To determine the molarity of a sodium hydroxide (NaOH) solution using a sample of potassium acid phthalate (KHC₈H₄O₄), we start by understanding the reaction between the acid and the base. The balanced equation is:
KHC₈H₄O₄ (aq) + NaOH (aq) ⟶ H₂O (l) + KNaC₈H₄O₄ (aq)
First, we need to calculate the number of moles of KHC₈H₄O₄ in the 0.902 g sample. The molar mass of potassium acid phthalate is given as 204.22 g/mol. The formula to calculate moles is:
Moles = Mass (g) / Molar Mass (g/mol)
Substituting the values:
Moles of KHC₈H₄O₄ = 0.902 g / 204.22 g/mol ≈ 0.00442 mol
From the balanced equation, we see that the reaction between KHC₈H₄O₄ and NaOH is a 1:1 ratio. This means that the moles of NaOH will also be 0.00442 mol.
Next, we need to know the volume of the NaOH solution used during the titration to find its molarity. If, for example, you used 50.0 mL of the NaOH solution, we can convert this volume to liters:
Volume (L) = Volume (mL) / 1000
Volume of NaOH = 50.0 mL / 1000 = 0.0500 L
Now, we can calculate the molarity (M) of the NaOH solution using the formula:
Molarity (M) = Moles of solute / Volume of solution (L)
Substituting the values we calculated:
Molarity of NaOH = 0.00442 mol / 0.0500 L = 0.0884 M
Therefore, the molarity of the NaOH solution is approximately 0.0884 M. This method can be applied to any titration using a standard acid to find the concentration of a base.