Final answer:
Lactic acid (CH3CH(OH)CO₂ H) is a weak acid that dissociates in water to form lactate ions (CH₃CH(OH)COO⁻) and hydrogen ions (H⁺). The pKa of lactic acid is 3.86 at 25°C. By titrating a 18.0 ml sample of the lactic acid solution with 0.1010 M NaOH, it was found that 14.5 ml of NaOH were required to reach the equivalence point. The concentration of the lactic acid solution is approximately 0.0814 M.
Step-by-step explanation:
Lactic acid (CH3CH(OH)CO₂ H) is a weak acid that dissociates in water to form lactate ions (CH₃CH(OH)COO⁻) and hydrogen ions (H⁺). The equilibrium between lactic acid and lactate ions is described by the acid dissociation constant, Ka. The pKa is a measure of the acidity of an acid and is equal to the negative logarithm of Ka. In this case, the pKa of lactic acid is 3.86 at 25°C.
The relationship between Ka and pKa is given by the equation:
Ka = 10^(-pKa)
Using the given pKa of lactic acid, we can calculate Ka as follows:
Ka = 10^(-3.86)
To determine the concentration of the lactic acid solution in moles per liter, we need to use the information provided about the titration of the solution with NaOH. The volume of NaOH required to reach the equivalence point is 14.5 ml, and the concentration of NaOH is 0.1010 M. By applying the concept of stoichiometry, we can determine the moles of lactic acid in the solution and then calculate the concentration. Let's go through the calculations:
- Convert the volume of NaOH used to liters: 14.5 ml = 0.0145 L
- Use the mole ratio between NaOH and lactic acid from the balanced equation:
- 1 mole of NaOH reacts with 1 mole of lactic acid
- 0.0145 L of NaOH x 0.1010 mol/L = 0.0014645 moles of NaOH
- 0.0014645 moles of NaOH = 0.0014645 moles of lactic acid
Calculate the concentration of lactic acid in moles per liter:
- Using the given volume of the lactic acid solution (18.0 ml = 0.018 L):
- Concentration (in moles per liter) = 0.0014645 moles / 0.018 L ≈ 0.0814 M