To determine the pH of the solution, we first need to calculate the concentration of hydroxide ions (OH⁻). Here's how we can do it step by step:
Step 1: Calculate the number of moles of NaOH.
The molar mass of NaOH (sodium hydroxide) is 40.00 gmol⁻¹. To find the number of moles, we use the formula:
moles of NaOH = mass of NaOH (in grams) / molar mass of NaOH (in gmol⁻¹)
Plugging in the given values:
moles of NaOH = 13.46 g / 40.00 gmol⁻¹
Calculating the moles of NaOH, we get:
moles of NaOH = 0.3365 mol (rounded to 4 decimal places)
Step 2: Convert the volume of the solution from milliliters to liters.
Since concentration is usually expressed in moles per liter (mol/L), we need the volume in liters:
volume of solution in liters = volume of solution in mL / 1000 mL/L
volume of solution in liters = 500.0 mL / 1000
volume of solution in liters = 0.500 L
Step 3: Calculate the concentration of NaOH in the solution.
Concentration is defined as:
concentration of NaOH (mol/L) = moles of NaOH / volume of solution in liters
Using the values we have:
concentration of NaOH = 0.3365 mol / 0.500 L
Therefore:
concentration of NaOH = 0.673 mol/L
Step 4: Since NaOH is a strong base, it completely dissociates in water to form Na⁺ and OH⁻ ions.
This means the concentration of OH⁻ ions is the same as the concentration of NaOH, which is 0.673 mol/L.
Step 5: Calculate the pOH of the solution.
The pOH is given by the negative logarithm (base 10) of the hydroxide ion concentration:
pOH = -log[OH⁻]
So, for our solution:
pOH = -log(0.673 mol/L)
Using a calculator, you would compute the pOH:
pOH ≈ 0.172 (value rounded to three decimal places)
Step 6: Calculate the pH of the solution.
The relationship between pH and pOH is given by:
pH + pOH = 14 (at 25°C)
So, substituting the value we have for pOH:
pH = 14 - pOH
pH = 14 - 0.172
Calculating pH, we get:
pH ≈ 13.828 (value rounded to three decimal places)
Thus, the pH of the NaOH solution is approximately 13.828.
