Determination of an Unknown Ka This experiment was designed by Stephen B Block and Chad C Wilkinson Adapted from a lab by G Hardgrove and J March and Gordon Bain Copyright 2026 by Department of Chemistry University of Wisconsin Madison Academic Goals To understand the relationship between the terms strong and weak as applied to an acid or base and the pH of a solution To investigate the relationship if any between bulk conductivity of a solution and acidity To understand the use of a pH meter To evaluate the comparative merits of identifying the acid dissociation constant using pH and conductivity measurements Background According to Arrhenius definitions substances such as hydrochloric acid HCl and ascorbic acid C6H8O6 better known as vitamin C hereafter abbreviated as HOAsc are classified as acids because they give off H ions in aqueous solution The more general definition of Br nsted and Lowry classifies acids as substances that are able to donate H ions HOAsc and HCl donate H to water forming H3O so they also behave as Br nsted Lowry acids at least in interactions such as they have with water For convenience H aq is often used as shorthand for H3O aq The best representations of an acidic proton in water are somewhere between the two pictures Strong acids are completely ionized in solution Hydrochloric acid dissolves in water to form H3O and Cl ions so the concentration of HCl is really just the concentration of H3O H3O or Cl Some acids such as ascorbic acid dissolve in water largely as molecules with just a small fraction of them ionizing into H3O and Asc ions Under these circumstances H3O is less than the concentration of the acid When placed in water HOAsc ionizes according to the equilibrium equation HOAsc aq H2O H3O aq OAsc aq Like all equilibria this is a reversible process Some molecules are dissociating into ions while some ions are combining to form molecules When the rates of these forward and reverse reactions are equal a state of equilibrium exists A weak acid dissociation equilibrium may be described quantitatively by Ka H3O OAsc HOAsc an equilibrium constant expression where H3O and OAsc refer to the concentrations of the ions and HOAsc refers to the concentration of undissociated molecules A very small value of Ka like 10 8 implies that there is a very low concentration of the ions compared to the molecules The differences between strong and weak acids of equal concentration can be detected by pH meters conductivity measurements and indicators Determination of an Unknown Ka Solution pH The pH of a solution is defined as log10 H3O Thus a 0 100 molar solution of H would have a pH of 1 00 Conversely we can calculate the H3O from the pH by the following relation H3O 10 pH Measurement of the pH of a weak acid solution of known concentration provides the means to measure the H3O and thereby calculate the value of the equilibrium constant Ka Hydrogen fluoride HF dissociates according to the equation with the corresponding equilibrium constant expression HF aq H2O H3O aq F aq Ka H3O F HF Suppose that 0 100 moles of this acid are dissolved in 1 00 L of solution and the measured pH is 2 24 The H3O is 10 2 24 or 5 74 x 10 3 M Since we get equal numbers of H3O and F ions the F value is also 5 74 x 10 3 M In order for these ions to form an equal number of HF molecules must have dissociated and so their concentration must be reduced by the same amount to 0 100 M 5 74 x 10 3 M or 0 0943 M Substituting these values into the equilibrium constant expression we get the value of Ka Ka 5 74 10 3 5 74 10 3 0 0943 3 49 10 4 A note about pH probes pH probes are complicated measuring devices The pH probe measures the potential difference between the acidic solution sealed inside the probe and the solution whose pH is being measured The measurement is based on proton ion exchange equilibria on the surface of the thin glass interface of the probe It takes time for that equilibrium to be reached so it takes time for pH probe measurements to settle It is common to stir a solution when measuring the pH as doing so improves the rate of physically transporting protons ions to the surface of the probe allowing the ion exchange equilibrium to be reached and the measurement to settle more quickly To obtain accurate results the pH probe also requires sufficient conductivity in the solution being measured Thus for solutions with very low conductivity a neutral soluble salt may be added to the solution to allow an accurate pH to be measured Additionally to ensure accurate measurements it is important that the pH probes have been recently calibrated using buffers near the expected pH range to be measured Solution Conductivity Conductivity is due to mobile ions in solution For example when KMnO4 dissolves in water the ions K and MnO4 dissociate or Similarly when HCl dissolves in water KMnO4 s K aq MnO4 aq HCl g H2O l H3O aq Cl aq These ions are now mobile and will conduct electricity in water In almost all cases an increase in the number of ions will allow the solution to conduct electricity more effectively One can Determination of an Unknown Ka then compare the concentration of ions in various solutions by comparing their relative conductivities Conductivity is related to the inverse of electrical resistivity but also takes account of how much solution the electrical current is trying to travel through The units of conductivity are siemens meter or for solutions of common concentrations microsiemens centimeter S cm For electrolyte solutions that are very dilute the conductivity will be approximately proportional to the total concentration of ions in solution and their charges Rigorous analyses require careful consideration of complex ion ion and ion solvent interactions as they vary with temperature concentration ion identity and solvent selection In this experiment concentrations have been chosen to stay in this range of proportional relationship reasonably well only monoprotic acids will be used and the conductivity probe will account for temperature variations As a result the relationship between total ion concentration and conductivity can be determined from measurements of a strong acid solution of known concentration HCl in this case Once the proportionality constant relating ion concentration and conductivity is determined it can be used to determine the concentration of ions in solutions of weak acids From there it is possible to calculate a value of that acid s Ka in a manner that