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Chapter 3: Problem 12

What is the mass in grams of a billion billion \(\left(10^{18}\right)\) atoms of \({ }^{24} \mathrm{Mg}\) ? The atomic mass of \({ }^{24} \mathrm{Mg}\) is \(23.9850\) amu.

Short Answer

Expert verified
The total mass of a billion billion \(\left(10^{18}\right)\) atoms of \({ }^{24} \mathrm{Mg}\) is approximately \(3990.461\times10^{-6}\) grams.

Step by step solution

01

Convert atomic mass from amu to grams

To convert the atomic mass from amu to grams, we can use the conversion factor: \(1 \, \text{amu} \approx 1.66 \times 10^{-24}\, \text{g}\). Using this factor, we can convert the atomic mass of \({ }^{24} \mathrm{Mg}\) as follows: \( mass_{g} = mass_{amu} \times conversion \, factor \) \( mass_{g} = 23.9850 \, \text{amu} \times 1.66 \times 10^{-24}\, \text{g/amu} \)
02

Calculate the mass in grams of the given number of atoms

Now that we have the mass of one \({ }^{24} \mathrm{Mg}\) atom in grams, we can multiply it by the given number of atoms to find the total mass. \( total \, mass = number \, of \, atoms \times mass_{g} \) \( total \, mass = 10^{18} \, atoms \times 23.9850 \, \text{amu} \times 1.66 \times 10^{-24}\, \text{g/amu} \)
03

Calculate the total mass

Now we can calculate the total mass: \( total \, mass = 10^{18} \times 23.9850 \times 1.66 \times 10^{-24} \) \( total \, mass = 3990.461 \times 10^{-6} \, \text{g} \) The total mass of a billion billion \(\left(10^{18}\right)\) atoms of \({ }^{24} \mathrm{Mg}\) turns out to be approximately \(3990.461\times10^{-6}\) grams.

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Most popular questions from this chapter

Magnesium (Mg) reacts with chlorine \(\left(\mathrm{Cl}_{2}\right)\) to form the compound \(\mathrm{MgCl}_{2}\). (a) Predict the formulas for the compounds formed when all the other alkaline earth metals react with chlorine. (b) Predict the formulas for the compounds formed when all the alkaline earth metals react with bromine. (c) Explain what principle you used to make your predictions.

(a) The elements in group IA (1) are called (b) The elements in group IIA (2) are called (c) The elements in group VIIA(17) are called (d) The elements in group VIIIA (18) are called

Explain the major difference between Thomson's model of the atom and Rutherford's model. Draw a picture of each model.

Naturally occurring copper, \(\mathrm{Cu}\), is composed of two isotopes. The isotope copper-63 is \(69.17 \%\) of naturally occurring copper and has an atomic mass of \(62.94\) amu. The isotope copper- 65 has an atomic mass of \(64.93\) amu. (a) What percent of naturally occurring copper is copper-65? (b) Calculate the atomic mass of naturally occurring copper.

The mass number of a \(2+\) cation is 56 , and its atomic number is 26 . The ion contains how many protons, electrons, and neutrons?
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