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A 1.00-L aqueous solution contained \(5.80 \mathrm{~g}\) of sodium hydroxide, \(\mathrm{NaOH}\). What was the \(\mathrm{pH}\) of the solution at \(25^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
The pH of the solution is approximately 13.162.

Step by step solution

01

Calculate Moles of Sodium Hydroxide

First, determine the number of moles of sodium hydroxide (NaOH) in the solution. The molar mass of NaOH is the sum of the atomic masses of its elements: \(\mathrm{Na} = 22.99 \, \text{g/mol}\), \(\mathrm{O} = 16.00 \, \text{g/mol}\), \(\mathrm{H} = 1.01 \, \text{g/mol}\), resulting in approximately \(39.99 \, \text{g/mol}\). Use the formula: \[\text{Moles of NaOH} = \frac{\text{Mass of NaOH}}{\text{Molar mass of NaOH}} = \frac{5.80 \, \text{g}}{39.99 \, \text{g/mol}}\approx 0.145 \, \text{mol}\]
02

Determine the Concentration of NaOH

Calculate the concentration of NaOH in the solution using the formula for molarity, which is moles of solute per liter of solution. Since the solution volume is 1.00 L: \[\text{Molarity of NaOH} = \frac{0.145 \, \text{mol}}{1.00 \, \text{L}} = 0.145 \, \text{M}\]
03

Calculate the Concentration of OH鈦 Ions

As NaOH is a strong base, it dissociates completely in water: \[\text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^-\] Thus, the concentration of OH鈦 ions is equal to the concentration of NaOH, which is 0.145 M.
04

Calculate the pOH of the Solution

Calculate the pOH using the concentration of hydroxide ions: \[\text{pOH} = -\log[\text{OH}^-] = -\log(0.145) \approx 0.838\]
05

Determine the pH using the pH-pOH Relationship

Using the relationship between pH and pOH at 25掳C, which is given by: \[\text{pH} + \text{pOH} = 14\] Solve for pH: \[\text{pH} = 14 - \text{pOH} = 14 - 0.838 \approx 13.162\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity
Molarity is a key concept in chemistry that describes the concentration of a solute in a given volume of solution. It is defined as the number of moles of solute per liter of solution, and is expressed in units of moles per liter (M). To calculate the molarity, use the formula:
  • Molarity = Moles of solute / Liters of solution
For the problem involving sodium hydroxide (NaOH), we first need to determine the number of moles of NaOH in the 1-liter solution. By dividing the mass of NaOH by its molar mass, we calculate the moles. Once the moles are known, the molarity can be easily found since the solution volume is provided, which is 1.00 L. This makes our calculation straightforward because the molarity is directly equal to the moles of NaOH, thanks to our convenient 1-liter volume. Understanding molarity helps us grasp how concentrated or dilute a solution is, and it's a fundamental step in calculating other properties, like pH.
Strong Base
A strong base is a compound that completely dissociates into its ions when dissolved in water. Sodium hydroxide (NaOH) is a classic example of a strong base. When NaOH is dissolved in water, it splits entirely into sodium ions (Na+) and hydroxide ions (OH鈭). This complete dissociation is why NaOH is classified as a strong base.
For strong bases, the concentration of the base is equal to the concentration of hydroxide ions, because each unit of base produces one hydroxide ion when dissolved. The strong nature of these bases is their ability to dramatically alter the pH of a solution, due to the increase in hydroxide ion concentration. This is why understanding whether a base is strong or weak is crucial when predicting the chemical behavior of solutions in various reactions. Always remember this total dissociation when performing calculations involving strong bases.
Hydroxide Ion Concentration
The hydroxide ion concentration [OH鈦籡 in a solution tells us how basic the solution is. It is particularly crucial when dealing with strong bases like NaOH, which dissociates completely in solution. Since NaOH dissociates fully, the molarity of the NaOH solution directly equals the concentration of hydroxide ions in solution.
For our solution, with 0.145 M NaOH, the concentration of OH鈦 ions is also 0.145 M. This means each liter of the solution contains 0.145 moles of hydroxide ions.
  • The higher this concentration, the more basic the solution.
  • Hydroxide ion concentration influences the solution's pOH, which in turn helps in calculating the pH.
Monitoring [OH鈦籡 helps predict the reactivity and corrosive capacity of the solution. It's vital in pH calculations, especially for strong bases that fully contribute their hydroxide ions to the solution.
pH and pOH Relationship
The pH and pOH relationship is a simple yet powerful concept that helps us understand the acid-base balance in a solution. At 25掳C, pH and pOH are related by the equation:
  • pH + pOH = 14
This equation results from the water autoionization constant. Using this relationship, if you know either the pH or the pOH, you can easily find the other.
In our NaOH solution example, once the pOH is calculated from the hydroxide ion concentration, we subtract it from 14 to determine the pH.
This relationship is critical for understanding the acidity or basicity of a solution:
  • A low pH indicates high acidity.
  • A high pH indicates high basicity.
  • Neutral solutions have a pH around 7.
Mastering this relationship allows you to tackle a wide range of chemistry problems involving acids, bases, and buffer solutions.

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Most popular questions from this chapter

What is the sum of the \(\mathrm{pH}\) and the \(\mathrm{pOH}\) for a solution at \(37^{\circ} \mathrm{C}\), where \(K_{w}\) equals \(2.5 \times 10^{-14} ?\)

Aluminum chloride, \(\mathrm{AlCl}_{3}\), reacts with trimethylamine, \(\mathrm{N}\left(\mathrm{CH}_{3}\right)_{3} .\) What would you guess to be the product of this reaction? Explain why you think so. Describe the reaction in terms of one of the acid-base concepts. Write an appropriate equation to go with this description. Which substance is the acid according to this acid-base concept? Explain.

Which of the following substances are acids in terms of the Arrhenius concept? Which are bases? Show the acid or base character by using chemical equations. a. \(\mathrm{P}_{4} \mathrm{O}_{10}\) b. \(\mathrm{K}_{2} \mathrm{O}\) c. \(\mathrm{N}_{2} \mathrm{H}_{4}\) d. \(\mathrm{H}_{2} \mathrm{Se}\)

Phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}\), and phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4}\), have approximately the same acid strengths. From this information, and noting the possibility that one or more hydrogen atoms may be directly bonded to the phosphorus atom, draw the structural formula of phosphorous acid. How many grams of sodium hydroxide would be required to completely neutralize \(1.00 \mathrm{~g}\) of this acid?

The following are solution concentrations. Indicate whether each solution is acidic, basic, or neutral. a. \(2 \times 10^{-11} \mathrm{M} \mathrm{OH}^{-}\) b. \(2 \times 10^{-9} \mathrm{M} \mathrm{H}_{3} \mathrm{O}^{+}\) c. \(6 \times 10^{-5} \mathrm{M} \mathrm{OH}^{-}\) d. \(6 \times 10^{-3} \mathrm{M} \mathrm{H}_{3} \mathrm{O}^{+}\)

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