In: Chemistry
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 |
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.