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Chapter 5: Problem 126

A \(1.0-\mathrm{L}\) sample of air is collected at \(25^{\circ} \mathrm{C}\) at sea level \((1.00 \mathrm{atm}) .\) Estimate the volume this sample of air would have at an altitude of 15 \(\mathrm{km}\) ( see Fig.5.30) .At \(15 \mathrm{km},\) the pressure is about 0.1 \(\mathrm{atm} .\)

Short Answer

Expert verified
The final volume of the air sample at an altitude of 15 km is 10 L, which can be calculated using the variant of the Ideal Gas Law: \(V2 = \frac{P1 × V1}{P2} = \frac{(1.0 \, L) × (1.00 \, atm)}{0.1 \, atm} = 10 \, L\).

Step by step solution

01

Write down the given values

Here, we are given: Initial volume of air, V1 = 1.0 L Initial pressure, P1 = 1.00 atm Temperature, T = 25°C = 25 + 273.15 = 298.15 K (convert Celsius to Kelvin) Final pressure at 15 km altitude, P2 = 0.1 atm We need to find the final volume, V2.
02

Use the variant of the Ideal Gas Law

As we know the initial and final pressure values and the initial volume, we can use the formula P1V1 = P2V2 to find the final volume.
03

Solve for V2

Rearrange the formula to find V2: \[V2 = \frac{P1 × V1}{P2}\] Now, substitute the given values and find the final volume: \[V2 = \frac{(1.0 \, L) × (1.00 \, atm)}{0.1 \, atm}\]
04

Calculate V2

Divide the nominator by the denominator to get the result: \[V2 = \frac{1.0}{0.1}\] \[V2 = 10 \, L\]
05

Final answer

The sample of air would have a volume of 10 L at an altitude of 15 km.

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