Question

Consider separate equal mass samples of magnesium, zinc, and silver. Rank them from greatest to least number of atoms and support your answer.

Short answer

The ranking of separate equal mass samples of magnesium, zinc, and silver from greatest to least number of atoms is: Magnesium > Zinc > Silver. This is because the number of atoms in each sample is inversely proportional to their molar masses, and magnesium has the smallest molar mass (24.31 g/mol), zinc has an intermediate molar mass (65.38 g/mol), and silver has the greatest molar mass (107.87 g/mol).

Step-by-step solution

Find the molar masses of the elements

To find the molar mass of each element, we can consult a periodic table. The molar masses are: - Magnesium (Mg): 24.31 g/mol - Zinc (Zn): 65.38 g/mol - Silver (Ag): 107.87 g/mol

Convert the mass to moles

For equal mass samples, we can use the molar mass values to convert the mass of each element to moles. Since the mass is equal, we can represent it as 'm'. Therefore, for each element, the number of moles (n) can be calculated as follows: \(n_{Mg} = \frac{m}{M_{Mg}}\) \(n_{Zn} = \frac{m}{M_{Zn}}\) \(n_{Ag} = \frac{m}{M_{Ag}}\)

Calculate the number of atoms in each sample

To find the number of atoms in each sample, we can use Avogadro's number, which gives the number of atoms in one mole of an element. Avogadro's number is approximately \(6.022 \times 10^{23}\) atoms/mol. Therefore, for each element, the number of atoms (N) can be calculated as follows: \(N_{Mg} = n_{Mg} \times Avogadro's \, Number\) \(N_{Zn} = n_{Zn} \times Avogadro's \, Number\) \(N_{Ag} = n_{Ag} \times Avogadro's \, Number\)

Compare the number of atoms and rank them

We can now compare the number of atoms in each sample. Note that since all samples have equal mass and Avogadro's number is constant, the number of atoms in each sample is inversely proportional to their respective molar masses: - The element with the smallest molar mass will have the greatest number of atoms. - The element with the greatest molar mass will have the least number of atoms. From the molar masses in Step 1, we can rank the samples in order of greatest to least number of atoms: 1. Magnesium (Mg) - Smallest molar mass (24.31 g/mol) 2. Zinc (Zn) - Intermediate molar mass (65.38 g/mol) 3. Silver (Ag) - Greatest molar mass (107.87 g/mol) Thus, the ranking of separate equal mass samples of magnesium, zinc, and silver from greatest to least number of atoms is: Magnesium > Zinc > Silver.

Key concepts

Avogadro's number

When we talk about Avogadro's number, we are pointing to a fundamental constant in chemistry. It tells us how many entities, typically atoms or molecules, are in one mole of a substance. Avogadro's number is approximately \(6.022 \times 10^{23}\). This is a very large number and helps us understand how many particles are involved at the atomic and molecular levels where they can't be counted individually due to their sheer quantity.

Using Avogadro's number, we can link the macroscopic scale of grams (used in lab experiments) to the microscopic world of atoms and molecules. For instance, when we have one mole of any element, it contains exactly \(6.022 \times 10^{23}\) of its atoms. This applies to elements like magnesium, zinc, and silver. When dealing with large numbers of moles or atoms, this consistency allows chemists to predict and compare chemical reactions and discover interesting things about elements they work with.

Mole concept

The mole concept is a cornerstone of chemistry that revolves around the idea of grouping atoms into moles, making it easier to handle quantitatively. A mole is a standard unit in chemistry that represents \(6.022 \times 10^{23}\) units of a substance—which we know as Avogadro's number.

This concept allows chemists to convert between the number of atoms, molecules, or ions and the mass of a substance. For example, when considering equal mass samples of different elements like magnesium, zinc, and silver, we can calculate the number of moles for each. Because a mole of any element has a constant number of entities, this calculation helps us understand and quantify chemical reactions and material properties by directly linking mass to atomic count.

• Helps transitions between the microscopic world of atoms and the macroscopic world of materials.
• Enables accurate predictions in chemical reactions.

Periodic table

The periodic table is a chart that organizes all known elements in a systematic way based on their atomic numbers, electron configurations, and recurring chemical properties. It is an indispensable tool for chemists and helps in predicting the properties of elements.

Here, each element is listed with key information, such as its symbol and atomic mass, which is approximately the sum of its protons and neutrons. For instance, when you look up magnesium, zinc, and silver on the periodic table, you'll find their molar masses, which are 24.31 g/mol, 65.38 g/mol, and 107.87 g/mol respectively.

• Facilitates the quick identification of an element's properties.
• Helps compare different elements, such as ranking them based on atomic count when dealing with equal masses.

By providing this information, the periodic table allows chemists to calculate how much of each element is present in a given sample, which is used to predict reactions and interactions.

Rank elements by atomic count

When asked to rank elements by the number of atoms present in equal mass samples, we need to make calculations based on their molar masses. The molar mass, found on the periodic table, is the mass of one mole of a given element in grams. This is crucial because it allows us to convert the sample's mass into moles, and thereafter, into atoms using Avogadro's number.

In our example with magnesium, zinc, and silver, even if each sample weighs the same, they differ in their atomic count. Why? Because of varying molar masses:

• Magnesium has the smallest molar mass, indicating more atoms.
• Zinc has an intermediate molar mass, meaning a moderate number of atoms.
• Silver, with the highest molar mass, has the fewest number of atoms.

So, when ranked by atomic count from greatest to least, the order is Magnesium, Zinc, then Silver. In such comparisons, the smaller the molar mass, the greater the number of atoms in an equal mass sample.