Calculate the pH of the solution formed by adding 15.0ml of 0.1M sodium hydroxide to 30.0ml of 0.1M propanoic acid.
To calculate the pH of the solution, we need to consider the reaction between sodium hydroxide (NaOH) and propanoic acid (CH3CH2COOH). This reaction will produce water (H2O) and sodium propanoate (CH3CH2COONa). The equation for this reaction is as follows:
CH3CH2COOH + NaOH -> CH3CH2COONa + H2O
To calculate the pH, we need to determine the number of moles of propanoic acid and sodium hydroxide in the solution.
First, let's calculate the number of moles of sodium hydroxide:
Moles of NaOH = (Volume of NaOH * Concentration of NaOH) / 1000
= (15.0 ml * 0.1 M) / 1000
= 0.0015 moles
Next, let's calculate the number of moles of propanoic acid:
Moles of propanoic acid = (Volume of propanoic acid * Concentration of propanoic acid) / 1000
= (30.0 ml * 0.1 M) / 1000
= 0.003 moles
Now that we have the number of moles of sodium hydroxide and propanoic acid, we can determine the limiting reactant. The limiting reactant is the one with fewer moles. In this case, sodium hydroxide is the limiting reactant because we have 0.0015 moles of NaOH and 0.003 moles of propanoic acid.
Since sodium hydroxide is a strong base and propanoic acid is a weak acid, we can assume that all of the sodium hydroxide reacts with propanoic acid to form sodium propanoate and water.
Now, let's calculate the concentration of sodium propanoate formed:
Concentration of sodium propanoate = Moles of sodium propanoate / Total volume of solution
= 0.0015 moles / (15.0 ml + 30.0 ml)
= 0.0015 moles / 45.0 ml
= 0.0333 M
Since sodium propanoate is a salt and completely dissociates in water, the concentration of the conjugate base (propanoate) will be equal to the concentration of sodium propanoate.
Now, we can calculate the pH using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this equation, pKa is the acid dissociation constant of propanoic acid, [A-] is the concentration of the conjugate base (propanoate), and [HA] is the concentration of propanoic acid.
The pKa of propanoic acid is approximately 4.87.
Now, let's plug in the values to calculate the pH:
pH = 4.87 + log(0.0333/0.003)
After evaluating this expression, the pH of the solution is approximately 4.14.