Question

The Goodyear blimp, which frequently fly over sporting events, hold approximately 175,000ft of helium. If the gas is at 23 degrees Celsius and 1.0 atm, what mass of helium is in the blimp?

Answer 1

Volume of helium present in blimp is \(175000 \mathrm{ft}^{3}\).

Convert the volume into liters by using the following conversion factors.

\(1 \mathrm{ft}=30.48 \mathrm{~cm}\)

\(1 \mathrm{~mL}=1 \mathrm{~cm}^{3}\)

\(\mathrm{IL}=1000 \mathrm{~mL}\)

The volume of helium gas in liters \(=175,000 \mathrm{ft}^{3} \times \frac{(30.48 \mathrm{~cm})^{3}}{1 \mathrm{ft}^{3}} \times \frac{1 \mathrm{~mL}}{1 \mathrm{~cm}^{3}} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}}\)

\(=4.95 \times 10^{6} \mathrm{~L}\)

Temperature \(=23^{\circ} \mathrm{C}\) \(=23+273\)

\(=296 \mathrm{~K}\)

Pressure, \(\mathrm{P}\) is \(1.0 \mathrm{~atm}\).

The ideal gas equation is as follows:

\(\mathrm{PV}=\mathrm{nRT}\)

Here, \(\mathrm{n}\) is nu8mber of moles, \(\mathrm{R}\) is gas constant.

Calculate the mass of helium blimp as shown below:

\(\mathrm{PV}=\frac{\mathrm{m}}{\mathrm{M}} \mathrm{RT}\)

Here, \(m\) is mass of the gas, and \(M\) is molar mass of the gas.

Since mole,

\(\begin{aligned} n &=\frac{\operatorname{mass}(\mathrm{g})}{\text { molar mass }(\mathrm{g} / \mathrm{mol})} \\ m &=\frac{\text { PVM }}{\mathrm{RT}} \end{aligned}\)

Substitute the values.

\(\mathrm{m}=\frac{(1.0 \mathrm{~atm})\left(4.95 \times 10^{6} \mathrm{~L}\right)(4.0026 \mathrm{~g} / \mathrm{mol})}{(0.0821 \mathrm{L.atm} / \mathrm{mol} \mathrm{K})(296 \mathrm{~K})}\)

\(=8.15 \times 10^{5} \mathrm{~g}\)

\(\mathrm{~m}=8.15 \times 10^{5} \mathrm{~g} \times \frac{1 \mathrm{~kg}}{10^{3} \mathrm{~g}}\)

Therefore, the mass of the helium gas will be \(8.15 \times 10^{2} \mathrm{~kg}\)

Answer 2

I suppose the volume of the blimp is 175, 000 ft³ and not ft.Convert this volume to inch cubed, then to centimeter cubed,then to milliliter and then to literUse the conversion factors:.
Temperature = 23 C = 296 KP = 1.0 atmR = 0.0821 L-atm/ (mol.K)Volume V is obtained from the above step in liters.Substitute in the ideal gas equation to get moles ofheliumn = P V / RT.From the moles of helium, calculate mass using theformula:Mass = moles * molar massMolar mass of Helium = 4.0 g/mol.
Hope this helps !