A British artist Roger Hiorns entirely filled a flat with a supersaturated copper sulfate solution. — Physical Chemistry — Kinetics Chemistry Question
Copper sulfate and its hydrates
A British artist Roger Hiorns entirely filled a flat with a supersaturated copper sulfate solution. After removal of the solution, blue crystals remained on the walls, floor, and ceiling.
Copper sulfate is often used in laboratories as a drying agent, for example, to obtain absolute ethanol.
For further dehydration of ethanol, anhydrous copper sulfate is added. After a while the liquid is decanted and treated with a new portion of anhydrous copper sulfate. These operations are repeated 2-3 times until copper sulfate will stop turning blue. Then ethanol is filtered and distilled.
Two chemists argued at what temperature – high or low – should the process of drying be performed in order to achieve lower residual water content.
Necessary information. Vapor pressure of water over its dilute solution in ethanol is given by psat = pw * x * γ, where psat is the saturated vapor pressure of water, x is the mole fraction of water in solution, γ is the activity coefficient of water, which only slightly depends on temperature and can be assumed to be 2.45.
Substance | ∆fH°298 / (kJ mol–1) | psat / Pa at 298K
CuSO4 · 5 H2O | –2277.4 | 1047
CuSO4 · 3 H2O | –1688.7 | 576
CuSO4 · H2O | –1084.4 | 107
CuSO4 | –770.4 |
H2O(l) | –285.83 | 3200
H2O(g) | –241.83 |
Write down the formula of these crystals.
Model Answer
CuSO4 · 5 H2O.
Humidity inside this flat has a constant low level. Using the Clausius-Clapeyron equation, calculate the temperature at which the humidity will be 35% (of the saturated vapor pressure of water at the same temperature).
Model Answer
The Clausius-Clapeyron equation for the decomposition of a solid hydrate:
CuSO4· 5 H2O(s) = CuSO4· 3 H2O(s) + 2 H2O(g)
has the form:
dln p_h / dT = ∆H_d / RT^2,
where p_h is the vapor pressure of water over the hydrate, ∆H_d is the enthalpy of decomposition. The solution of this equation is:
where p_h0 = 1047 Pa is the saturated vapor pressure over CuSO4· 5 H2O and T0 = 298 K. Enthalpy of decomposition of CuSO4· 5 H2O is:
∆H_d = 2 × (–241.83) – 1688.7 + 2277.4 = 105.04 kJ mol–1.
The similar equation describes the temperature dependence of the vapor pressure of water pw:
The enthalpy of vaporization of water is: ∆H_vap = –241.83 + 285.83 = 44.0 kJ mol–1. The humidity is the ratio of two vapor pressures:
From this equation we find the required temperature:
T = 304 K or 31 °C.
By rectification of aqueous ethanol one can increase its concentration to not more than 95.5 wt.%. This is due to the fact that:
a) pressures of water and ethanol vapor are the same
b) mole fractions of ethanol in the gas and liquid phases are equal
c) water forms a stable complex with ethanol
d) ethanol absorbs water vapor from the air
Choose the correct answer.
Model Answer
b)
What is the minimum residual water content (in mass percent) that can be achieved by using this method at room temperature?
Model Answer
After several repetitions of the procedure, the equilibrium is established between the anhydrous copper sulfate and its monohydrate: CuSO4· H2O = CuSO4 + H2O. In this case the saturated vapor pressure of water over its solution in ethanol is equal to the saturated vapor pressure of water over CuSO4·H2O. Thus, p_h = p_w * x * γ,
x = p_h / (p_w * γ) = 0.0136, the mass fraction of water is:
or 0.54 %
Calculate the minimum residual water contents if ethanol was dried at 0 °C and 40 °C.
Model Answer
Enthalpy of decomposition of CuSO4 · H2O is: ∆H_d = –241.83 – 770.4 + 1084.4 = 72.17 kJ mol–1. From the equations above it follows that:
At T = 273 K, x = 0.0048, w = 0.19 %; at T = 313 K x = 0.0235, w = 0.93 %.