Comparing Mass: 0.8 Gram Atom of Hydrogen vs. 3.011×1023 Hydrogen Atoms

When dealing with the fundamental elements of chemistry, such as hydrogen, it is essential to understand the concepts of gram atoms, moles, and atomic mass. This article will explore the mass comparisons and the reasoning behind why 0.8 grams of hydrogen atoms is approximately 0.5 moles, while 3.011×1023 hydrogen atoms corresponds to a mass of 0.5 grams.

Understanding Gram Atoms and Moles

In chemistry, the concept of a gram atom (also known as a gram atomic mass) is a crucial tool for comparing the mass of atoms. A gram atom is defined as the mass of an atom that equals the atomic mass of the element in grams. For hydrogen, the atomic mass is approximately 1.00794 atomic mass units (amu), which means one gram atom of hydrogen has a mass of 1.00794 grams.

A mole, on the other hand, is a unit of amount in chemistry, defined as the amount of substance that contains as many elementary entities (atoms, molecules, ions, etc.) as there are atoms in exactly 12 grams of carbon-12. This number is known as Avogadro's number, which is approximately 6.022×1023 particles per mole.

Comparing the Mass of 0.8 Gram Atom of Hydrogen

Let's start by examining the mass of 0.8 gram atoms of hydrogen. Since one gram atom of hydrogen has a mass of approximately 1.00794 grams, we can calculate the mass of 0.8 gram atoms as follows:

0.8 gram atoms of hydrogen 0.8 × 1.00794 grams ≈ 0.806352 grams

This calculation shows that 0.8 gram atoms of hydrogen is slightly more than 0.8 grams. However, in practical chemistry, we often approximate this value to 0.8 grams for simplicity. This value is, in fact, approximately equal to 0.5 moles of hydrogen atoms, as we will see in the next section.

3.011×1023 Hydrogen Atoms and Avogadro's Number

Next, let's consider 3.011×1023 hydrogen atoms. Given that Avogadro's number is 6.022×1023 atoms per mole, we can use this information to determine the mass of 3.011×1023 hydrogen atoms:

Mass of 3.011×1023 hydrogen atoms (3.011×1023 atoms) / (6.022×1023 atoms/mole) × 1.00794 grams/mole ≈ 0.500 grams

This calculation shows that 3.011×1023 hydrogen atoms have a mass of approximately 0.500 grams, which is equivalent to half a gram atom of hydrogen. Thus, 3.011×1023 hydrogen atoms and 0.8 grams of hydrogen atoms have the same mass, both approximately 0.5 grams.

Why 0.8 Gram Atom of Hydrogen is Approximately 0.5 Moles

It is important to understand why 0.8 grams of hydrogen atoms is approximately 0.5 moles. This relationship arises from the relationship between atomic mass and Avogadro's number. Since the atomic mass of hydrogen is 1.00794 grams per mol, and Avogadro's number is 6.022×1023 atoms per mole, we can calculate the mass of 0.5 moles of hydrogen atoms as:

Mass of 0.5 moles of hydrogen atoms 0.5 moles × 1.00794 grams/mole ≈ 0.50397 grams

Thus, 0.8 grams of hydrogen atoms is a slightly overestimate to 0.50397 grams, which is approximately 0.5 moles of hydrogen atoms.

Conclusion

To summarize, the mass of 0.8 grams of hydrogen atoms is approximately 0.5 moles of hydrogen atoms. Meanwhile, the mass of 3.011×1023 hydrogen atoms is also approximately 0.500 grams, which is equivalent to 0.500 moles of hydrogen atoms. This equivalence is due to the relationship between the atomic mass of hydrogen and Avogadro's number.

FAQs

Q1: What is the relationship between gram atoms and moles?

A1: A gram atom is a measure of the mass of an atom, and the mass of one gram atom is equal to the atomic mass of the element in grams. One mole of a substance contains Avogadro's number of elementary entities (atoms, molecules, etc.). Therefore, one gram atom of an element is approximately 1/6.022×1023 moles of that element.

Q2: Why is the mass of 3.011×1023 hydrogen atoms approximately 0.5 grams?

A2: The mass of 3.011×1023 hydrogen atoms can be calculated using Avogadro's number (6.022×1023 atoms/mole) and the atomic mass of hydrogen (1.00794 grams/mole). This calculation shows that 3.011×1023 hydrogen atoms have a mass of approximately 0.500 grams, which is equivalent to 0.500 moles of hydrogen atoms.

Q3: How do you calculate the mass of an element using moles and atomic mass?

A3: To calculate the mass of an element using moles and atomic mass, you multiply the number of moles by the atomic mass of the element. The atomic mass is the mass of one mole of the element.

References

[1] International Union of Pure and Applied Chemistry (IUPAC). (2013). Compendium of Chemical Terminology (IUPAC Gold Book). Oxford: Blackwell Publishing.

[2] National Institute of Standards and Technology (NIST). (2019). Atomic Weights and Isotopic Compositions for Elements (delete “Version” somewhere). NIST Standard Reference Database 69.

[3] International Union of Pure and Applied Chemistry (IUPAC). (2014). Devised G-7 guide to group conventions in chemical nomenclature (Nomenclature of Organic Chemistry Recommendations, 1979, Organometallic Chemistry Recommendations, 1979, Stereochemistry of Organic Molecules and Compounds Recommendations, 1974, Chemical Nomenclature and Structure Representations). Royal Society of Chemistry.