Respuesta :
atmospheric pressure at sea level is 760 mmHg.
We have been told that at the summit the pressure is only one third the pressure at sea level.
Then the pressure at the mountain top is [tex] \frac{760}{3} [/tex] mmHg
Air is made of a mixture of gases. the pressure that each gas exerts individually contributes to the total pressure of the system. The pressure that each gas exerts is the partial pressure of that gas which depends on the mole fraction of that gas or percentage composition of the individual gas.
Partial pressure of Oxygen - total pressure x percentage composition
Therefore pO₂ - [tex] \frac{760 * 0.21}{3} [/tex] = 53.2 mmHg
Answer is 53 mmHg
We have been told that at the summit the pressure is only one third the pressure at sea level.
Then the pressure at the mountain top is [tex] \frac{760}{3} [/tex] mmHg
Air is made of a mixture of gases. the pressure that each gas exerts individually contributes to the total pressure of the system. The pressure that each gas exerts is the partial pressure of that gas which depends on the mole fraction of that gas or percentage composition of the individual gas.
Partial pressure of Oxygen - total pressure x percentage composition
Therefore pO₂ - [tex] \frac{760 * 0.21}{3} [/tex] = 53.2 mmHg
Answer is 53 mmHg
The partial pressure of oxygen [tex]\left({{{\text{O}}_2}}\right)[/tex] at Mount Everest is approximately 53 mmHg.
Further explanation:
Dalton’s law:
In accordance to Dalton’s law, the total pressure is the sum of partial pressure of each gas. The expression to calculate total pressure is as follows:
[tex]{P_{total}}={P_a}+{P_b}+....[/tex] …… (1)
Here,
[tex]{P_{total}}[/tex]is total pressure of the gas mixture.
[tex]{P_a}[/tex], [tex]{P_b}[/tex] are the partial pressures of gas [tex]a[/tex] and [tex]b[/tex] respectively.
The expression for partial pressure of a particular gas is,
[tex]{P_{{\text{gas}}}} = {X_{{\text{gas}}}}\cdot {P_{{\text{total}}}}[/tex] …… (2)
Here,
[tex]{P_{{\text{gas}}}}[/tex]is the partial pressure of the gas.
[tex]{P_{{\text{total}}}}[/tex]is the total pressure of the mixture.
[tex]{X_{{\text{gas}}}}[/tex]is the mole fraction of gas.
The atmospheric pressure at Mount Everest is one-third of the pressure of sea level which is 760 mmHg, therefore,
[tex]\begin{aligned}{\text{Atmospheric pressure at Mount Everest}}&=\frac{{{\text{atmospheric pressure at sea level}}}}{3}\\&=\frac{{760\;{\text{mmHg}}}}{3}\\&=253.33\;{\text{mmHg}}\\\end{aligned}[/tex]
In given question, the oxygen present in the atmosphere is 21 % thus the mole fraction of oxygen in the atmosphere is 0.21.
Substitute 0.21 for [tex]{X_{{{\text{O}}_2}}}[/tex] and 253.33 mmHg for [tex]{P_{{\text{total}}}}[/tex]in equation (2) to calculate the pressure of [tex]{{\text{O}}_2}[/tex] gas at Mount Everest.
[tex]\begin{aligned}{P_{{\text{gas}}}}&={X_{{\text{gas}}}} \cdot{P_{{\text{total}}}}\\&=\left({0.21}\right)\left({253.33{\text{mmHg}}}\right)\\&={\text{53}}{\text{.2 mmHg}}\\&\simeq {\mathbf{53 mmHg}}\\\end{aligned}[/tex]
The partial pressure of [tex]{{\text{O}}_2}[/tex] at Mount Everest is 53 mmHg.
Learn more:
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Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Kinetic theory of gases
Keywords: Atmospheric pressure, Mount Everest, one third, partial pressure, sea level, oxygen, 21% ,volume and 53 mmHg.
