Question

The partial pressure of ${O_2}$ in air is $0.21$ atm at sea level. If aquatic life requires a concentration of ${O_2}$ at least 4.16$$${\text{mg/litre}}$$, will the aquatic life sustain in sea level lake. {{\text{K}}_{\text{H}}}$for${O_2}$is$1.3 \times {10^{ - 3}}$${\text{mol/litre - atm}}$$. A.0.82$mg/litre B.$0.87$mg/litre C.$0.95$mg/litre D.$0.9$mg/litre

Answer 1

To solve this question, you must recall Henry’s Law. Henry’s law states that the amount of gas dissolved in a liquid is proportional to its partial pressure above the liquid.

Formula used: ${\text{s}} = {{\text{K}}_{\text{H}}}{\text{P}}$
Where, ${\text{s}}$is the solubility of gas in moles per litre
${{\text{K}}_{\text{H}}}$ is the Henry’s law constant
${\text{P}}$ is the partial pressure of gas in atm

Complete step by step solution:
We know that the total pressure is $1{\text{atm}}$.
The mole fraction of oxygen is given as $0.21$.
Hence, the partial pressure of oxygen is $0.21 \times 1 = 0.21{\text{atm}}$.
Using the formula for Henry’s law, ${\text{s}} = {{\text{K}}_{\text{H}}}{\text{P}}$.
Now we substitute the values in the formula,
$\Rightarrow {\text{s}} = \left( {1.3 \times {{10}^{ - 4}}} \right) \times 0.21$
$\therefore {\text{s}} = 2.73 \times {10^{ - 5}}{\text{M}}$
Thus, we have the moles of oxygen dissolved per litre of water are $2.73 \times {10^{ - 5}}$moles.
Thus, we can write the mass of oxygen dissolved per litre of water as,
${\text{m}} = \left( {2.73 \times {{10}^{ - 5}}} \right) \times 32$
$\Rightarrow {\text{m}} = 8.736 \times {10^{ - 4}}{\text{g}}$
Converting into milligrams:
${\text{m}} = 0.8736{\text{ mg}}$of oxygen is dissolved per litre of water.

Thus, the correct option is B.

Note: Henry’s law has various applications.
At high altitude, due to low atmospheric pressure concentration of oxygen in the blood and tissues is very low and people feel weak and are unable to think properly.
It also has applications in underwater diving.
Gas can be breathed at ambient pressure which increases with increasing depth due to hydrostatic pressure. Solubility of gases increases at depth as per Henry's law, so the body tissues dissolve more oxygen over time till it is saturated for the depth. When ascending the diver is exposed to lower pressure conditions and the solubility of the oxygen dissolved in the tissues decreases as well. If the supersaturation is too great it can cause blockages in capillaries or distortion in the solid tissues.