Question

In: Chemistry

Assuming a planar surface, calculate how long it will take to dissolve 1 mm thick layer...

Assuming a planar surface, calculate how long it will take to dissolve 1 mm thick layer from the mineral. The dissolution rate is a zeroth-order reaction

Mineral Formula Density (g/cm3) Log Rate (mol/m2) pH Concentration (moles/L) Temperature (°C)
Quartz SiO2 2.65 -13.39 5 0.00001 25

Solutions

Expert Solution

First calculate the number of moles dissolved from a 1 m2 area and 1 mm thickness.

The volume dissolved is 100 dm2 x 0.01 dm = 1 dm3 = 1000 cm3

The mass dissolved is 1000 cm3 x 2.65 g/cm3 = 2650 g

The molar mass of SiO2 is 60.08 g/mol

The quantity dissolved is

              2650 g / 60.08 g/mol = 44.11 mol SiO2 / (m2.mm)

Then calculate the dissolution rate ( in fact a rate constant) :

            Rate = 10-13.39 = 4.074x10-14 mol/m2

The measurement unit for rate is wrong. It is in fact

    4.074x10-14 mol/ (m2.s)      (for dissolution in water, acidic pH)

The integral rate law of dissolution is

    Quantity dissolved = rate x time

   44.11 mol SiO2 / (m2.mm) x 1 mm = 4.074x10-14 mol/ (m2.s) x t

t = 1.083x1015 s

The other data are useless.


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