Sure, let's go through the calculations step by step to find the molarity of the NaOH solution.
### Step 1: Determine the Molar Mass of KHP (Potassium Hydrogen Phthalate)
The chemical formula for KHP is [tex]\(KHC_8H_4O_4\)[/tex]. To find its molar mass, we add up the atomic masses of each atom in the formula:
- Potassium (K): 39.1 g/mol
- Hydrogen (H): 1.0 g/mol
- Carbon (C): 12.0 g/mol
- Oxygen (O): 16.0 g/mol
[tex]\[
\text{Molar mass of KHP} = 39.1 + 1 \times 1.0 + 8 \times 12.0 + 4 \times 1.0 + 4 \times 16.0 = 204.1 \ \text{g/mol}
\][/tex]
### Step 2: Calculate the Moles of KHP
Given that the mass of KHP used is 1.019 grams, we can find the number of moles of KHP by dividing the mass by its molar mass:
[tex]\[
\text{Moles of KHP} = \frac{\text{Mass of KHP}}{\text{Molar mass of KHP}} = \frac{1.019 \ \text{g}}{204.1 \ \text{g/mol}} = 0.00499265066144047 \ \text{moles}
\][/tex]
### Step 3: Calculate the Volume of NaOH Used
In the titration, we measure the initial volume ([tex]\(V_i\)[/tex]) and the final volume ([tex]\(V_f\)[/tex]). For trial 1, the values are:
- [tex]\(V_i = 33.87 \ \text{mL}\)[/tex]
- [tex]\(V_f = 45.73 \ \text{mL}\)[/tex]
The volume of NaOH used in the titration is:
[tex]\[
\text{Volume of NaOH} = V_f - V_i = 45.73 \ \text{mL} - 33.87 \ \text{mL} = 11.86 \ \text{mL}
\][/tex]
To convert the volume from milliliters to liters:
[tex]\[
\text{Volume of NaOH in liters} = \frac{11.86 \ \text{mL}}{1000} = 0.011860 \ \text{L}
\][/tex]
### Step 4: Calculate the Molarity of the NaOH Solution
Molarity ([tex]\(M\)[/tex]) is defined as the number of moles of solute per liter of solution. Here, the solute is NaOH, and we use the moles of KHP which, due to the 1:1 reaction stoichiometry, equals the moles of NaOH used.
[tex]\[
\text{Molarity of NaOH} = \frac{\text{Moles of KHP}}{\text{Volume of NaOH in liters}} = \frac{0.00499265066144047 \ \text{moles}}{0.011860 \ \text{L}} = 0.4209654857875607 \ \text{M}
\][/tex]
### Summary:
Through these calculations, we determined that the molarity of the NaOH solution used in the titration is approximately [tex]\(0.421 \ \text{M}\)[/tex].
