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

Short Answer

Expert verified
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 by step solution

01

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.
02

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:\[mass (g) = \frac{atomic~mass~(amu) \times 1~g}{6.022 \times 10^{23}~atoms}\]
03

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:\[mass~of~Ne~(g) = \frac{20.18~amu \times 1~g}{6.022 \times 10^{23}~atoms} = 3.35 \times 10^{-23}~g\]

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