Consider the following gases, all at STP: Ne, SF 6 , N 2 , CH 4 . (d) Which one has the highest total molecular volume relative to the space occupied by the gas?

Hi everyone for this problem, it reads which one of the following four gasses is expected to have the lowest total molecular volume compared to the total occupied volume. We have nitrogen gas, nitrogen dioxide, sulfur dioxide and boron try fluoride. And we want to know which one is going to have the lowest total molecular volume. Okay, so molecular volume for gasses depends on the molecular size and complexity. So for this problem we're going to want to look at the number of atoms. So the lower the number of atoms, the lower the molecular volume. So let's go ahead and write out our four gasses. So we have nitrogen gas, we have nitrogen dioxide, we have sulfur dioxide and we have boron try fluoride. So if we look at the number of atoms here and count them up, we see for nitrogen gas we have two for nitrogen dioxide, we have three for sulfur dioxide, we have three. And for boron try fluoride. There is four. Okay, so here we see that the smallest molecule is going to be the one with the lowest number of atoms. And so we see here that our smallest molecule is going to be our nitrogen gas and because it is the one with the smallest number of atoms, that means it's going to have the lowest molecular volume. So out of the four options here, the gas that is expected to have the lowest total molecular volume is nitrogen gas. That's the end of this problem. I hope this was helpful

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

Problem 113d

Chapter 10, Problem 113d

Consider the following gases, all at STP: Ne, SF₆, N₂, CH₄. (d) Which one has the highest total molecular volume relative to the space occupied by the gas?

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Understand that at STP (Standard Temperature and Pressure), all gases occupy the same volume per mole, which is 22.4 L.

Recognize that the total molecular volume of a gas is related to the size of its molecules and the number of molecules present.

Consider that the molecular volume of a gas is negligible compared to the volume it occupies at STP, but larger molecules will have a slightly higher molecular volume.

Compare the molecular sizes: Ne (neon) is a noble gas with small atomic size, SF_6 (sulfur hexafluoride) is a large molecule due to its six fluorine atoms, N_2 (nitrogen) is a diatomic molecule, and CH_4 (methane) is a small tetrahedral molecule.

Conclude that SF_6, being the largest molecule among the given gases, will have the highest total molecular volume relative to the space occupied by the gas.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. At standard temperature and pressure (STP), gases behave ideally, allowing for the comparison of their volumes. Understanding this law is crucial for analyzing how different gases occupy space under the same conditions.

Molar Volume of Gases

At STP, one mole of an ideal gas occupies a volume of 22.4 liters. This concept allows for the comparison of the volumes of different gases based on their molar masses and molecular structures. Gases with larger molar masses or more complex structures may occupy more space, influencing their total molecular volume.

Density of Gases

The density of a gas is defined as its mass per unit volume. It is influenced by the molecular weight and the conditions of temperature and pressure. In the context of the question, understanding the densities of Ne, SF6, N2, and CH4 helps determine which gas has the highest total molecular volume relative to the space it occupies, as denser gases will have more mass in the same volume.

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Consider the following gases, all at STP: Ne, SF6, N2, CH4. (d) Which one has the highest total molecular volume relative to the space occupied by the gas?

Verified Solution

Key Concepts

Ideal Gas Law

Molar Volume of Gases

Density of Gases

Consider the following gases, all at STP: Ne, SF₆, N₂, CH₄. (d) Which one has the highest total molecular volume relative to the space occupied by the gas?