To determine the number of electrons present in 1.6 grams of methane ([tex]\(\text{CH}_4\)[/tex]), we can follow a methodical, step-by-step approach.
### Step 1: Understand the Given Data
- We know that 16 grams of methane ([tex]\(\text{CH}_4\)[/tex]) contain 10 moles of electrons.
### Step 2: Establish a Proportion
We need to find out how many moles of electrons are in 1.6 grams of methane. We can set up a proportion based on the given data.
Given:
- 16 grams of methane [tex]\(\rightarrow\)[/tex] 10 moles of electrons
We need to find:
- 1.6 grams of methane [tex]\(\rightarrow\)[/tex] X moles of electrons
This translates to the proportion:
[tex]\[ \frac{1.6 \ \text{grams of methane}}{X \ \text{moles of electrons}} = \frac{16 \ \text{grams of methane}}{10 \ \text{moles of electrons}} \][/tex]
### Step 3: Solve the Proportion
Now we solve for X:
[tex]\[ X = \frac{1.6 \ \text{grams} \times 10 \ \text{moles of electrons}}{16 \ \text{grams}} \][/tex]
[tex]\[ X = \frac{16}{16} \][/tex]
[tex]\[ X = 1 \ \text{mole of electrons} \][/tex]
### Step 4: Interpret the Result
The number of moles of electrons in 1.6 grams of methane is 1 mole of electrons.
Since we're asked specifically for the number of electrons, and the moles of electrons are a direct indicator of the number of electrons when expressed in Avogadro's number base (although not numerically asked here, 1 mole of electrons corresponds to [tex]\(6.022 \times 10^{23}\)[/tex] electrons, but the precise calculation aligns with the simplified result we need here).
### Step 5: Conclusion
Therefore, the number of electrons present in 1.6 grams of methane is 1 mole of electrons.
