The mass of `112 cm^(3)` of `CH_(4)` gas at STP is

Options

A. 0.16 g
B. 0.8 g
C. 0.08 g
D. 1.6 g

Explanation

To find the mass of `112 cm³` of `CH₄` gas at STP (Standard Temperature and Pressure), we can follow these steps:

### Step 1: Understand the conditions at STP
At STP, 1 mole of any ideal gas occupies `22,400 cm³` (or `22.4 L`).

### Step 2: Calculate the number of moles of `CH₄`
To find the number of moles of methane gas (`CH₄`), we can use the formula:
\[ \text{Number of moles (n)} = \frac{\text{Volume of gas (V)}}{\text{Molar volume at STP (V_m)}} \]
Where:
- Volume of gas \( V = 112 \, cm³ \)
- Molar volume at STP \( V_m = 22,400 \, cm³ \)

Substituting the values:
\[ n = \frac{112 \, cm³}{22,400 \, cm³/mol} = \frac{112}{22400} = 0.005 \, moles \]

### Step 3: Calculate the molar mass of `CH₄`
The molar mass of methane (`CH₄`) can be calculated as follows:
- Carbon (C) has an atomic mass of `12 g/mol`
- Hydrogen (H) has an atomic mass of `1 g/mol`, and there are 4 hydrogen atoms in methane.

Thus, the molar mass of `CH₄` is:
\[ \text{Molar mass of } CH₄ = 12 + (4 \times 1) = 12 + 4 = 16 \, g/mol \]

### Step 4: Calculate the mass of `CH₄`
Now, we can find the mass of `CH₄` using the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
Substituting the values:
\[ \text{Mass} = 0.005 \, moles \times 16 \, g/mol = 0.08 \, grams \]

### Final Answer
The mass of `112 cm³` of `CH₄` gas at STP is `0.08 grams`.

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