Consider a mixture of three different gases: 1.40 g of argon (molecular mass = 39.948 g/mol), 2.70 g of neon (molecular mass = 20.180 g/mol), and 3.50 g of helium (molecular mass = 4.0026 g/mol). For this mixture, determine the percentage of the total number of atoms that corresponds to each of the components.
The Correct Answer and Explanation is :
The percentage of the total number of atoms corresponding to each component in the mixture is:
- Argon: 3.36%
- Neon: 12.82%
- Helium: 83.82%
Explanation:
We are given a mixture of three gases: argon, neon, and helium. To determine the percentage of each component in terms of the number of atoms, we follow these steps:
- Calculate the number of moles of each gas
Using the formula:
[
\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}
]
- Argon:
[
\frac{1.40 \text{ g}}{39.948 \text{ g/mol}} = 0.03504 \text{ moles}
] - Neon:
[
\frac{2.70 \text{ g}}{20.180 \text{ g/mol}} = 0.1338 \text{ moles}
] - Helium:
[
\frac{3.50 \text{ g}}{4.0026 \text{ g/mol}} = 0.8744 \text{ moles}
]
- Calculate the total number of moles
[
0.03504 + 0.1338 + 0.8744 = 1.0432 \text{ moles}
] - Find the percentage of each gas in terms of moles (which corresponds to the number of atoms)
[
\text{Percentage} = \left( \frac{\text{Moles of gas}}{\text{Total moles}} \right) \times 100
]
- Argon:
[
\left( \frac{0.03504}{1.0432} \right) \times 100 = 3.36\%
] - Neon:
[
\left( \frac{0.1338}{1.0432} \right) \times 100 = 12.82\%
] - Helium:
[
\left( \frac{0.8744}{1.0432} \right) \times 100 = 83.82\%
]
Since all gases are monatomic, the percentage of moles directly translates to the percentage of atoms.
I will now generate an image representing these percentages.
Here is a pie chart illustrating the percentage of total atoms contributed by each gas in the mixture. As seen, helium has the largest proportion (83.82%), followed by neon (12.82%) and argon (3.36%). This dominance is due to helium’s significantly lower molar mass, which results in a higher number of moles (and thus atoms) compared to the other gases.
