Question

How many atoms are present in four grams of hydrogen gas at STP?
A. $$6.02\times {10}^{23}$$ atoms
B. $$12.04\times {10}^{23}$$ atoms
C.12.04 atoms
D. $$1.2\times {10}^{23}$$ atoms
E. $$2.40\times {10}^{24}$$ atoms

Answer 1

Hint: To solve this question, follow these steps: first calculate the number of moles of the gas present. Then multiply the number of moles with Avogadro’s number to find the number of molecules. Then multiply this quantity with the number of atoms present in a molecule.

Complete step by step answer:
Before we move forward with the solution of this question, let us discuss some important concepts.
Mole: a mole is a physical quantity which represents the amount of mass of the substance required to have a collective of $$6.022\times {10}^{23}$$ atoms of the given substance. Mole is a widely used unit for calculating the amount of matter of a substance. One mole of any substance weighs about the same as the molecular mass of that substance.
Hydrogen has an atomic number of 1. This means that there is only 1 electron present in its 1s orbital. Hence to satisfy its duplet, and exist as a stable element, hydrogen gas is a diatomic molecule.
Now moving back to the question, we have been given a sample of 4 grams of hydrogen gas. We know that the atomic weight of hydrogen is 1 amu, while the molecular weight of hydrogen is 2 amu. Since, the given sample contains hydrogen gas, we must consider the molecular structure of hydrogen, i.e. molecular mass = 2 amu.
Hence the weight of one mole of hydrogen gas is 2 grams. Since the given sample weighs 4 grams, we can say that the number of moles of hydrogen present is 2 moles.
Now, the number of atoms/molecules present in 1 mole of a substance is represented by a quantity known as Avogadro’s Number. This quantity is equivalent to $$6.02\times {10}^{23}$$ atoms per mole of a substance. Since, we have 2 moles of hydrogen gas, the number of molecules of hydrogen present are:
Number of molecules = (Avogadro’s number) (number of moles of hydrogen)
  $=(6.02\times {10}^{23})(2)$
  $=12.04\times {10}^{23}$
Since each molecule consists of 2 atoms,
Number of atoms = (number of molecules) (number of atoms in every molecule)
  $=(12.04\times {10}^{23})(2)$
  $=(24.08\times {10}^{23})$
  $=2.4\times {10}^{24}$ atoms

Hence, Option E is the correct option.

Note:
Avogadro's number is defined as the number of elementary particles (molecules, atoms, compounds, etc.) per mole of a substance. With Avogadro's number, scientists can discuss and compare very large numbers, which is useful because substances in everyday quantities contain very large numbers of atoms and molecules.