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Chapter 15: Problem 52

Find the \(\mathrm{pH}\) of a solution prepared by dissolving 0.65 \(\mathrm{mol}\) of the strong base \(\mathrm{NaOH}\) in 1.0 \(\mathrm{L}\) of water.

Short Answer

Expert verified
The pH of the solution is approximately 13.81

Step by step solution

01

Understand the behavior of a strong base in a solution

When a strong base like NaOH is dissolved in water, it completely dissociates. This means, one mole of NaOH will give one mole of hydroxide ions (OH-). Since we are given that 0.65 moles of NaOH is dissolved in the solution, this same amount of hydroxide ions (0.65 moles) has been produced.
02

Calculate the concentration of OH-

Now, we calculate the concentration of OH- ions in the solution. The concentration is calculated as moles of solute (OH- ions in this case) divided by volume of the solution in liters. We are given that the volume is 1.0 L and from step 1 we know that the moles of OH- ions is 0.65 moles, so the concentration (c) is 0.65 mols/1.0 L = 0.65 M.
03

Calculate pOH

We can now calculate the pOH of the solution using the formula \(pOH = - \log [OH^-]\). Substituting the OH- concentration from step 2 into the formula gives \(pOH = - \log [0.65]\). Using a calculator to find the logarithm gives \(pOH \approx 0.19\).
04

Calculate pH

Finally, we can find pH from the pOH. The sum of the pH and pOH is 14, so the pH can be calculated with the formula \(pH = 14 - pOH\). Substituting the pOH from step 3 into the formula gives \(pH = 14 - 0.19 = 13.81\).

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Most popular questions from this chapter

A solution of acetic acid had the following solute concentrations: \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]=\) \(0.035 \mathrm{M},\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.4 \times 10^{-4} \mathrm{M},\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]=7.4 \times 10^{-4} \mathrm{M} .\) Calculate the \(K_{a}\) of acetic acid based on these data.

Why is a buret, rather than a graduated cylinder, used in titrations?

An HNO \(_{3}\) solution has a pH of \(3.06 .\) What volume of 0.015 \(\mathrm{M}\) LiOH will be required to titrate 65.0 \(\mathrm{mL}\) of the HNO \(_{3}\) solution to reach the equivalence point?

Identify each of the following compounds as an acid or a base according to the Bronsted-Lowry classification. For each species, write the formula and the name of its conjugate. \begin{equation} \begin{array}{l}{\text { a. } \mathrm{CH}_{3} \mathrm{COO}^{-}} \\ {\text { b. HCN }} \\ {\text { c. HOOCCOOH }} \\ {\text { d. } C_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}}\end{array} \end{equation}

Would the \(\mathrm{pH}\) at the equivalence point of a titration of a weak acid with a strong base be less than, equal to, or greater than 7.0\(?\)
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