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Chapter 5: Problem 38

Without looking at a table of values, which of the following gases would you expect to have the largest value of the van der Waals constant $b : \mathrm{H}_{2}, \mathrm{N}_{2}, \mathrm{CH}_{4}, \mathrm{C}_{2} \mathrm{H}_{6},\( or \)\mathrm{C}_{3} \mathrm{H}_{8} ?$

Short Answer

Expert verified
The gas with the largest value of the van der Waals constant \(b\) would be \(\mathrm{C}_{3} \mathrm{H}_{8}\) (propane), as it has the largest molecular size among the given molecules.

Step by step solution

01

Understand the van der Waals constant b

The van der Waals constant b accounts for the size of the gas particles and represents the excluded volume of the gas molecules. Larger molecules will have larger values of the van der Waals constant b.
02

Compare the sizes of the gas molecules

Examine the given gas molecules: 1. \(\mathrm{H}_{2}\): This molecule consists of 2 hydrogen atoms. 2. \(\mathrm{N}_{2}\): This molecule consists of 2 nitrogen atoms. 3. \(\mathrm{CH}_{4}\): This molecule consists of 1 carbon atom and 4 hydrogen atoms. 4. \(\mathrm{C}_{2} \mathrm{H}_{6}\): This molecule consists of 2 carbon atoms and 6 hydrogen atoms. 5. \(\mathrm{C}_{3} \mathrm{H}_{8}\): This molecule consists of 3 carbon atoms and 8 hydrogen atoms.
03

Determine the gas with the largest molecular size

Comparing the number of atoms and the size of the atoms, we can rank the gas molecules from smallest to largest molecular size: 1. \(\mathrm{H}_{2}\) 2. \(\mathrm{N}_{2}\) 3. \(\mathrm{CH}_{4}\) 4. \(\mathrm{C}_{2} \mathrm{H}_{6}\) 5. \(\mathrm{C}_{3} \mathrm{H}_{8}\) Based on this ranking, the largest molecule is \(\mathrm{C}_{3} \mathrm{H}_{8}\).
04

Conclusion

Since the van der Waals constant \(b\) is larger for larger molecules, we can expect the gas with the largest value of \(b\) to be propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\).

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Most popular questions from this chapter

A steel cylinder contains 5.00 mole of graphite (pure carbon) and 5.00 moles of \(\mathrm{O}_{2} .\) The mixture is ignited and all the graphite reacts. Combustion produces a mixture of \(\mathrm{CO}\) gas and \(\mathrm{CO}_{2}\) gas. After the cylinder has cooled to its original temperature, it is found that the pressure of the cylinder has increased by 17.0\(\%\) . Calculate the mole fractions of \(\mathrm{CO}, \mathrm{CO}_{2},\) and \(\mathrm{O}_{2}\) in the final gaseous mixture.

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