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

Options

A. 0.16 g
B. 0.8 g
C. 0.08g
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: Convert the volume from cm³ to liters
We know that:
1 cm³ = 1 mL = 10⁻³ L

So, to convert 112 cm³ to liters:
\[ 112 \, \text{cm}^3 = 112 \times 10^{-3} \, \text{L} = 0.112 \, \text{L} \]

### Step 2: Calculate the number of moles of CH₄
At STP, 1 mole of any ideal gas occupies 22.4 L. Therefore, we can find the number of moles of CH₄ in 0.112 L using the formula:
\[ \text{Number of moles} = \frac{\text{Volume of gas (L)}}{\text{Molar volume at STP (L/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{0.112 \, \text{L}}{22.4 \, \text{L/mol}} = 0.005 \, \text{mol} = 5 \times 10^{-3} \, \text{mol} \]

### Step 3: Calculate the molar mass of CH₄
The molecular mass of CH₄ can be calculated as follows:
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Hydrogen (H) = 1 g/mol

Thus, the molar mass of CH₄ (1 C + 4 H) is:
\[ \text{Molar mass of CH}_4 = 12 + (4 \times 1) = 16 \, \text{g/mol} \]

### 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:
\[ \text{Mass} = 5 \times 10^{-3} \, \text{mol} \times 16 \, \text{g/mol} = 0.08 \, \text{g} \]

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

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