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Chapter 10: Problem 35

The Goodyear blimps, which frequently fly over sporting events, hold approximately \(4955 \mathrm{~m}^{3}\) of helium. If the gas is at $23{ }^{\circ} \mathrm{C}\( and \)101.33 \mathrm{kPa},$ what mass of helium is in a blimp?

Short Answer

Expert verified
The mass of helium in the blimp can be calculated using the Ideal Gas Law formula, \(PV = nRT\), with the given conditions of volume, temperature, and pressure. After converting the temperature to Kelvin and the pressure to Pascals, we find the number of moles (n) to be approximately \(203183.8\). Using the molar mass of helium, we calculate the mass of helium to be approximately \(812.74 kg\).

Step by step solution

01

Convert temperature to Kelvin

To start, we need to convert the given temperature in Celsius to Kelvin. We can do this using the formula: \(T(K) = T(°C) + 273.15\) Given temperature, \(T = 23 ^{\circ}C\) So, in Kelvin: \(T(K) = 23 + 273.15 = 296.15 K\)
02

Convert pressure to Pascals

Next, we need to convert the given pressure in kilopascals to Pascals using the formula: \(1 kPa = 1000 Pa\) Given pressure, \(P = 101.33 kPa\) So, in Pascals: \(P = 101.33 * 1000 = 101330 Pa\)
03

Plug values into Ideal Gas Law

Now that we have all the required values, we can plug them into the Ideal Gas Law formula: \(PV = nRT\) Given volume, \(V = 4955 m^3\) So, to find the number of moles, n: \(\frac{PV}{RT} = n\) Therefore, \(n = \frac{101330 * 4955}{8.314 * 296.15}\)
04

Calculate the number of moles

To calculate the number of moles, we can plug in the values: \(n = \frac{101330 * 4955}{8.314 * 296.15} = 203183.8\)
05

Convert number of moles to mass

Finally, we can use the molar mass of helium to convert the number of moles to mass. The molar mass of helium is approximately 4 g/mol. Molar mass of helium: \(M_{He} = 4 g/mol\) So, to find the mass of helium, m: \(m = n * M_{He}\) Therefore, \(m = 203183.8 * 4 = 812735.2 g\)
06

Convert mass to kilograms (if necessary)

Our answer is in grams, but we can convert it to kilograms if necessary by using the conversion factor: \(1 kg = 1000 g\) So, converting the mass to kilograms: \(m = \frac{812735.2}{1000} = 812.74 kg\) Thus, there are approximately 812.74 kg of helium in the blimp.

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Most popular questions from this chapter

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

A deep-sea diver uses a gas cylinder with a volume of \(10.0 \mathrm{~L}\) and a content of \(51.2 \mathrm{~g}\) of \(\mathrm{O}_{2}\) and \(32.6 \mathrm{~g}\) of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is \(19^{\circ} \mathrm{C}\).

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(a) List two experimental conditions under which gases deviate from ideal behavior. (b) List two reasons why the gases deviate from ideal behavior.

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