mass of KHP) / (molar mass of KHP) Moles of KHP = \(0.1082\ g / 204.22\ g/mol = 5.30 \times 10^{-4}\ mol\)
03

3. Determine the moles of NaOH that reacted with KHP

From the balanced equation, we know that one mole of NaOH reacts with one mole of KHP. So, the moles of NaOH that reacted with KHP will be the same as the moles of KHP. Moles of NaOH = moles of KHP = \(5.30 \times 10^{-4} \ mol\)
04

4. Calculate the molarity of the sodium hydroxide

We are given the volume of the sodium hydroxide solution used in the titration, 34.67 mL. To calculate the molarity (M) of the NaOH solution, we will use the following formula: Molarity of NaOH = (moles of NaOH) / (volume of NaOH in liters) First, we need to convert the volume of NaOH to liters: \(34.67\ mL \times \frac{1\ L}{1000\ mL} = 0.03467\ L\) Now, we can calculate the molarity of the NaOH solution: Molarity of NaOH = \(\frac{5.30 \times 10^{-4} \ mol}{0.03467\ L} = 0.0153\ M\) So, the molarity of the sodium hydroxide solution is 0.0153 M.

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