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How many number of molecules and atoms respectively are present in 2.8 litres of a diatomic gas at STP?

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Solution

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  1. At Standard Temperature and Pressure (STP), one mole of any gas occupies 22.4 litres.

  2. So, the number of moles of the gas in 2.8 litres can be calculated as follows: Number of moles = Volume of gas at STP / Volume of one mole of gas at STP Number of moles = 2.8 litres / 22.4 litres per mole = 0.125 moles

  3. Avogadro's law states that one mole of any substance contains 6.022 x 10^23 entities (atoms, molecules, etc.).

  4. Therefore, the number of molecules in 0.125 moles of gas can be calculated as follows: Number of molecules = Number of moles x Avogadro's number Number of molecules = 0.125 moles x 6.022 x 10^23 molecules per mole = 7.5275 x 10^22 molecules

  5. Since the gas is diatomic, each molecule is composed of two atoms.

  6. Therefore, the number of atoms in the gas can be calculated as follows: Number of atoms = Number of molecules x Number of atoms per molecule Number of atoms = 7.5275 x 10^22 molecules x 2 atoms per molecule = 1.5055 x 10^23 atoms

So, there are approximately 7.53 x 10^22 molecules and 1.51 x 10^23 atoms in 2.8 litres of a diatomic gas at STP.

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