Question

Weight of $6.023\times {10}^{21}$ atoms of zinc (At. wt. of $\mathrm{Zn}=$ $65.4)$ is (1) $0.645\mathrm{g}$ (2) $0.0654\mathrm{g}$ (3) $6.54\mathrm{g}$ (4) $0.00654\mathrm{g}$

Short answer

Option (3) $0.654\text{ g}$ is correct.

Step-by-step solution

- Understand the Given Information

Identify the given data: the number of zinc atoms is given as $6.023\times {10}^{21}$ and the atomic weight of zinc ($Zn$) is $65.4$.

- Recall Avogadro's Constant

Recall that Avogadro's constant ($N_A$) is $6.023\times {10}^{23}$ atoms/mol. This is the number of atoms in one mole of a substance.

- Calculate the Number of Moles

Use the formula: $$\text{Number of moles}=\frac{\text{Number of atoms}}{N_A}$$ Substitute the values: $$\text{Number of moles}=\frac{6.023\times {10}^{21}}{6.023\times {10}^{23}}=0.01\text{ mol}$$

- Calculate the Weight of Zinc

Multiply the number of moles by the atomic weight of zinc to find the weight: $$\text{Weight}=\text{Number of moles}\times \text{Atomic weight}$$ $$\text{Weight}=0.01\times 65.4=0.654\text{ g}$$

- Choose the Correct Option

The calculated weight of $0.654\text{ g}$ matches option (3) after adjusting for the right decimal place.

Key concepts

zinc atomic weight

Zinc is a chemical element with the symbol Zn and atomic number 30. The atomic weight of zinc is an important concept in chemistry. Atomic weight (or relative atomic mass) represents the average mass of atoms of an element, calculated using the relative abundance of isotopes found in nature. For zinc, the atomic weight is 65.4. It is calculated in atomic mass units (amu), where 1 amu is defined as one twelfth the mass of a carbon-12 atom.
Knowing the atomic weight helps in understanding the quantities involved in reactions and calculations, such as determining the mass of a specific number of atoms.

Avogadro's constant

Avogadro's constant (or Avogadro's number), denoted as $N_A$, is a fundamental constant in chemistry. It is the number of atoms, ions, or molecules in one mole of any substance. Specifically, Avogadro's constant is $6.023\times {10}^{23}$ particles/mole.
This constant allows chemists to count and quantify atoms in a given sample by relating macroscopic amounts of material to the number of particles they contain. It is essential for converting between the mass of a substance and the number of entities (atoms, molecules) present.

mole concept

The mole is a standard unit of measure in chemistry. One mole of any substance contains exactly $6.023\times {10}^{23}$ particles (this could be atoms, molecules, ions, etc.), which is Avogadro's constant.
The mole concept allows chemists to perform calculations that relate atomic mass units to grams, making it easier to work with elements and compounds in practical laboratory settings.
For example, knowing that 1 mole of zinc weighs 65.4 grams (from its atomic weight), you can calculate the mass of a different number of moles based on this proportion.

number of moles calculation

To find the number of moles from a given number of atoms, you use the formula: $\text{Number of moles}=\frac{\text{Number of atoms}}{N_A}$.
In the provided example, you are given $6.023\times {10}^{21}$ atoms of zinc. Using Avogadro's constant $N_A=6.023\times {10}^{23}$, the calculation would be:
$$\text{Number of moles}=\frac{6.023\times {10}^{21}}{6.023\times {10}^{23}}=0.01\text{ mol}$$
This calculation shows that there are 0.01 moles in $6.023\times {10}^{21}$ atoms of zinc.

step-by-step problem solving in chemistry

Solving chemistry problems often involves a step-by-step approach to ensure accuracy and clarity. Here's an outline to solve the provided problem:
1. **Understand the Given Information**: Identify all given data, such as the number of atoms and the atomic weight of zinc.
2. **Recall Key Constants**: Remember critical constants like Avogadro's number ($N_A=6.023\times {10}^{23}$).
3. **Calculate Number of Moles**: Use the formula $\text{Number of moles}=\frac{\text{Number of atoms}}{N_A}$, substituting the given values.
4. **Find the Weight**: Multiply the number of moles by the atomic weight to find the mass.
5. **Verify Answer**: Compare the calculated weight to the given options in the problem to choose the correct one.
This structured method can be applied to various problems, aiding in better comprehension and problem-solving efficiency.