Number of atoms present in 1.6 g of methane is

Options

A. `6.02xx10^(23)`
B. `3.01xx10^(23)`
C. `3.01xx10^(22)`
D. `6.02xx10^(22)`

Explanation

To find the number of atoms present in 1.6 g of methane (CH₄), we can follow these steps:

### Step 1: Determine the molar mass of methane (CH₄)
Methane consists of one carbon atom and four hydrogen atoms. The atomic masses are approximately:
- Carbon (C): 12 g/mol
- Hydrogen (H): 1 g/mol

So, the molar mass of methane (CH₄) is calculated as follows:
\[ \text{Molar mass of CH}_4 = 1 \times 12 + 4 \times 1 = 12 + 4 = 16 \text{ g/mol} \]

### Step 2: Calculate the number of moles in 1.6 g of methane
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
we can find the number of moles in 1.6 g of methane:
\[ \text{Number of moles} = \frac{1.6 \text{ g}}{16 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 3: Use Avogadro's number to find the number of molecules
Avogadro's number (Nₐ) is \(6.022 \times 10^{23}\) molecules/mol. To find the number of molecules in 0.1 moles of methane:
\[ \text{Number of molecules} = \text{Number of moles} \times Nₐ = 0.1 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ \text{Number of molecules} = 6.022 \times 10^{22} \text{ molecules} \]

### Step 4: Calculate the number of atoms
Since each molecule of methane (CH₄) contains 5 atoms (1 carbon + 4 hydrogen), we can find the total number of atoms:
\[ \text{Number of atoms} = \text{Number of molecules} \times 5 \]
\[ \text{Number of atoms} = 6.022 \times 10^{22} \text{ molecules} \times 5 = 3.011 \times 10^{23} \text{ atoms} \]

### Final Answer
The number of atoms present in 1.6 g of methane is approximately \(3.011 \times 10^{23}\) atoms.

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