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Chapter 10: Problem 35

The Goodyear blimps, which frequently fly over sporting events, hold approximately \(175,000 \mathrm{ft}^{3}\) of helium. If the gas is at \(23^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\), what mass of helium is in a blimp?

Short Answer

Expert verified
The mass of helium in the Goodyear blimp is approximately 880,705.12 g, calculated using the Ideal Gas Law, given the volume of \(175,000 ft^3\), temperature of \(23^\circ\mathrm{C}\), and pressure of \(1.0 \mathrm{~atm}\).

Step by step solution

01

Convert given temperature to Kelvin

To use the Ideal Gas Law, the temperature should be in Kelvin. The given temperature is 23掳C. To convert Celsius to Kelvin, add 273.15: \( T = 23^\circ\mathrm{C} + 273.15 = 296.15\mathrm{K} \)
02

Apply Ideal Gas Law to calculate moles

Now, we will use the Ideal Gas Law formula: PV = nRT Given, pressure P = 1.0 atm, volume V = 175,000 ft鲁, temperature T = 296.15 K, and ideal gas constant R = 0.0821 L atm / K mol. Note that we need to convert the volume from ft鲁 to L before using the formula. There are approximately 28.3168 L in 1 ft鲁: \( V = 175,000\mathrm{ft^3} * \frac{28.3168\mathrm{L}}{1\mathrm{ft^3}} = 4,955,440\mathrm{L} \) Now, plug in the values into the Ideal Gas Law formula and solve for n: \( (1.0\mathrm{atm}) (4,955,440\mathrm{L}) = n (0.0821\frac{\mathrm{L\,atm}}{\mathrm{K\,mol}})(296.15\mathrm{K}) \) Divide both sides by 0.0821 L atm / K mol and 296.15 K: \( n = \frac{(1.0\mathrm{atm})(4,955,440\mathrm{L})}{(0.0821\frac{\mathrm{L\,atm}}{\mathrm{K\,mol}})(296.15\mathrm{K})} \) Calculate the number of moles, n: \( n \approx 219916.22\, \mathrm{mol} \)
03

Calculate the mass of helium

We now have the number of moles of helium. To find the mass, we will use the molar mass of helium, which is 4.0026 g/mol: Mass = moles 脳 molar mass \( \mathrm{Mass} = (219916.22\, \mathrm{mol}) (4.0026\, \frac{\mathrm{g}}{\mathrm{mol}}) \) Calculate the mass of helium: \( \mathrm{Mass} \approx 880705.12\, \mathrm{g} \) The mass of helium in the blimp is approximately 880,705.12 g.

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