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? - Chemistry

Exercise | Q 8 | Page 46

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 partial pressure is 2.2 × 10-3 mol/L.

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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 = K_HP

Calculation: Pressure = 1 atm = 1.013 bar

Now, using formula and rearranging,

${\displaystyle {\text{K}}_{\text{H}}=\frac{\text{S}}{\text{P}}=\frac{2.2\times {10}^{-3}\text{mol / L}}{1.013 \text{bar}}=2.17\times {10}^{-3}{\text{mol L}}^{-1}{\text{bar}}^{-1}}$

O₂ concentration in water required for fishes

= 3.8 mg/L = ${\displaystyle \frac{3.8\times {10}^{-3}\text{g/L}}{32 \text{g/mol}}=1.19\times {10}^{-4}{\text{mol L}}^{-1}}$

Now, using formula and rearranging,

P = ${\displaystyle \frac{\text{S}}{{\text{K}}_{\text{H}}}=\frac{1.19\times {10}^{-4}{\text{mol L}}^{-1}}{2.17\times {10}^{-3}{\text{mol L}}^{-1}{\text{bar}}^{-1}}}$ = 0.0548 bar

The partial pressure of O₂ above the water needed for the survival of fish is 0.0548 bar.