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Solubility, Exams of Medical imaging

Stanford UniversityMedical imaging

Realize that, with ionic compounds, they are completely ionized in water, but ONLY WHEN THEY ARE DISSOLVED. Thus, the only the portion that dissolves is ionized ...

Typology: Exams

2022/2023

Uploaded on 02/28/2023

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Solubility 1
Solubility
A. Solubility Product
• In this chapter, we will be discussing the solubility of ionic
compounds (salts) in water. However, solubility, at least
qualitatively, is very roughly defined. A salt is…
o Soluble if at least 0.1 mol dissolves in 1 L water
o Slightly soluble if about 0.001 – 0.1 mol dissolves in 1 L
o Insoluble if less than 0.001 mol dissolves in 1 L
• Realize that, with ionic compounds, they are completely
ionized in water, but ONLY WHEN THEY ARE DISSOLVED.
Thus, the only the portion that dissolves is ionized!
• In other words, we have a heterogenous equilibrium between
the undissolved solid and the ions that are in solution. e.g.
BaSO4(s) Ba2+(aq) + SO42−(aq)
][SO ][BaK 2
4
2
sp
−
+
= = 1.1×10−10 at 25 °C
• We use the symbol Ksp for the equilibrium constant, and it is
referred to as the solubility product.
• Note that for an equilibrium to be established, we must have
some solid present (doesn’t matter how much, just some).
• Application: Ba2+ is very toxic, yet BaSO4 is used in humans
for medical imaging because very little BaSO4 dissolves.
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Solubility

A. Solubility Product

  • In this chapter, we will be discussing the solubility of ionic compounds (salts) in water. However, solubility, at least qualitatively, is very roughly defined. A salt is…

o Soluble if at least 0.1 mol dissolves in 1 L water

o Slightly soluble if about 0.001 – 0.1 mol dissolves in 1 L

o Insoluble if less than 0.001 mol dissolves in 1 L

  • Realize that, with ionic compounds, they are completely ionized in water, but ONLY WHEN THEY ARE DISSOLVED. Thus, the only the portion that dissolves is ionized!
  • In other words, we have a heterogenous equilibrium between the undissolved solid and the ions that are in solution. e.g.

BaSO 4 (s) Ba 2+(aq) + SO 42 −(aq)

K (^) sp = [Ba^2 +][SO 42 −] = 1.1×10−^10 at 25 °C

  • We use the symbol Ksp for the equilibrium constant, and it is referred to as the solubility product.
  • Note that for an equilibrium to be established, we must have some solid present (doesn’t matter how much, just some).
  • Application: Ba 2+^ is very toxic, yet BaSO 4 is used in humans for medical imaging because very little BaSO 4 dissolves.
  • Calculations are quite straightforward and no different from those of other equilibria, such as weak acids and bases.
  • Example: How much barium sulfate dissolves in a litre of water? (K (^) sp = 1.1×10−^10 )

BaSO 4 (s) Ba 2+(aq) + SO 42 −(aq)

  • Note that if you’re given the solubility, either in moles or grams per litre, you can do the reverse calculation to determine K (^) sp.
  • Example: What is the concentration of Ca 2+^ present in a solution made by equilibrating solid CaF 2 (K (^) sp = 4.1×10−^11 ) with 0.20 potassium fluoride?

C. Unsaturated, Saturated, and Supersaturated

  • A solution is deemed to be saturated if the equilibrium between the solid and the dissolved ions is established.

o In this case, reaction quotient Q = Ksp (we also call Q the ion product)

  • What if the value of Q < Ksp? Then the solution is considered to be unsaturated, and more BaSO 4 (s) will dissolve, provided that there is some present.
  • Yet, if Q > Ksp the solution is supersaturated, and it contains more of the product ions than it could hold. Thus, when Q is larger than the solubility product, some precipitation will always occur!
  • Example: If solid Ba(NO 3 ) 2 is added to a 0.1 M solution of Na 2 SO 4 , assuming no volume change, how much Ba(NO 3 ) (^2) can be added before barium sulfate starts to precipitate?

o Note: we assume that precipitation will occur at the point where Q just exceeds Ksp

D. pH and Complexation

  • The solubility of many substances influences, or is influenced by, the pH of the solution. 1. Metal hydroxides (usually have low solubility)
  • Example: What is the pH of a solution made by equilibrating water with solid Ca(OH) 2 , which has K (^) sp = 7.9 × 10−^6?

o This solution is quite basic. Some other metal hydroxides have very low solubilities, so their solutions are not basic.

  • Another example: Cu(OH) 2 has 1.6 × 10−^19. What is the maximum [Cu 2+] possible in neutral solution? What is the maximum pH of a solution in which Cu 2+^ = 0.50 M?

o Reasonable [Cu 2+] are only possible in acidic solution!

2. Solubilities of salts of weak acids

  • Solubilities of such salts are affected by pH. However, we will only look at them from a qualitative point of view.
  • Example: AgCl and AgBr are not very soluble; when HNO 3 is added, nothing happens. Silver acetate (CH 3 COOAg) also has a low solubility in water, but when HNO 3 is added, it dissolves. Explain this behaviour.

E. Applications of Solubility: Limestone

  • Limestone is used to construct many historically important buildings, statues, monuments, and tombstones.

o Greek Parthenon

o Government buildings

o UWO buildings

o $270,000 monoliths welcoming visitors to London at the corner of Oxford St and Airport Rd

  • Limestone contains CaCO 3 , which has a K (^) sp of 3.8 × 10−^9.

CaCO 3 (s) Ca 2+(aq) + CO 32 −(aq)

  • With the small K (^) sp , it is virtually insoluble in pure water. However, rain water gradually dissolves it away. Why?

o Rain water contains both carbonic and sulfuric acids, both of which react with carbonate.

1. Carbonic Acid

  • CO 2 in the air dissolves in water to form carbonic acid.

H 2 O + CO 2 H 2 CO 3

  • This reacts with the carbonate (CO 32 −) in an acid-base neutralization reaction, thereby decreasing [CO 32 −].

H 2 CO 3 + CO 32 −^ 2 HCO 3 −

  • So, more CaCO 3 dissolves to compensate for the amount of carbonate that was used up. The dissolved products are washed away by the rain. 2. Sulfuric Acid
  • SO 2 is produced from the burning of fossil fuels that contain sulfur. Power plants, steel mills, paper mills, refineries, and smelters are the largest producers, as are auto emissions.
  • SO 2 is oxidized to SO 3 in the atmosphere. This then combines with water to form H 2 SO 4.
  • The sulfuric acid reacts with the carbonate from the limestone, which causes more limestone to dissolve.

H +^ + CO 32 −^ HCO 3 −

H +^ + HCO 3 −^ H 2 CO 3 H 2 O + CO 2

(If limestone is dropped in acid, it dissolves as CO 2 is evolved)