Question

If the \(\mathrm{pH}\) of an \(\mathrm{NaOH}\) solution is \(13.0\), what is the concentration of \(\mathrm{NaOH}\) ?

Short answer

The concentration of the NaOH solution is 0.1 M.

Step-by-step solution

Calculate the pOH value

First, the pOH value needs to be calculated using the relationship pH + pOH = 14, where pH is given as 13. Therefore, pOH = 14 - 13 = 1.

Calculate the OH- ion concentration

Next, the concentration of OH- ions is calculated using the formula: [OH-] = 10^-pOH. Substituting pOH = 1 into this formula gives: [OH-] = 10^-1 = 0.1 M.

Determine the concentration of NaOH

Since NaOH is a strong base and completely ionizes in water, the concentration of NaOH is equal to the concentration of OH- ions. Therefore, the concentration of the NaOH solution is also 0.1 M.

Key concepts

Understanding pOH and its Relationship with pH

The pOH scale is a measure of the hydroxide ion concentration \(\text{[OH}^-\text{]}\) in a solution. It's complementary to the pH scale, which measures the hydrogen ion concentration. Together, pH and pOH are related through the equation: \[ \text{pH} + \text{pOH} = 14 \] This relationship is valid for all aqueous solutions at 25°C. By knowing the pH of a solution, you can easily determine its pOH. Simply subtract the pH value from 14. For instance, if a solution has a pH of 13, the corresponding pOH is \(14 - 13 = 1\). Therefore, understanding and calculating pOH is essential for solving various chemistry problems, like determining the concentration of ions present in the solution.

In summary, to calculate pOH, remember these steps:

• Recognize the relationship: \(\text{pH} + \text{pOH} = 14\).
• Subtract the given pH value from 14 to find the pOH.

OH- Concentration Calculation

Once you know the pOH of a solution, it's straightforward to calculate the concentration of hydroxide ions \(\text{[OH}^-\text{]}\). The formula used to determine the \(\text{[OH}^-\text{]}\) is: \[ \text{[OH}^-\text{]} = 10^{-\text{pOH}} \] This equation tells us that the hydroxide ion concentration is equal to \(10\) raised to the negative power of the pOH value. For instance, with a pOH of 1, the concentration of \(\text{OH}^-\text{]}\) becomes \(10^{-1} = 0.1\) M.

It's crucial to understand this concept for quick calculations in chemistry, especially when dealing with alkaline solutions. Calculating \(\text{[OH}^-\text{]}\) gives insight into how basic a solution is and prepares you for the next steps in determining other chemical properties.

To sum it up, the key steps for computing \(\text{[OH}^-\text{]}\) are:

• Use the pOH value obtained.
• Apply the equation: \(\text{[OH}^-\text{]} = 10^{-\text{pOH}}\) and solve.

Calculating NaOH Concentration

Sodium hydroxide \(\text{(NaOH)}\) is a strong base and completely dissociates in water. When solving problems involving \(\text{NaOH}\), the concentration of \(\text{NaOH}\) is equal to the concentration of hydroxide ions \(\text{[OH}^-\text{]}\) it produces. Thus, once \(\text{[OH}^-\text{]}\) is calculated, you directly know the \(\text{NaOH}\) concentration. For example, if \(\text{[OH}^-\text{]}\) is found to be \(0.1\) M, then the concentration of \(\text{NaOH}\) is also \(0.1\) M.

This principle is vital for understanding how strong bases like \(\text{NaOH}\) behave in solutions. They dissociate completely, meaning each formula unit of \(\text{NaOH}\) adds a complete unit of \(\text{OH}^-\text{]}\) to the solution. This direct equivalence simplifies calculations in chemistry, especially when working with strong bases.

Review the process with these steps:

• Understand that \(\text{NaOH}\) dissociates completely in water.
• The \(\text{NaOH}\) concentration equals the \(\text{[OH}^-\text{]}\) concentration.