How many atoms of neon are in 5.8 moles of neon gas
The Correct Answer and Explanation is:
Problem:
How many atoms of neon are in 5.8 moles of neon gas?
Solution:
To calculate the number of atoms, use Avogadro’s number, which states that 1 mole of any substance contains 6.022×10236.022 \times 10^{23}6.022×1023 representative particles (in this case, atoms).
Number of atoms = (number of moles) × (Avogadro’s number)
Number of atoms = 5.8 mol×6.022×1023 atoms/mol5.8 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol}5.8mol×6.022×1023atoms/mol
Number of atoms = 34.9276×102334.9276 \times 10^{23}34.9276×1023
Number of atoms = 3.49276×10243.49276 \times 10^{24}3.49276×1024 atoms
Rounded to correct significant figures (2 significant figures, since 5.8 has 2), the answer is:
3.5×10243.5 \times 10^{24}3.5×1024 atoms of neon
Textbook-Style Explanation (around 300 words):
In chemistry, the concept of the mole is essential for relating the macroscopic amounts of substances to the number of particles involved. The mole serves as a bridge between the atomic scale and laboratory-scale quantities. One mole of any pure substance contains exactly 6.022×10236.022 \times 10^{23}6.022×1023 representative particles. This constant is known as Avogadro’s number and applies universally to atoms, molecules, ions, or other entities depending on the context.
To determine the number of atoms present in a given sample of neon gas, first identify the number of moles provided. In this case, the sample contains 5.8 moles of neon. Since neon is a monatomic gas (its formula is simply Ne), each mole directly corresponds to the same number of neon atoms as given by Avogadro’s number.
The calculation proceeds by multiplying the number of moles by Avogadro’s constant: Number of atoms=moles of Ne×6.022×1023 atoms/mol.\text{Number of atoms} = \text{moles of Ne} \times 6.022 \times 10^{23} \, \text{atoms/mol}.Number of atoms=moles of Ne×6.022×1023atoms/mol.
Substituting the values: 5.8 mol×6.022×1023 atoms/mol=3.49276×1024 atoms.5.8 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 3.49276 \times 10^{24} \, \text{atoms}.5.8mol×6.022×1023atoms/mol=3.49276×1024atoms.
When reporting the final answer, consider significant figures. The given data (5.8 moles) has two significant figures, so the result is rounded accordingly to 3.5×10243.5 \times 10^{24}3.5×1024 atoms.
This result indicates that in 5.8 moles of neon gas, there are approximately 3.5×10243.5 \times 10^{24}3.5×1024 individual neon atoms. This enormous number reflects the extremely small size of individual atoms and illustrates why the mole is such a practical unit in chemistry.
