Question

You have a 20.0-g sample of silver metal. You are given 10.0 g of another metal and told that this sample contains twice the number of atoms as the sample of silver metal. Is this possible?

Short answer

The moles of silver in the 20.0 g sample are \( \frac{20.0 \, \text{g}}{107.87 \, \text{g/mol}} \) which gives us the number of silver atoms as \( \text{Moles of silver} \times (6.022 \times 10^{23} \, \text{atoms/mol}) \). The other metal sample has twice the number of atoms, so we have \( \frac{\text{Number of other metal atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}} \) moles of the other metal. To find the molar mass of the other metal, we use \( \frac{10.0 \, \text{g}}{\text{Moles of other metal}} \). Compare the calculated molar mass of the other metal to known values of molar masses in the periodic table. If it closely matches the molar mass of an existing element, then it is possible; otherwise, it is not possible.

Step-by-step solution

Find the moles of silver in the sample

To determine the number of moles of silver in the 20.0 g sample, we will use the molar mass of silver (Ag), which is 107.87 g/mol. The formula to find the moles of a substance is: Moles = mass of substance (g) / molar mass (g/mol) Moles of silver = 20.0 g / 107.87 g/mol

Calculate the number of atoms in the silver sample

Now we have the moles of silver, we can use Avogadro's number (6.022 x 10^23 atoms/mol) to determine the number of atoms in the silver sample. We can use the formula: Number of atoms = moles x Avogadro's number Number of silver atoms = Moles of silver x (6.022 x 10^23 atoms/mol)

Calculate the number of atoms in the other metal sample

It's given that the other metal sample has twice the number of atoms as the silver sample. Therefore, the number of atoms in the other metal sample is: Number of other metal atoms = 2 x Number of silver atoms

Determine the moles of the other metal sample

Now that we have the number of atoms in the other metal sample, we can use Avogadro's number to determine the number of moles of the other metal: Moles of other metal = Number of other metal atoms / Avogadro's number

Calculate the molar mass of the other metal

As we now have the number of moles of the other metal and its mass (10.0 g), we can calculate its molar mass using the formula: Molar mass (g/mol) = mass of substance (g) / moles of substance Molar mass of other metal = 10.0 g / Moles of other metal

Conclusion

After calculating the molar mass of the other metal, we can determine if it is possible for the other metal sample to have twice the number of atoms as the silver sample. Compare the calculated molar mass of the other metal to known values of molar masses in the periodic table. If it closely matches the molar mass of an existing element, then it is possible; otherwise, it is not possible.

Key concepts

Molar Mass

Molar mass is a key concept in chemistry that reflects the mass of one mole of a substance, usually specified in grams per mole. It directly relates to the atomic structure of an element. For any chemical element, you can determine its molar mass by summing the atomic masses of its constituent atoms, as listed in the periodic table.

To compute the number of moles in a given sample, you can use the formula:

• \( \text{Moles} = \frac{\text{mass of substance (g)}}{\text{molar mass (g/mol)}} \)

In the provided exercise, for a 20.0 g sample of silver, you would use silver's molar mass of 107.87 g/mol to determine the total moles of silver. Understanding how to calculate molar mass is crucial for solving problems relating to chemical quantities and reactions.

Avogadro's Number

Avogadro's number is an essential constant in chemistry, defined as the number of atoms, ions, or molecules in one mole of a substance. This number is approximately \(6.022 \times 10^{23}\). It's a fundamental bridge between the atomic scale and the macroscopic measurements we observe.

When you know the number of moles of a substance and want to find out how many atoms are present, you can apply Avogadro's number:

• \( \text{Number of atoms} = \text{moles} \times 6.022 \times 10^{23} \)

In our exercise, after determining the moles of silver, multiplying by Avogadro's number will give the number of atoms in the silver sample. This concept helps translate mole calculations into actual discrete particles like atoms or molecules.

Periodic Table

The periodic table is a detailed map used by chemists to understand the properties of elements. It organizes all known elements by atomic number, electron configuration, and recurring chemical properties. Each element’s position gives valuable data on its molar mass, essential for calculations involving atoms and moles.

To use the periodic table effectively:

• Find the atomic mass on the table. This value serves as the element's molar mass in grams per mole.
• Use this weight to find quantities in chemical calculations, such as determining the number of moles from a given mass.

In the discussed scenario, determining the molar mass for silver and comparing it with other metals can tell if a doubled atom count is feasible for the given mass. This utility of the periodic table allows chemists to predict reactions and solve comparative problems accurately.