## Calculations for synthetic reactions where a strong mineral acid is used.

Concentrated hydrochloric, sulfuric, and nitric acids are not pure HCl, H2SO4, or HNO3. Rather, they are aqueous solutions of these substances in the form of the hydronium ion and the conjugate base. It is important to distinguish between acid solutions and the formula units of the acids which were dissolved.

Examine the table below. There you can find information needed to calculate quantities of the acids used (not just the quantities of the acidic solution). (You can cite the Lab Manual as the source for these data.)

For example, in the column "HCl", you can see that hydrochloric acid is actually a 37.3% solution of HCl in water. This means that for every 100 grams of hydrochloric acid, 37.3 grams are from the HCl and the remainder of the mass is water. If you weigh 7.04 grams of hydrochloric acid, only [7.04 g x 0.373] = 2.63 g of it is HCl (again, in the form of solvated H3O+ and Cl-).

Normally, we don't weigh liquid solutions, we measure the volume. To convert volume to mass, we need the density of the solution. The specific gravity (density relative to the density of water) of hydrochloric acid solution is 1.18 g/mL. If 13.7 mL of hydrochloric acid solution is taken, then [13.7 mL x (1.18 g/mL) = 16.2 g is the mass of the hydrochloric acid solution.

Usually, we are ultimately interested in the number of moles of acid used. To convert mass to moles, we need the molecular weight. The molecular weight of HCl is 36.47 g/mol. Using the above example of 13.7 mL (16.2 g) of hydrochloric acid solution measured, remember that the mass is of the solution, not HCl. The completed calculation is:

[16.2 g sol'n x [37.3 g HCl /100 g sol'n] / [36.47 g HCl/ mol HCl] = 0.166 mol HCl

(Write out the equation in a standard numerator-denominator format to see the cancellation of units.)

 Reagent HCl HNO3 H2SO4 CH3CO2H NH3(NH4OH) Density (g/mL) 1.18 1.41 1.84 1.06 0.90 % Acid or base (by mass) 37.3 70.0 96.5 99.7 29.0 Molecular weight (g/mol) 36.47 63.02 98.08 60.05 17.03 Molarity of conc. acid or base (mol/L) 12 16 18 17.5 15.3 Normality of conc. acid or base (equiv./L) 12 16 36 17.5 15.3