Question

What mass of KOH is necessary to prepare 800.0 \(\mathrm{mL}\) of a solution having a \(\mathrm{pH}=11.56 ?\)

Short answer

The mass of KOH needed to prepare 800.0 mL of a solution having a pH of 11.56 is \(0.163 g\).

Step-by-step solution

Determine the concentration of the KOH solution using the given pH value.

The pH value determines the concentration of hydrogen ions (H+) in the solution. Since KOH is a strong base, the pH value provided gives us information about the pOH value, which determines the concentration of hydroxide ions (OH-). The relationship between pH and pOH is: \[pH + pOH = 14\] First, we need to find the pOH value: \: pOH = 14 - pH Then, we can use the pOH value to find the concentration of the OH- ions in the solution: \[ [OH^-] = 10^{-pOH} \]

Calculate the concentration of the KOH solution.

Now, we can calculate the pOH value and use it to determine the concentration of the OH- ions in the solution. \ \: pOH = 14 - 11.56 = 2.44 \ \: [OH^-] = 10^{-2.44} = 3.63 × 10^{-3} M Since KOH is a strong base and it dissociates completely in water, the concentration of the KOH solution is equal to the concentration of OH-. Therefore, the concentration of the KOH solution is 3.63 ×10^{-3} M.

Use the volume of the solution to find the moles of KOH needed.

To find the number of moles of KOH required for the given volume, we can use the formula: \[moles\ of\ KOH = Volume\ of\ solution × Concentration\ of\ solution\] We have the volume of the solution in mL, so we need to convert it to liters: \[ Volume\ of\ solution = 800.0 mL × \frac{1\: L}{1000\: mL} = 0.800 L \] Now, we can calculate the moles of KOH: \: moles\ of\ KOH = 0.800 L × 3.63 × 10^{-3} M = 2.904 × 10^{-3} mol

Calculate the mass of KOH required.

Lastly, we will use the molar mass of KOH to convert moles to mass. The molar mass of KOH is: \[Molar\ mass\ of\ KOH\ = 39.1\ (K) + 15.999\ (O) + 1.008\ (H) = 56.1\: g/mol\] Now, we can calculate the mass of KOH required: \[mass\ of\ KOH = moles\ of\ KOH × Molar\ mass\ of\ KOH\] \: mass\ of\ KOH = 2.904 × 10^{-3} mol × 56.1 g/mol = 0.163 g

Final Answer:

The mass of KOH needed to prepare 800.0 mL of a solution having a pH of 11.56 is 0.163 g.

Key concepts

pH and pOH relationship

When dealing with solutions, understanding the relationship between pH and pOH is crucial. These two measures are part of a logarithmic scale used to express the acidity or basicity of a solution. The pH scale ranges from 0 to 14, where a low pH indicates high acidity, and a high pH indicates high basicity. The pOH scale, while less commonly used, is a similar measure but for the concentration of hydroxide ions. The fundamental relationship between these two scales is given by the equation: \[ pH + pOH = 14 \].Whenever you know the pH of a solution and need to know how basic it is, you can simply subtract the pH from 14 to find the pOH. For instance, for a solution with a pH of 11.56, the pOH would be calculated as:\[ pOH = 14 - 11.56 = 2.44 \].This relationship is especially useful in calculating the concentrations of ions in the solution, particularly when dealing with strong acids or bases like KOH, which dissociates fully in water.

hydroxide ion concentration

Once you have the pOH value, calculating the hydroxide ion concentration becomes straightforward. The concentration of hydroxide ions \( [OH^-] \) can be found using the formula:\[ [OH^-] = 10^{-pOH} \].This formula allows you to determine the number of hydroxide ions in the solution, from which you can understand its basic nature. For our base, potassium hydroxide (KOH), the calculation with a pOH of 2.44 is:\[ [OH^-] = 10^{-2.44} = 3.63 \times 10^{-3} \, \text{M}\].It’s important to note that since KOH completely dissociates in water, the hydroxide ion concentration is equal to the molarity of the KOH solution. This tells us that for every mole of KOH dissolved, one mole of hydroxide ions is produced, allowing us to directly link the concentration of the base to the concentration of hydroxide ions.

molar mass calculation

The molar mass of a compound is determined by adding up the atomic masses of all the atoms in a molecule. For potassium hydroxide (KOH), this involves calculating the sum of the atomic masses of potassium (K), oxygen (O), and hydrogen (H).Here's how you do it:

• Potassium (K): 39.1 g/mol
• Oxygen (O): 16.0 g/mol
• Hydrogen (H): 1.008 g/mol

Adding these together gives:\[ \text{Molar mass of KOH} = 39.1 + 16.0 + 1.008 = 56.1 \, \text{g/mol} \].This calculation is essential for translating the number of moles of a substance into a mass, which is usually what we measure in practical scenarios. With this molar mass, we can convert the amounts of moles derived from molarity into grams, which is particularly helpful when preparing precise quantities of solutions.

moles to mass conversion

Converting the number of moles into mass is a fundamental concept in chemistry that allows for precise preparation of solutions. The relationship between moles and mass is defined by the equation:\[ \text{Mass} = \text{Moles} \times \text{Molar mass} \].Using our example of KOH, we calculated the moles of KOH needed for an 800.0 mL solution as 2.904 \times 10^{-3} mol. To find the mass, multiply this number by the molar mass of KOH, which we've established as 56.1 g/mol:\[ \text{Mass of KOH} = 2.904 \times 10^{-3} \, \text{mol} \times 56.1 \, \text{g/mol} = 0.163 \, \text{g} \].This conversion is instrumental in lab settings where solutions must be prepared accurately. Knowing how to switch between moles and grams ensures that the correct amount of a solute is used to achieve the desired concentration in a solution. It allows scientists and students alike to create solutions that are both precise and reliable.