Which gas would occupy more volume at a constant temperature and pressure, 1.5 g of N₂ gas or 1.5 g of O₂ gas?

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11ecba2d_11e1_d528_a3bf_637f00aaf503_MD0008_00 At a constant temperature and pressure, the volume that a gas occupies depends on its number of moles (or molecules). This is known as Avogadro's law, and it can be expressed as the following equation (V is volume and n is number of moles): 11ecba2d_11e1_d529_a3bf_2543411adc93_MD0008_00 In other words, volume is directly proportional to the number of moles. Therefore, the gas with more moles occupies a larger volume. When the mass of a gas is given, its number of moles can be determined by dividing by its molar mass (mass per mole): 11ecba2d_11e1_d52a_a3bf_57d90a108eb9_MD0008_00 Because the masses of both N₂ and O₂ are equal (1.5 g each), the gas with the lower molar mass has more molecules. Using the periodic table, the molar mass of N₂ is calculated to be 28 g/mol, and the molar mass of O₂ is 32 g/mol. Therefore, the N₂ gas has more moles and occupies a larger volume. (Choice B) The size of a gas' molecules is negligible compared to the volume the gas occupies. In addition, oxygen atoms have a smaller atomic radius than nitrogen atoms, which gives O₂ molecules a smaller size than N₂ molecules. However, O₂ molecules do have more mass in the nuclei than N₂ molecules, which decreases the number of moles of O2 in a 1.5-g sample. (Choice C) Gases assume the size and shape of their container and therefore have the same volume as the container. This is different from size of the molecules themselves, which is considered to be negligible. (Choice D) The volume occupied by two gases is equal if they share the same pressure, temperature, and number of moles. However, there are more moles of N₂ than moles of O₂ in a 1.5-g sample. Educational objective: Avogadro's law states that the volume occupied by a gas is directly proportional to its number of moles if the temperature and pressure are constant. When two gases at the same temperature and pressure are compared, the gas with more moles occupies the larger volume.

Which Gas Would Occupy More Volume at a Constant Temperature