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Chapter 5: Problem 93

The volume of a sample of pure HCl gas was \(189 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\) and \(108 \mathrm{mmHg}\). It was completely dissolved in about \(60 \mathrm{~mL}\) of water and titrated with an \(\mathrm{NaOH}\) solution; \(15.7 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution were required to neutralize the \(\mathrm{HCl}\). Calculate the molarity of the \(\mathrm{NaOH}\) solution.

Short Answer

Expert verified
The molarity of the NaOH solution is calculated using the given data in the problem by implementing the steps present in the solution and using concepts in chemistry such as stoichiometry, ideal gas laws, and titration.

Step by step solution

01

Determine the Number of Moles of HCl

Use the ideal gas law \(PV = nRT\) to find the number of moles \(n\) of HCl. Given that \(P = 108 \mathrm{mmHg}\) (convert to atm by dividing by 760), \(V = 189 \mathrm{mL}\) (convert to L by dividing by 1000), \(R = 0.0821 \mathrm{L \cdot atm/mol \cdot K}\), and \(T = 25\degree C\) (convert to K by adding 273), solve for \(n\).
02

Determine the Number of Moles of NaOH

Since HCl and NaOH react in a 1:1 ratio, stoichiometry tells us that the number of moles of HCl is equal to the number of moles of NaOH. So, the number of moles of NaOH is the same as the number of moles of HCl calculated in step 1.
03

Calculate the Molarity of the NaOH Solution

The molarity (M) is determined by dividing the number of moles of the solute (NaOH) by the volume of the solution in liters. The volume of the NaOH solution was \(15.7 \mathrm{mL}\) (convert to L by dividing by 1000). Substitute the values for the number of moles of NaOH and the volume of the NaOH solution into the formula to calculate the molarity.

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