Which of the following gases has a density greater than that of oxygen gas under the same conditions of temperature and pressure?

Introduction / Context:
This question tests basic gas behaviour under the ideal gas approximation and relates gas density to molar mass. At the same temperature and pressure, gases with higher molar mass will have higher density. Learners must compare the molar masses of four common gases and identify which one is heavier than oxygen gas. This concept is useful in practical situations such as gas leakage and ventilation safety.

Given Data / Assumptions:
- The gases in the options are carbon dioxide, ammonia, methane, and helium.
- We compare their densities with that of oxygen gas at the same temperature and pressure.
- We assume ideal gas behaviour, so density is proportional to molar mass when conditions are equal.

Concept / Approach:
Under the same temperature and pressure, one mole of any ideal gas occupies the same volume. Therefore, density, which is mass per unit volume, is directly proportional to molar mass. Oxygen gas O2 has a molar mass of about 32 g mol minus1. Carbon dioxide CO2 has a molar mass of 44 g mol minus1, ammonia NH3 is 17 g mol minus1, methane CH4 is 16 g mol minus1, and helium He is 4 g mol minus1. The gas with molar mass greater than 32 g mol minus1 will be denser than oxygen under identical conditions, so carbon dioxide is the correct choice.

Step-by-Step Solution:
Step 1: Calculate or recall the molar mass of oxygen gas O2. Each oxygen atom has atomic mass about 16, so O2 has molar mass 2 multiplied by 16 equals 32 g mol minus1.
Step 2: For carbon dioxide CO2, carbon contributes 12 and each oxygen contributes 16, giving total molar mass 12 plus 2 multiplied by 16 equals 44 g mol minus1.
Step 3: For ammonia NH3, nitrogen contributes 14 and hydrogen contributes 3 multiplied by 1, giving molar mass 17 g mol minus1.
Step 4: For methane CH4, carbon contributes 12 and hydrogen contributes 4 multiplied by 1, giving molar mass 16 g mol minus1.
Step 5: For helium He, the molar mass is 4 g mol minus1, as it is a monoatomic noble gas.
Step 6: Since at the same temperature and pressure gas density is proportional to molar mass, only carbon dioxide with molar mass 44 g mol minus1 is denser than oxygen gas with molar mass 32 g mol minus1.

Verification / Alternative check:
One way to verify this is to compare known common facts about these gases. Helium balloons rise in air because helium is lighter than both oxygen and nitrogen. Methane and ammonia are also often mentioned as lighter gases. Carbon dioxide is known to accumulate in low lying areas in mines and volcanic regions because it is heavier than air, which is mainly nitrogen and oxygen. These observations confirm the molar mass comparisons and show that carbon dioxide is indeed heavier than oxygen under similar conditions.

Why Other Options Are Wrong:
- Ammonia: With molar mass 17 g mol minus1, it is significantly lighter than oxygen and will be less dense under the same conditions.

Why Other Options Are Wrong (continued):
- Methane: With molar mass 16 g mol minus1, it is lighter than oxygen and therefore has lower density.
- Helium: It has a very low molar mass of 4 g mol minus1 and is much lighter than oxygen, which is why helium balloons float.

Common Pitfalls:
Some students may rely on everyday impressions, thinking methane or ammonia are heavy due to their odour or flammability, but density is determined by molar mass, not smell or reactivity. Others may forget that oxygen itself is not extremely heavy compared to gases like carbon dioxide. Always calculate or recall molar masses and compare them directly when dealing with relative gas densities under equal conditions.

Final Answer:
Carbon dioxide has a higher molar mass and density than oxygen gas at the same temperature and pressure.