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Chapter 13: Problem 90

The volume of air taken in by a warm-blooded vertebrate in the Andes mountains is \(210 \mathrm{L} /\) day at standard temperature and pressure (i.e., \(\left.0^{\circ} \mathrm{C} \text { and } 1 \text { atm }\right) .\) If the air in the lungs is at \(39^{\circ} \mathrm{C},\) under a pressure of $450 \mathrm{mm} \mathrm{Hg}$ and we assume that the vertebrate takes in an average volume of \(100 \mathrm{cm}^{3}\) per breath at the temperature and pressure of its lungs, how many breaths does this vertebrate take per day?

Short Answer

Expert verified
Assume the average volume per breath is 100 cm鲁. Answer: To find the number of breaths the vertebrate takes per day, follow these steps: 1. Convert the given information to consistent units: - Temperature at STP: 273.15 K - Pressure at STP: 760 mmHg - Temperature in the lungs: 312.15 K - Air intake volume per day at STP: 210,000 cm鲁 2. Calculate the number of moles of air taken in per day at STP using the Ideal Gas Law: \(n = \frac{(210000 \, \mathrm{cm}^3)(760 \, \mathrm{mmHg})}{(62.36 \frac{\mathrm{L} \cdot \mathrm{mmHg}}{\mathrm{mol} \cdot \mathrm{K}})(273.15 \, \mathrm{K})}\) 3. Convert the volume at STP to the volume at the conditions in the lungs: \(V_{\text{lungs}} = \frac{nRT_{\text{lungs}}}{450 \, \mathrm{mmHg}}\) 4. Compute the number of breaths taken per day by dividing the volume at the lung conditions by the average volume per breath: \(Number \, of \, breaths = \frac{V_{\text{lungs}}}{100 \, \mathrm{cm}^3}\)

Step by step solution

01

Convert the given information to consistent units

First, we will convert the given information to consistent units. We will use the following conversion factors: \(1 \, \mathrm{L} = 1000 \, \mathrm{cm}^3\), \(1 \, \mathrm{atm} = 760 \, \mathrm{mmHg}\), and \(T (\mathrm{K}) = T (\mathrm{掳C}) + 273.15\). - Temperature at STP: \(0^{\circ} \mathrm{C} = 273.15 \, \mathrm{K}\) - Pressure at STP: \(1 \, \mathrm{atm} = 760 \, \mathrm{mmHg}\) - Temperature in the lungs: \(39^{\circ} \mathrm{C} = 312.15 \, \mathrm{K}\) - Pressure in the lungs: already given as \(450 \, \mathrm{mmHg}\) - Air intake volume per day at STP: \(210 \, \mathrm{L} = 210000 \, \mathrm{cm}^3\)
02

Calculate the amount of moles of air taken in per day

Using the Ideal Gas Law (PV = nRT), we calculate the amount of moles (n) of air taken in per day at STP. We will use the gas constant, R = \(62.36 (\frac{\mathrm{L} \cdot \mathrm{mmHg}}{\mathrm{mol} \cdot \mathrm{K}})\). \(Ideal \, Gas \, Law: PV = nRT\) \(n = \frac{PV}{RT}\) \(n = \frac{(210000 \, \mathrm{cm}^3)(760 \, \mathrm{mmHg})}{(62.36 \frac{\mathrm{L} \cdot \mathrm{mmHg}}{\mathrm{mol} \cdot \mathrm{K}})(273.15 \, \mathrm{K})}\)
03

Convert the volume at STP to the volume at the conditions in the lungs

Now that we have the number of moles, we will convert the volume at STP to the volume at the conditions in the lungs using the Ideal Gas Law: \((PV)_{\text{lungs}} = nRT_{\text{lungs}}\) Now solve for the lung volume, \(V_{\text{lungs}}\): \(V_{\text{lungs}} = \frac{nRT_{\text{lungs}}}{P_{\text{lungs}}} = \frac{nRT_{\text{lungs}}}{450 \, \mathrm{mmHg}}\)
04

Compute the number of breaths taken per day

Finally, we will calculate the number of breaths taken per day by dividing the volume at the lung conditions by the average volume per breath: \(Number \, of \, breaths = \frac{V_{\text{lungs}}}{100 \, \mathrm{cm}^3}\)

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Most popular questions from this chapter

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