Question

A sodium hydroxide solution is prepared by dissolving \(6.0 \mathrm{~g} \mathrm{NaOH}\) in \(1.00 \mathrm{~L}\) of solution. What is the molar concentration of \(\mathrm{OH}^{-}\) in the solution? What are the \(\mathrm{pOH}\) and the \(\mathrm{pH}\) of the solution? What is the hydrogen ion concentration in the solution?

Short answer

Molarity of NaOH (and hence OH-) is 0.15 M, pOH of the solution is 0.8239, pH of the solution is 13.1761, and the hydrogen ion concentration is approximately 6.76 x 10^{-14} M.

Step-by-step solution

Calculate the number of moles of NaOH

Use the molar mass of NaOH to convert the mass of NaOH to moles. The molar mass of NaOH is approximately 40.00 g/mol. Moles of NaOH = Mass of NaOH / Molar mass of NaOHMoles of NaOH = 6.0 g / 40.00 g/mol

Determine the molarity of the NaOH solution

Molarity is defined as moles of solute per liters of solution. Use the volume of the solution and the number of moles of NaOH calculated in Step 1 to find the molarity (M) of the NaOH solution.Molarity (M) = Moles of NaOH / Volume of solution in litersMolarity (M) = Moles of NaOH / 1.00 L

Find the molar concentration of OH- ions

Since each NaOH molecule dissociates into one Na+ ion and one OH- ion, the molarity of NaOH is equal to the molarity of OH- ions.Molar concentration of OH- = Molarity of NaOH

Calculate the pOH of the solution

The pOH of a solution is calculated using the formula: pOH = -log[OH-]Use the molar concentration of OH- from Step 3 to calculate the pOH.

Calculate the pH of the solution

pH and pOH are related by the following equation at 25 degrees Celsius:pH + pOH = 14Use the pOH calculated in Step 4 to find the pH of the solution.pH = 14 - pOH

Calculate the hydrogen ion concentration

The relationship between pH and the hydrogen ion concentration [H+] is given by:[H+] = 10^{-pH}Use the pH calculated in Step 5 to find the hydrogen ion concentration.

Key concepts

Sodium Hydroxide Solution

Sodium hydroxide (NaOH) is a common base used in chemistry, often found in the form of a white solid or in aqueous solutions. When dissolved in water, NaOH dissociates completely into sodium (Na+) and hydroxide (OH-) ions, making it a strong base. Chemists frequently use it to neutralize acids and in saponification reactions to make soap.

When preparing a sodium hydroxide solution, it's essential to carefully manage the quantity because of its reactivity. Understanding the properties of sodium hydroxide solutions is crucial in many chemical processes, including titrations and pH control in various industrial processes.

Molarity of NaOH

Molarity, symbolized by M, is a measure of the concentration of a solute in a solution. For a solution of NaOH, molarity indicates how many moles of NaOH are present in one liter of solution. To calculate molarity, you can use the formula:
\[ \text{Molarity (M)} = \frac{\text{Moles of NaOH}}{\text{Volume of solution in liters}} \]

Molarity is fundamental when discussing solutions in chemistry because it directly relates the amount of substance with the volume of solution, allowing chemists to predict the outcome of reactions and understand solution behavior.

pH and pOH Relationship

The pH Scale

The pH scale is a measure of the acidity or basicity of a solution. It ranges from 0 to 14, with 7 being neutral, values below 7 indicating acidity, and values above 7 indicating alkalinity. The pOH scale is the counterpart to pH and represents the concentration of hydroxide ions.

Understanding pH and pOH

The pH and pOH of a solution are related and interdependent. At a constant temperature of 25 degrees Celsius, their relationship is described by the equation:\[ \text{pH} + \text{pOH} = 14 \]
This means that by knowing either the pH or the pOH of a solution, you can calculate the other. This relationship is a cornerstone of acid-base chemistry and is essential for understanding the behavior of substances in a solution.

Hydrogen Ion Concentration

Hydrogen ion concentration in a solution is indicative of its acidity or basicity. It is directly related to pH, which is a logarithmic measure of hydrogen ion concentration. The formula to relate these two is given by:\[ [\text{H}^+] = 10^{-\text{pH}} \]

Low pH values correspond to high hydrogen ion concentrations and hence, acidic solutions, while high pH values correspond to lower hydrogen ion concentrations, characterizing basic or alkaline solutions. In practice, chemists can control the hydrogen ion concentration to manipulate the properties and reactions of a solution, making this concept crucial in fields like biochemistry and environmental science.