Question

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Confirm by calculation that the pH of CO2 saturated waterat 25C is 5.6, given that the CO2 concentration in air is 390 ppm. For CO2 Henry's constant is 3.4*10^(-2)M atm^(-) at 25C. The Ka for H2CO3 is 4.5*10^(-7) at that temp. (b) Recalculate the pH for a CO2 concentration of 560ppm, ie, double that of the pre-industrial age.

Answer 1

Molecular weight of air = 29

CO2 = 390ppm = 0.39gm of CO2 per kg of air*1/44.01 mol/gm of CO2=

0.00886 mol CO2 per kg of air =

0.00886*10^-3 per gm of air*29 gm/mol =

0.000257mol of CO2 per mole of air

Mole fraction of CO2 =

0.000257

Partial pressure of CO2 = 1atm*0.000257 = 0.000257atm

pco2 = M/KHcp

M = pco2*KHcp = 3.4*10^(-2)*.000257 = 8.74*10^(-6)M

H2CO3=8.74*10^(-6)

H2CO3 = H+ + HCO3-

H+ = HCO3-

Ka=(H+)^2/H2CO3 =4.5*10^(-7)

H^2 = 8.74*10^(-6)*4.5*10^(-7)

H=1.98*10^(-6)

pH = 5.7

(b) Recalculate the pH for a CO2 concentration of 560ppm, ie, double that of the pre-industrial age.

CO2 = 560ppm =

0.56gm of CO2 per kg of air*1/44.01 mol/gm of CO2=

0.0127mol CO2 per kg of air =

0.0127*10^-3 per gm of air*29 gm/mol =

0.000369mol of CO2 per mole of air

Mole fraction of CO2 =

0.000369

Partial pressure of CO2 = 1atm*0.000369 = 0.000369atm

pco2 = M/KHcp

M = pco2*KHcp = 3.4*10^(-2)*.000369 = 12.546*10^(-6)M

H2CO3=8.74*10^(-6)

H2CO3 = H+ + HCO3-

H+ = HCO3-

Ka=(H+)^2/H2CO3 =4.5*10^(-7)

H^2 = 12.546*10^(-6)*4.5*10^(-7)

H=2.376*10^(-6)

pH = 5.6