Calcium carbonate frequently scales the interior of pipes and boilers, hence per

Question

Calcium carbonate frequently scales the interior of pipes and boilers, hence periodic de-scaling maintenance is required. The reaction below illustrates the dissolving of the calcium carbonate in the presence of an acid. In the descaling process, dilute weak acids are typically used in order to prevent extensive damage to metallic parts.

CaCO3(s) + 2H+ (aq) <--> CO2 (g) + H2O (l) + Ca2+ (aq)

H°@25°C = -15.06 kJ and S°@25°C = 141.75 J/K

Is this reaction spontaneous under the following conditions?

T = 25°C pH = 5.00 PCO2 = 3.00 x 10-4 atm [Ca2+]=0.100 M

Explanation / Answer

we know that

dGo = dHo - TdSo

given

dHo = -15.06 x 1000 J

dSo = 141.75 J / K

T = 25 C = 298 K

now

dGo = ( -15.06 x 1000) - ( 298 x 141.75)

dGo = -57.3015 kJ

now

consider the given reaction

CaC03 (s) + 2H+   (aq) ---> C02 (g) + H20 (l) + Ca+2 (aq)

we know that

pH = -log [H+]

so

-log [H+] = 5

[H+] = 10-5

given

[Ca+2] = 0.1

now

for C02

PV = nRT

n / V = P / RT

conc ( n/V) = 3 x 10-4 / 0.0821 x 298

[C02] = 1.226 x 10-5

now

CaC03 (s) + 2H+ ---> C02 (g) + H20 (l)   + Ca+2 (aq)

the reaction quotient is given by

Q = [C02] [Ca+2] / [ H+] ^2

Q = [1.226 x 10-5 ] [0.1] / [10-5]^2

Q = 12260

now

we know that

dG = dGo + RT lnQ

so

dG = ( -57.3015 x 1000) + ( 298 x 8.314 x ) ln 12260

dG = -33.977 kJ

we know that

for a reaction to be sponatenous dG < 0

so

the given reaction is spontaneous at the given conditions

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