Question

What is the average mass of one atom of argon in atomic mass units and in units of grams?

Short answer

The average mass of one atom of Argon is 39.95u or \(6.64 \times 10^{-23}\) grams.

Step-by-step solution

Identify the atomic mass of Argon in atomic mass units

Using the periodic table, we see that the atomic mass of Argon is approximately 39.95 atomic mass units (u).

Convert atomic mass units to grams

To convert atomic mass units into grams, multiply the number of atomic mass units by the conversion factor, which is \(1.6605 \times 10^{-24}\) grams/atomic mass unit. So, the calculation would be: \(39.95u \times 1.6605 \times 10^{-24} grams/u\).

Calculate and round the answer

Perform multiplication to obtain the answer. The result is \(6.64 \times 10^{-23}\) grams. Round the answer to a reasonable number of significant figures, in this case, three significant figures would suffice, leading to a final answer of \(6.64 \times 10^{-23}\) grams.

Key concepts

Understanding Atomic Mass of Argon

Argon, a noble gas found in the Earth's atmosphere, plays a vital role in various scientific applications due to its inertness. However, to use argon effectively, it's crucial to understand its atomic mass. The atomic mass of argon is approximately 39.95 atomic mass units (u), a value that can be found on the periodic table. This measurement reflects the average mass of all the isotopes of argon, weighted by their respective abundances.

It's essential to recognize that atomic mass is different from atomic number, which is the count of protons in an atom's nucleus. Atomic mass takes into account both protons and neutrons, as their masses are quite similar. Knowing the atomic mass is fundamental when computing the molar mass of substances, thereby enabling chemists to measure the amount of substance in moles, which is a key step in many stoichiometric calculations.

The Process of Mass Unit Conversion

When working in chemistry, it's often necessary to convert the atomic mass from atomic mass units to grams to understand a substance's mass on a macroscopic scale. To perform this conversion, we use a standard conversion factor. This conversion factor is the mass of one atomic mass unit in grams, which is approximately \(1.6605 \times 10^{-24}\) grams.

To convert the atomic mass of argon from atomic mass units to grams, you simply multiply the atomic mass in atomic mass units by the conversion factor: \(39.95\,u \times 1.6605 \times 10^{-24}\,\frac{grams}{u}\). This calculation bridges the gap between the minuscule mass scale of atoms and the more familiar gram scale which is easier to conceptualize and work with in a laboratory setting.

Applying Significant Figures

Significant figures are used in science to indicate the precision of a measurement. When performing calculations, it's essential to manage significant figures correctly to ensure that the precision of the final answer reflects the precision of the initial data. In the context of the atomic mass of argon, after converting to grams, the calculated value might have more digits than necessary.

Therefore, when the mass of argon is computed as \(6.64 \times 10^{-23}\) grams, rounding to three significant figures gives us \(6.64 \times 10^{-23}\) grams. The choice of three significant figures correlates with the initial data's precision, indicating that the answer should be reported with the same level of accuracy. This ensures that the data presented is both meaningful and reliably conveys the measurement's accuracy without implying an unwarranted level of precision.