Solubility problems - Aqueous and Environmental Geochemistry

Chemistry for Earth Sciences
DM Sherman, University of Bristol
Homework: Solubility Equilibria
Concentration calculations:
In A-level and GCSE chemistry, they had you write out “R.M.M.” in the course
of your calculations. Hence, given the problem: what is the concentration of Na in a
solution prepared by adding 2.3 grams of NaCl (RMM= 58.4 g) to 0.2 litres of water.
You’d then plug all the information into a formula:
⎛ mass of NaCl ⎞ ⎛ 2.3 ⎞
Concentration = ⎜
⎟ = ⎜ ⎟ = 0.197
⎝ RMM ×Volume⎠
⎝ 58.4 × 0.2⎠
Don’t do this any more. From now on, use the unit factor method instead:
€
€
⎛
⎜
⎝
2.3g NaCl
0.2 litres
⎞ ⎛ 1.0 moles NaCl⎞
⎛
⎟ ⎜
⎟ = ⎜
⎠ ⎝ 58.4 g NaCl ⎠ ⎝
0.197 moles NaCl
litre
You might have been taught to use dm 3 (cubic decimetres) in calculations for volume.
Don’t do this; scientists use litres (= 1 dm 3 ) or ml (= 1 cm 3 ) for liquid volumes.
Sometimes you’ll see volumes in m 3 . Solid volumes are often in cm 3 .
⎞
⎟
⎠
In chemistry, concentrations in aqueous solutions are usually given in moles/litre of
solution. In geochemistry, however, liquid volumes are often poorly defined since they
change so greatly with pressure and temperature. Moreover, we often deal with very
concentrated solutions (hydrothermal ore-forming fluids can be 10-20 moles NaCl/l) so
that the amount of water in a litre is unclear. To cope with this, we use a concentration
unit called molality which is the number of moles of a solute per 1 kg of water.
A very common unit in geochemistry is parts per million (ppm). These are common
when talking about the concentration of trace metals in rocks. In aqueous geochemistry,
these units are common when communicating to regulatory agencies. When discussing
trace metals in seawater, we might use parts per billion (ppb) or even parts per trillion
(ppt). These are somewhat awkward units to use until you recognize that 1 ppm = 1
mg/kg. For example, a mine waste-water contains 1.0 x 10 -5 m As. What is the
concentration in ppm (mg/kg) given the atomic mass of As is 74.9 g/mole?
⎛ 1.0 ×10 -5 mole As⎞
⎛ 74.9 g As⎞
⎛ 1000 mg⎞
⎛ 0.749 mg As⎞
⎜
⎟ ⎜ ⎟ ⎜ ⎟ = ⎜
⎟ or 0.749 ppm As
⎝ kg H 2
O ⎠ ⎝ mole As ⎠ ⎝ g ⎠ ⎝ kg H 2
O ⎠
€
Now try this: A solution contains 23.0 ppm Cr. What is the concentration in moles
Cr/kg water given that there are 52.0 g Cr/mole? Here is the way do to it:
⎛
⎜
⎝
23.0 mg Cr
kg H 2
O
⎞ ⎛ 1 g ⎞ ⎛ 1 mole Cr⎞
⎛
⎟ ⎜ ⎟ ⎜ ⎟ = 4.42 x 10-4 moles Cr⎞
⎜
⎟ or 4.4 x 10 −4 m Cr
⎠ ⎝ 1000 mg⎠
⎝ 52.0 g Cr ⎠ ⎝ kg H 2
O ⎠
€

Chemistry for Earth Sciences
DM Sherman, University of Bristol
This explicit writing-out of the units might seem to be a needless tedium to you; however,
it will save you much grief down the road and will enable you to solve problems that you
couldn’t do otherwise. Cr and As are carcinogenic. Getting your calculations wrong
may land you in court!
Problems:
1. Calculate the molal concentration of Ca when 0.05 g of CaCl 2 is dissolved in 350 ml of
water. The formula mass of CaCl 2 is 111.4 g/mole.
2. The concentration of Zn in acid-mine waste is 50 ppm (= 50 mg/kg). What is the
molar concentration of Zn given that the atomic mass of Zn is 65.4 g/mole.
3. The equilibrium constant for the reaction
BaSO 4 = Ba +2 + SO 4
-2
is 1.07 x 10 -10 . What is the concentration of Ba +2 in a solution in equilibrium with BaSO 4 ?
4. Solve problem 3 again but when the solution is also saturated with gypsum
CaSO 4 .2H 2 O. The equilibrium constant for the reaction
is 3.31 x 10 -5
CaSO 4 = Ca +2 + SO 4
-2