Calculate the pH during the titration of 20.00 mL of 0.1000 M CH3CH2CH2COOH with 0.1000 M NaOH after 26.5 mL of the base have been added. Ka of butanoic acid = 1.54 x 10-5.
To calculate the pH during the titration of butanoic acid (CH3CH2CH2COOH) with sodium hydroxide (NaOH), we need to determine the moles of butanoic acid and sodium hydroxide at the equivalence point.
First, let's calculate the moles of butanoic acid (CH3CH2CH2COOH) using the given volume and molarity:
Moles of CH3CH2CH2COOH = volume (L) x molarity (mol/L)
Moles of CH3CH2CH2COOH = 0.02000 L x 0.1000 mol/L
Moles of CH3CH2CH2COOH = 0.00200 mol
At the equivalence point, the moles of CH3CH2CH2COOH react with an equal number of moles of NaOH. Therefore, if 26.5 mL of 0.1000 M NaOH have been added, we can determine the moles of NaOH used:
Moles of NaOH used = volume (L) x molarity (mol/L)
Moles of NaOH used = 0.02650 L x 0.1000 mol/L
Moles of NaOH used = 0.00265 mol
Since CH3CH2CH2COOH and NaOH react in a 1:1 ratio, the moles of CH3CH2CH2COOH remaining would be:
Moles of CH3CH2CH2COOH remaining = Moles of CH3CH2CH2COOH - Moles of NaOH used
Moles of CH3CH2CH2COOH remaining = 0.00200 mol - 0.00265 mol
Moles of CH3CH2CH2COOH remaining = -0.00065 mol (note that the negative sign indicates that all the CH3CH2CH2COOH has been consumed)
Since the moles of NaOH and CH3CH2CH2COOH are equal at the equivalence point, we can calculate the concentration of CH3CH2CH2COOH and NaOH.
Concentration of CH3CH2CH2COOH at equivalence point = moles of CH3CH2CH2COOH remaining / volume at equivalence point (L)
The volume at the equivalence point is given as 26.5 mL, so we need to convert it to liters:
Volume at equivalence point = 26.5 mL = 0.0265 L
Concentration of CH3CH2CH2COOH at equivalence point = -0.00065 mol / 0.0265 L
Now that we have calculated the concentration of CH3CH2CH2COOH at the equivalence point, we can determine its pOH and then convert it to pH.
pOH = -log10(OH- concentration)
The concentration of OH- ions at the equivalence point can be determined by using the concept of stoichiometry. Since CH3CH2CH2COOH is a weak acid, it does not completely ionize. However, when it reacts with NaOH, it forms a salt (CH3CH2CH2COONa) and water (H2O), where the OH- ions come from NaOH.
Since the reaction is 1:1 between CH3CH2CH2COOH and NaOH, the concentration of OH- ions at the equivalence point is equal to the concentration of NaOH.
Concentration of OH- ions at equivalence point = concentration of NaOH
Concentration of OH- ions at equivalence point = 0.1000 M
pOH = -log10(0.1000)
pOH = -1
To convert pOH to pH, we use the equation:
pH = 14 - pOH
pH = 14 - (-1)
pH = 15
Therefore, the pH at the equivalence point during the titration of butanoic acid with sodium hydroxide is 15.