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GATE 2022 ES – Question 55

Environmental Chemistry · Principles of Water Chemistry · 2 marks · Numerical answer

CO₂ Henry constant at 25°C is .034 M/atm in neutral water. CO₂·H₂O⇌H⁺+HCO₃⁻ has K₁=4.3×10⁻⁷ M; HCO₃⁻⇌H⁺+CO₃²⁻ has K₂=4.7×10⁻¹¹ M. Ambient CO₂300 ppm. Find total dissolved inorganic CO₂ in µM, to one decimal.

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Correct answer: 54.0 to 54.2

Explanation

With total gas pressure1 atm and neutral pH7 maintained, dissolved CO₂*=$.034(.000300)=10.2$ µM. Total inorganic carbon is $C_T=C^*[1+K_1/H+K_1K_2/H^2]=10.2(1+4.3+.002021)=\mathbf{54.1}$ µM. This uses fixed neutral pH; unbuffered pure water exposed to CO₂ would acidify and require a different equilibrium calculation.

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