Textbook Problem

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A study of climbers who reached the summit of Mount Everest without supplemental oxygen showed that the partial pressures of O₂ and CO₂ in their lungs were 35 mm Mg and 7.5 mm Hg, respectively. The barometric pressure at the summit was 253 mm Hg. Assume the lung gases are saturated with moisture at a body temperature of 37 °C [which means the partial pressure of water vapor in the lungs is P(H₂O) = 47.1 mm Hg]. If you assume the lung gases consist of only O₂, N₂, CO₂, and H₂O, what is the partial pressure of N₂?

Interpretation Introduction

Interpretation:

From the given set of conditions the partial pressure of $N_2$ should be determined.

Concept Introduction:

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas.  Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained.  It is referred as ideal gas equation.

  $\begin{array}{l}\text{V }\propto \frac{\text{nT}}{\text{P}}\\ \text{V = R}\frac{\text{nT}}{\text{P}}\\ \text{PV = nRT}\\ \text{where,}\\ \text{n = moles of gas}\\ \text{P = pressure}\\ \text{T = temperature}\\ \text{R = gas }\text{constant}\end{array}$

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Avogadro’s Hypothesis:

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

Explanation of Solution

Given:

  $\begin{array}{l}{\text{Partial pressure}}_{{\text{O}}_{\text{2}}}=35mmHg\\ {\text{Partial pressure}}_{{\text{CO}}_{\text{2}}}=7.5mmHg\\ Barometricpressure=253mmHg\\ T={37}^{\circ }C\\ {\text{Partial pressure}}_{{\text{HO}}_{\text{2}}}=47.1mmHg\end{array}$

The total pressure of the gas is equal to the sum of the individual pressure of the gases present in the mixture