Answer :

To determine the weight in grams of [tex]\(4.3 \times 10^{21}\)[/tex] molecules of [tex]\(CH_4\)[/tex], we can follow these steps:

1. Understand the context: We want to find the mass of a given number of methane ([tex]\(CH_4\)[/tex]) molecules. The mass of a substance is often found using its molar mass and the concept of moles.

2. Use Avogadro's number: Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex] molecules/mol) tells us how many molecules are in one mole of a substance.

3. Calculate the number of moles:
[tex]\[
\text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} = \frac{4.3 \times 10^{21}}{6.022 \times 10^{23}}
\][/tex]
The result is approximately [tex]\(0.00714048\)[/tex] moles of [tex]\(CH_4\)[/tex].

4. Find the molar mass of [tex]\(CH_4\)[/tex]: Methane is composed of one carbon atom and four hydrogen atoms. The atomic masses are approximately:
- Carbon ([tex]\(C\)[/tex]): 12.01 g/mol
- Hydrogen ([tex]\(H\)[/tex]): 1.008 g/mol

Therefore, the molar mass of [tex]\(CH_4\)[/tex] is:
[tex]\[
\text{Molar mass of } CH_4 = 12.01 + 4 \times 1.008 = 16.042 \text{ g/mol}
\][/tex]

5. Calculate the mass in grams:
[tex]\[
\text{Mass} = \text{Moles} \times \text{Molar mass} = 0.00714048 \times 16.042
\][/tex]
The result is approximately [tex]\(0.11455\)[/tex] grams.

So, [tex]\(4.3 \times 10^{21}\)[/tex] molecules of [tex]\(CH_4\)[/tex] weigh approximately 0.11455 grams.

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Rewritten by : Barada