James Richard Fromm
When a chemical reaction takes place in a solution, the molar stoichiometry of the reaction taken together with the known concentrations of solutions permits quantitative calculations of the masses or volumes of the reactants and products.
Example. The reaction of Ag+(aq) with Cl-(aq) proceeds under most conditions stoichiometrically to give AgCl, which is only slightly soluble in water. We can compute the volume of 0.06 molar aqueous Ag+ solution required to react with 27.35 mL of 0.18 molar aqueous Cl- solution as follows. The chloride solution contains (0.18 mmol/mL)(27.35 mL) or 4.923 mmol of chloride ion. Since the overall balanced reaction is:
Ag+(aq) + Cl- AgCl,
there will be 4.923 mmol of silver ion required as well. This will be contained in (4.923 mmol)/(0.06 mmol/mL) or 82.05 mL of the silver ion solution.
Solution concentrations are sometimes specified as ionic concentrations, as in the example above, because only one ion is of concern in a particular experiment. It is more common to specify the concentration of a solution in terms of a salt, such as NaCl or BaCl2, if the solution was actually prepared from the salt. The molar concentration of a solute ion will be equal to the concentration of the solute salt only if the salt dissolving is a 1:1 salt such as NaCl. A solution which has a molar concentration of 0.1 in BaCl2, however, is 0.1 molar in Ba2+(aq) and 0.2 molar in Cl-(aq) because two moles of chloride ions are released upon dissolution of one mole of solid BaCl2.
Example. We can compute the volume of 0.045 mol/L aqueous Ag+(aq) solution required to react with 10.41 mL of 0.156 molar aqueous BaCl2 solution as follows. The chloride solution contains (2)(10.41 mL)(0.156 mmol/mL) = 3.248 mmol Cl-(aq) and therefore (3.248 mmol)/(0.45 mmol/mL) = 72.18 mL of aqueous Ag+(aq) solution required.
When solutions are prepared by mixing other solutions and a chemical reaction takes place, both reaction and dilution must be taken into account. This is done by establishing the moles of reactants present in each solution and the moles of products present in the final solution, using the balanced chemical reaction. The volume of the final solution is taken as the sum of the volumes of the original solutions, which is quite accurate for dilute solutions in the same solvent. When concentrated solutions (above about 1.0 molar in water, for example) or solutions in different solvents are mixed, the actual final volume should be measured.
Example. We calculate the molar concentrations of the ions when 75 mL of 0.10 molar aqueous KCl are mixed with 25 mL of 0.25 molar aqueous Na2SO4 as follows. The total volume can be taken as 75 mL plus 25 mL which is 100 mL. The amount of K+ ion present is (0.100 mmol/mL)(75 mL) = 7.5 mmol. The amount of Cl- is likewise 7.5 mmol. The amount of SO42- is (0.25 mmol/mL)(25 mL) = 6.25 mmol. The amount of Na+ ion is twice that of sulfate ion, since
Na2SO4 SO42-(aq) + 2Na+(aq).
The molar concentrations are therefore K+(aq), 75 mmol/L; Cl-(aq), 75 mmol/L; SO42-, 62.5 mmol/L; and Na+(aq), 125 mmol/L. No reaction has occurred and only dilution need be considered.
Example. We calculate the molar concentrations of the ions when 63 mL of 0.14 molar aqueous NaCl are mixed with 41 mL of 0.30 molar aqueous sodium sulfate as follows. The total volume can be taken as 63 + 41 = 104 mL. The amount of chloride ion present is (0.14 mmol/mL)(63 mL) = 8.82 mmol Cl-(aq). The amount of sulfate ion present is (0.30 mmol/mL)(41 mL) = 12.30 mmol SO42-(aq). The amount of sodium ion present is (0.14)(63) + (2)(0.30)(41) = 33.42 mmol Na+(aq). The molar concentrations are Cl-(aq), 84.81 mmol/L; SO42-(aq), 118.27 mmol/L; and Cl-(aq), 321.35 mmol/L. There is no reaction between any of the ions but there are two sources of sodium ion.
Example. We calculate the molar concentrations of the ions when 57 mL of 0.46 molar aqueous NaCl are mixed with 74 mL of 0.51 molar aqueous AgNO3 as follows. The reaction between Cl-(aq) and Ag+(aq) can be assumed to be stoichiometric. The resulting slightly soluble AgCl can be assumed to be removed from the solution by precipitation as the solid. The total volume can be taken as 57 + 74 = 131 mL. The original amount of Na+(aq) is (0.46 mmol/mL)(57 mL) = 26.22 mmol and none of it is removed by reaction. The original amount of NO3-(aq) is (0.51 mmol/mL)(74 mL) = 37.74 mmol and none of it is removed by reaction. The original amount of Cl-(aq) is 26.22 mmol and the original amount of Ag+(aq) is 37.74 mmol. The limiting reagent is Cl-(aq), since a 1:1 stoichiometry is found in the balanced overall reaction. After reaction the amount of Cl-(aq) remaining is essentially zero, while the amount of Ag+(aq) remaining is 37.74 - 26.22 = 11.52 mmol. The final concentrations of the species after reaction are Na+(aq), 0.20 molar; NO3-(aq), 0.288 molar; Ag+(aq), 0.0879 molar; Cl-(aq), essentially zero.
The volumetric glassware shown in the following Figure is often used in chemical manipulations involving stoichiometric solution reactions. The pipet is used to transfer precisely known volumes of liquids from one container to another. The buret is used to deliver a precisely measurable volume of liquid into a container. These, together with the less precise graduated cylinder, are among the essential tools of any chemist.