Problem 17 - Chemistry

Question

What is the mass in grams of a single atom of each of the following elements? (a) \(\mathrm{Hg}\), (b) Ne.

Step-by-Step Solution

Answer

The mass of a single Hg atom is \(3.33 \times 10^{-22}\) g and the mass of a single Ne atom is \(3.35 \times 10^{-23}\) g.

Step 1: Understand the Atomic Mass

Atomic mass is usually expressed in atomic mass units (amu), and it gives the mass of one atom relative to the mass of a carbon-12 isotope taken as 12 amu. Now let's look up the atomic masses of the two elements. For Hg (Mercury), the atomic mass is 200.59 amu, and for Ne (Neon), it is 20.18 amu.

Step 2: Convert amu to Grams

In chemistry, we often deal with the mole concept, which is simply Avogadro's number (\(6.022 \times 10^{23}\)) of particles (atoms, molecules, etc.). Knowing that 1 mole of any element has a mass in grams equivalent to the atomic mass in amu, and also contains \(6.022 \times 10^{23}\) atoms, we can set up the proportion:\[\frac{atomic~mass~(amu)}{1~atom} = \frac{atomic~mass~(g)}{6.022 \times 10^{23} atoms}\]We rearrange this to give mass in grams per atom, yielding:\[mass (g) = \frac{atomic~mass~(amu) \times 1~g}{6.022 \times 10^{23}~atoms}\]

Step 3: Apply the Conversion to Hg and Ne

Substituting the atomic masses into the equation in step 2, we find the mass of a single Hg atom:\[mass~of~Hg~(g) = \frac{200.59~amu \times 1~g}{6.022 \times 10^{23}~atoms} = 3.33 \times 10^{-22}~g\]Doing the same for Ne, we find the mass of a single Ne atom:\[mass~of~Ne~(g) = \frac{20.18~amu \times 1~g}{6.022 \times 10^{23}~atoms} = 3.35 \times 10^{-23}~g\]

Key Concepts

Avogadro's Number

Avogadro's number is a cornerstone in chemistry, denoting the number of particles present in one mole of a substance. This staggering figure is approximately \(6.022 \times 10^{23}\),and it allows scientists to count tiny particles like atoms and molecules in measurable amounts. Just like a dozen signifies twelve items, a mole represents \(6.022 \times 10^{23}\) particles.

However, unlike a dozen, the mole defines a quantity that matches the substance’s weight in grams to its atomic or molecular mass in amu.

Consider this: a mole of carbon atoms weighs about 12 grams, equivalent to the atomic mass of carbon in amu. Understanding Avogadro's number helps bridge the micro-world of atoms with the macro-world we can observe and measure.

Mole Concept

The mole concept serves as a fundamental tool in chemistry, converting the microscopic world of atoms and molecules into the macroscopic world of grams and moles. A mole defines a specific number, \(6.022 \times 10^{23}\), of any entity. This concept helps chemists perform calculations involving amounts of substances at a human scale.

• The molar mass (in grams per mole) of an element or compound is numerically equal to its atomic or molecular mass (in amu).
• This means that, for instance, 1 mole of Mercury (Hg) atoms has a mass of 200.59 grams. Hence, if you know the atomic mass in amu, you can easily find the substance's weight in grams for one mole.

The mole has significance beyond mere measurement; it represents the way substances interact in chemical reactions. Since chemical reactions occur at the atomic level, using moles allows for accurate predictions of how substances will react based on mass.

Conversion of amu to Grams

Converting atomic mass units (amu) to grams is an essential calculation for understanding the weigh of individual atoms. The conversion is straightforward once one appreciates the role of Avogadro's number. Here’s the process broken down:

• First, remember that the atomic mass in amu corresponds to the mass of one mole of atoms in grams.
• By utilizing Avogadro's number, we can find the mass of a single atom. Simply divide the atomic mass in amu by \(6.022 \times 10^{23}\) (the number of atoms per mole).

So, when you calculate the weight of one atom in grams, multiply the atomic mass in amu by \(1\,\text{gram}\) and then divide by \(6.022 \times 10^{23}\) atoms.This method reveals how an atom's incredibly small mass is calculated precisely, allowing chemists to gain insights into the reactions and compounds they study at the molecular level. This simple conversion unleashes the power of quantitative analysis in chemistry, making it a pivotal part of the field.