At temperature $293$ K$,$ the surface tension liquid water $/$ air is $0\mathrm{.}07275$ J$/$m $2.$

a$/$ Compare the surface energy of liquid water droplets dispersed in air at this

temperature, with droplet diameters $2\backslash$mu m$,200$ nm$,20$ nm$.$

b$/$ Consider the density of liquid water at this temperature is $1$ kg$/$L$,$ calculate

the total surface energy in a system containing $10$ kg liquid water dispersed in

air as droplets with a single diameter $200$ nm$.$ Re$-$calculate for a single diameter

$20$ nm and $100$ nm$,$ respectively. Compare the resulting values.

c$/$ Consider these $3$ systems are contained in vessels of the same size, under the

same conditions. Try to compare $/$ comment on the dynamic properties of the

individual liquid water droplets, and the sedimentation processes in these $3$

vessels.

d$/$ Merge $3$ systems above and try to describe the new one. Try to comment on

the applicability of mathematic formulae from colloid chemistry to this new

system.

Problem $2$: The following data refer to the adsorption of the red$$mauve dye

from beetroot juice on porcelain at $25$ o C$.$

Equil. Conc. C$,$ mmol.dm $-30\mathrm{.}0120\mathrm{.}0260\mathrm{.}0470\mathrm{.}1010\mathrm{.}126$

Adsorb. Amount n$,$ nmol $2\mathrm{.}944\mathrm{.}987\mathrm{.}949\mathrm{.}009\mathrm{.}59$

$2\mathrm{.}1$ Show that the data obey the Langmuir adsorption isotherm.

$2\mathrm{.}2$ Demonstrate that $1\mathrm{.}2\backslash$times $108$ mol of dye adsorb to form a monolayer.

$2\mathrm{.}3$ Estimate the area of a single dye molecule if the radius of a plate was $17\mathrm{.}8$

cm $($we assume the formation of a complete monolayer$).$

Problem $3$: Given the saturated vapor pressure of N $2$ gas over pure liquid N $2$ at

temperature $77$ K is $76$ kPa. Based on the experimental data obtained from

sorption of N $2$ at this temperature onto a solid adsorbent in the following table,

equil. P N$2,$ kPa $17\mathrm{.}0218\mathrm{.}7220\mathrm{.}1722\mathrm{.}2226\mathrm{.}85$

Adsorb. V$,$ mm $310451076110411461254$

The values for adsorbed volumes are already corrected to $273$ K$,1\mathrm{.}0$ atm, and

referred to $1\mathrm{.}0$ g adsorbent.

$3\mathrm{.}1$ Construct the corresponding BET equation

$3\mathrm{.}2$ Find the specific surface area of this adsorbent, given the effective cross

section of N $2$ molecule is $0\mathrm{.}16$ nm $2.$

Problem $4$: Given $4$ references $($considered monodispersed$)$ of a

macromolecular compound with their nominal mole masses $62$ kDa$/$mol$,75$

kDa$/$mol$,92$ kDa$/$mol and $115$ kDa$/$mol$,$ respectively. Mix these $4$ references

with the weight ratio $1$:$2$:$2$:$1$ correspondingly. Find the number$-$average and the

weight$-$average mole mass of the macromolecular compound in this mixed

sample.

Problem $5$: Find $/$ comment on the relation between the weight$-$average and

number$-$average mole mass of a macromolecular compound with the

corresponding $($mean$??)$ values molecule sizes of this macromolecular

compound in a liquid solution.