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Question
Fish generally needs O2 concentration in water at least 3.8 mg/L for survival. What partial pressure of O2 above the water is needed for the survival of fish? Given the solubility of O2 in water at 0 °C and 1 atm-1 partial pressure is 2.2 × 10-3 atm mol/L.
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Solution
Given: O2 concentration in water required for fishes = 3.8 mg/L
Solubility of O2 in water = 2.2 × 10-3 mol/L
Pressure = 1 atm
To find: Partial pressure of O2 above the water needed for the survival of fish.
Formula: S = KHP
Calculation: Pressure = 1 atm = 1.013 bar
Now, using formula and rearranging,
`"K"_"H" = "S"/"P" = (2.2 xx 10^-3 "mol / L")/(1.013 "bar") = 2.17 xx 10^-3 "mol L"^-1 "bar"^-1`
O2 concentration in water required for fishes
= 3.8 mg/L = `(3.8 xx 10^-3 "g/L")/(32 "g/mol") = 1.19 xx 10^-4 "mol L"^-1`
Now, using formula and rearranging,
P = `"S"/"K"_"H" = (1.19 xx 10^-4 "mol L"^-1)/(2.17 xx 10^-3 "mol L"^-1 "bar"^-1)` = 0.0548 bar
The partial pressure of O2 above the water needed for the survival of fish is 0.0548 bar.
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