Answered: A helium-filled weather balloon has a…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

A helium-filled weather balloon has a volume of 686 L at 22.9°C and 751 mmHg. It is released and rises to an altitude of 7.30 km, where the pressure is 356 mmHg and the temperature is –25.1°C.

The volume of the balloon at this altitude is

Expert Solution

Step 1: Combined Gas Law

For two different states of an ideal gas with a constant number of moles, the combined gas law depicts:

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

where:

P₁ and P₂ are initial and final pressure respectively.

V₁ and V₂ are initial and final volumes respectively.

T₁ and T₂ are the initial and final temperatures (in the Kelvin scale) respectively.

Step 2: Calculation

According to the given problem, the following values are given:

P₁ = 751 mmHg

P₂ = 356 mmHg

T₁ = (273+22.9) K = 295.9 K

T₂ = (273-25.1) K = 247.9 K

V₁ = 686 L

Susbtituting the above values, we get:

$\frac{(751 m m H g) \times (686 L)}{(295.9 K)} = \frac{(356 m m H g) \times V_{2}}{(247.9 K)} \Rightarrow V_{2} = 1.21 \times 10^{3} L$

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