Chapter 1: Problem 49
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
Expert verified
Option (3) \(0.654 \text{ g}\) is correct.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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.
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.
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.
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.
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.
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.
