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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

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.

queen_honey_blossom answered 3 months ago

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