6. (8 points) The planet Araganose (which is made mostly of the mineral aragonit

Question

6. (8 points) The planet Araganose (which is made mostly of the mineral aragonite, or Caco,) has an atmosphere containing methane and carbon dioxide, each at a pressure of 0.10 bar. The oceans are saturated with aragonite and have a concentration of H' equal to 1.8 x 107M. Given the following equlibria, calculate how many grams of calcium are contained in 2.00 L of Aragonose seawater. qulibria, calculate how many grams of calcium are contained in 2.00 L of Ca2+(aq) + CO32-(aq) CO2(aq) CaCO3(s, aragonite) Ksp=6.0x10-9 Koo,-3.4 x 10-2 Ki = 4.5 x 10.7 K2-4.7 x 10"1 CO2(g) co2(aq) + H2O(I) HCO3(aq) + H+(aq) HCO3(aq) H+(aq) + CO32-(aq)

Explanation / Answer

We have,

K1 = [HCO3-][H+]/[CO2(aq)] = 4.5 x 10^-7

So, [HCO3-] = 4.5 x 10^-7[CO2(aq)]/[H+] = 2.5[CO2(aq)]

K2 = [H+][CO3^2-]/2.5[CO2(aq)] = 4.7 x10^-11

So, [CO3^2-]/[CO2(aq)] = 6.53 x 10^-4

Kco2 = [CO2(aq)]/[CO2(g)] = 3.4 x 10^-2

[CO2(aq)] = 3.4 x 10^-2[CO2(g)]

Feed in above equation,

[CO3^2-]3.4 x 10^-2[CO2(g)] = 6.53 x 10^-4

[CO3^2-] = 0.019/[CO2(g)]

Ksp = [Ca2+][CO3^2-] = [Ca2+](0.019[CO2(g)] = 6.0 x 10^-9

[Ca2+][CO2(g)] = 3.158 x 10^-7

let x be [Ca2+] = [CO2]

x^2 = 3.158 x 10^-7

x = [Ca2+] = 5.62 x 10^-4 M

So the moles of Ca = molarity x volume = 5.62 x 10^-4 M x 2 L = 1.124 x 10^-3 moles

grams of Ca = moles x molar mass = 1.124 x 10^-3 moles x 40.078 g/moles = 0.045 g

Thus, 0.045 g (45 mg) os Ca is present in 2 L of Aragonose seawater.

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