Using Avogadro’s Number Calculate the number of molecules in 9.00 moles H2S. Express your answer numerically in molecules. Calculate the number of moles of Cl atoms in 3.61.
The correct answer and explanation is :
To calculate the number of molecules in 9.00 moles of H₂S and the number of moles of Cl atoms in 3.61 moles of Cl₂, we will use Avogadro’s number, which is 6.022 × 10²³ molecules per mole. This is a fundamental constant used to convert between the number of moles and the number of molecules.
Part 1: Number of Molecules in 9.00 Moles of H₂S
We are given 9.00 moles of H₂S. To find the number of molecules, we use the following formula:
[
\text{Number of molecules} = \text{moles} \times \text{Avogadro’s number}
]
Substitute the known values:
[
\text{Number of molecules} = 9.00 \, \text{moles of H₂S} \times 6.022 \times 10^{23} \, \text{molecules per mole}
]
[
\text{Number of molecules} = 5.42 \times 10^{24} \, \text{molecules of H₂S}
]
Part 2: Number of Moles of Cl Atoms in 3.61 Moles of Cl₂
Next, we are given 3.61 moles of Cl₂, and we are asked to find the number of moles of Cl atoms. Each molecule of Cl₂ contains 2 chlorine (Cl) atoms. Therefore, the number of moles of Cl atoms in 3.61 moles of Cl₂ is calculated by multiplying the moles of Cl₂ by 2:
[
\text{Moles of Cl atoms} = 3.61 \, \text{moles of Cl₂} \times 2 \, \text{atoms of Cl per molecule of Cl₂}
]
[
\text{Moles of Cl atoms} = 7.22 \, \text{moles of Cl atoms}
]
Summary:
- Number of molecules of H₂S in 9.00 moles: 5.42 × 10²⁴ molecules
- Number of moles of Cl atoms in 3.61 moles of Cl₂: 7.22 moles
Explanation:
In the first calculation, we use Avogadro’s number to convert moles of a substance (H₂S) to individual molecules. Since 1 mole of any substance contains 6.022 × 10²³ molecules, multiplying 9.00 moles by Avogadro’s number gives us the total number of molecules.
In the second calculation, the compound Cl₂ consists of two chlorine atoms per molecule. Therefore, to determine the number of moles of chlorine atoms, we simply multiply the moles of Cl₂ by 2. This tells us how many individual Cl atoms are present in 3.61 moles of Cl₂.
Here is the scientific illustration showing the conversion of moles to molecules using Avogadro’s number, along with the calculation for the moles of Cl atoms. It should help visualize the process more clearly.