Questions: Which of the five gases occupies the smallest volume? N2 O2 Ar CO2 Xe

Transcript text: Which of the five gases occupies the smallest volume? $\mathrm{N}_{2}$ $\mathrm{O}_{2}$ Ar $\mathrm{CO}_{2}$ Xe

Solution

Solution Steps

Step 1: Understanding the Problem

The problem asks which of the five gases occupies the smallest volume. To determine this, we need to consider the conditions under which the gases are compared. Typically, gases are compared under the same conditions of temperature and pressure, following the ideal gas law.

Step 2: Applying the Ideal Gas Law

The ideal gas law is given by:

\[ PV = nRT \]

where $ P $ is the pressure, $ V $ is the volume, $ n $ is the number of moles, $ R $ is the ideal gas constant, and $ T $ is the temperature. Under the same conditions of $ P $, $ T $, and $ n $, the volume $ V $ is directly proportional to the number of moles $ n $.

Step 3: Considering Molar Mass

For a given number of moles, the volume occupied by a gas is independent of its molar mass. However, if we consider equal masses of each gas, the gas with the highest molar mass will occupy the smallest volume because fewer moles of that gas will be present.

Step 4: Comparing Molar Masses

The molar masses of the gases are approximately:

$\mathrm{N}_2$: 28.02 g/mol
$\mathrm{O}_2$: 32.00 g/mol
Ar: 39.95 g/mol
$\mathrm{CO}_2$: 44.01 g/mol
Xe: 131.29 g/mol

Final Answer

The gas with the highest molar mass is xenon (Xe), which means for an equal mass of each gas, xenon will have the fewest moles and thus occupy the smallest volume. Therefore, the gas that occupies the smallest volume is:

\[ \boxed{\text{Xe}} \]

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