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Chapter 5: Problem 24

As weather balloons rise from the earth's surface, the pressure of the atmosphere becomes less, tending to cause the volume of the balloons to expand. However, the temperature is much lower in the upper atmosphere than at sea level. Would this temperature effect tend to make such a balloon expand or contract? Weather balloons do, in fact, expand as they rise. What does this tell you?

Short Answer

Expert verified
As a weather balloon rises in the atmosphere, the pressure decreases, causing the volume to expand according to the Ideal Gas Law (\(PV = nRT\)). However, the decrease in temperature should cause the volume to contract. Since weather balloons do expand as they rise, it indicates that the pressure decrease is more dominant than the temperature decrease. As a result, the expansion of the volume primarily happens due to the decreasing pressure, and the temperature effect is not enough to prevent this expansion.

Step by step solution

01

Understand the Ideal Gas Law

The Ideal Gas Law is given by the equation: \(PV = nRT\), where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin. The relationship between pressure, volume, and temperature can help us understand how the volume of the weather balloon is affected by changing pressure and temperature.
02

Analyze the effect of pressure

As the weather balloon rises from the Earth's surface, the pressure of the atmosphere decreases. According to the Ideal Gas Law, when the pressure decreases and other variables remain constant, the volume of the gas increases. Thus, the decrease in pressure should cause the weather balloon to expand.
03

Analyze the effect of temperature

The temperature in the upper atmosphere is much lower than at sea level. To analyze the effect of temperature on the volume of the balloon, we have to consider the Ideal Gas Law again. When the temperature decreases and other variables remain constant, the volume of the gas should decrease. So, the decrease in temperature should cause the weather balloon to contract.
04

Balancing pressure and temperature effects

We have found that the decrease in pressure should cause the balloon to expand, while the decrease in temperature should cause the balloon to contract. Since weather balloons do expand as they rise, it means that the effect of the pressure decrease is more dominant than the effect of temperature decrease. Thus, as the balloon rises, its volume expands primarily due to decreasing pressure, and the temperature effect is not enough to prevent this expansion.

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Most popular questions from this chapter

A hot-air balloon is filled with air to a volume of \(4.00 \times 10^{3} \mathrm{~m}^{3}\) at 745 torr and \(21^{\circ} \mathrm{C}\). The air in the balloon is then heated to \(62^{\circ} \mathrm{C}\), causing the balloon to expand to a volume of \(4.20 \times 10^{3} \mathrm{~m}^{3}\). What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out. Thus the pressure in the balloon is always the same as that of the atmosphere.)

Metallic molybdenum can be produced from the mineral molybdenite, \(\mathrm{MoS}_{2}\). The mineral is first oxidized in air to molybdenum trioxide and sulfur dioxide. Molybdenum trioxide is then reduced to metallic molybdenum using hydrogen gas. The balanced equations are $$ \begin{aligned} \mathrm{MoS}_{2}(s)+\frac{2}{2} \mathrm{O}_{2}(g) & \longrightarrow \mathrm{MoO}_{3}(s)+2 \mathrm{SO}_{2}(g) \\ \mathrm{MoO}_{3}(s)+3 \mathrm{H}_{2}(g) & \longrightarrow \mathrm{Mo}(s)+3 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ Calculate the volumes of air and hydrogen gas at \(17^{\circ} \mathrm{C}\) and \(1.00\) atm that are necessary to produce \(1.00 \times 10^{3} \mathrm{~kg}\) pure molybdenum from \(\mathrm{MoS}_{2}\). Assume air contains \(21 \%\) oxygen by volume and assume \(100 \%\) yield for each reaction.

Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc. $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose \(240 . \mathrm{mL}\) of hydrogen gas is collected at \(30 .{ }^{\circ} \mathrm{C}\) and has a total pressure of \(1.032\) atm by this process. What is the partial pressure of hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor pressure of water is 32 torr at \(30^{\circ} \mathrm{C}\).)

You have a sealed, flexible balloon filled with argon gas. The atmospheric pressure is \(1.00 \mathrm{~atm}\) and the temperature is \(25^{\circ} \mathrm{C}\). Assume that air has a mole fraction of nitrogen of \(0.790\), the rest being oxygen. a. Explain why the balloon would float when heated. Make sure to discuss which factors change and which remain constant, and why this matters. Be complete. b. Above what temperature would you heat the balloon so that it would float?

A gauge on a compressed gas cylinder reads 2200 psi (pounds per square inch; 1 atm \(=14.7\) psi). Express this pressure in each of the following units. a. standard atmospheres b. megapascals (MPa) c. torr
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