In water, HCN is a weak acid with pKa = 9.6. — Equilibrium / Thermodynamics Chemistry Question
Problem Context
In water, HCN is a weak acid with pKa = 9.6.
Calculate the the Ka and the [H+] in a 0.15 M solution of HCN.
Model Answer
pKa = 9.6, so Ka = 10^-9.6 = 2.5×10^-10
Ka = [H+][CN–] / [HCN] = 2.5 × 10^-10 = x^2 / 0.15 so x = [H+] = 6.1×10^-6
In a closed system, these equilibria are established:
HCN(g) ⇌ HCN(aq)
HCN(aq) ⇌ H+(aq) + CN-(aq)
Calculate Kp for the equilibrium between HCN(g) and HCN(aq) at 298 K.
Model Answer
∆G° = 119.7 – 124.7 = –5.0 kJ·mol-1
∆G° = –RTlnK, so –5000 J·mol-1 = –(8.314 J·mol-1·K-1)(298 K)lnK
K = e^2.018 = 7.52
If the total cyanide concentration in solution (i.e. [CN-] + [HCN]) is 0.10M, calculate the partial pressure of HCN(g) in this system at pH = 7.
Model Answer
[CN–] + [HCN] = 0.10, pH = 7.0 so [H+] = 1.0×10^-7
2.5×10^-10 = (1.0×10^-7)(0.10 − x) / x
2.5×10^-10 x = 1.0×10^-8 − 1.0×10^-7 x
1.0025×10^-7 x = 1.0×10^-8 so x = [HCN]eq = 0.0998
Kp = [HCN]eq / pHCN so pHCN = 0.0998 / 7.52 = 0.0133 atm
A concentration of 300 ppm of HCN in air is reported to be toxic to humans after a few minutes exposure. Determine the ratio of the pressure calculated in 3.b.ii. to this value.
Model Answer
This problem is ambiguous in terms of how it might be solved – by mass or by volume
Perhaps, the more obvious method is to solve by volume:
0.0133 atm / 1 atm = 0.0133 = 13300 ppm (vol)
so the ratio is 13300 ppm / 300 ppm = 44.3
We can also use mass…
(0.0133 atm HCN / 1 atm air) × (27 g mol-1 HCN / 28.8 g mol-1 air) = 0.0125 = 12500 ppm (mass)
so the ratio is 12500 ppm / 300 ppm = 41.6
Gold can be extracted from its ores by reacting the ore with O2 gas in the presence of aqueous CN- ions according to this equation.
4Au(s) + 8CN-(aq) + O2(g) + 2H2O(l) ⇌ 4Au(CN)2 -(aq) + 4OH-(aq)
Write the equilibrium expression for this reaction.
Model Answer
K = [Au(CN)2–]^4 [OH–]^4 / ( [CN–]^8 [O2] )
At fixed [CN–] and O2 pressure will the amount of Au(CN)2– be greatest at high or low pH? Justify your answer.
Model Answer
Low pH should be used because it will lower the [OH–], shifting the equilibrium towards production of products.
What purpose does O2 serve in the extraction process?
Model Answer
O2 is an oxidizing agent in this reaction.