Volume of a gas at STP is `1.12xx10^(-7)` c c. Calculate the number of molecules in it

Options

A. (a)`3.01xx10^(20)`
B. (b)`3.0xx10^(12)`
C. (c )`3.01xx10^(23)`
D. (d)`3.0xx10^(24)`

Explanation

To calculate the number of molecules in a given volume of gas at Standard Temperature and Pressure (STP), we can follow these steps:

### Step 1: Understand the volume of one mole of gas at STP
At STP, one mole of any gas occupies a volume of 22.4 liters. To convert this to cubic centimeters (cc), we use the conversion factor:
\[ 1 \text{ liter} = 1000 \text{ cc} \]
Thus,
\[ 22.4 \text{ liters} = 22.4 \times 1000 \text{ cc} = 22400 \text{ cc} \]

### Step 2: Use Avogadro's number
Avogadro's number (\(N_A\)) is \(6 \times 10^{23}\) molecules per mole. This means that in 22400 cc of gas, there are \(6 \times 10^{23}\) molecules.

### Step 3: Set up the proportion
We need to find the number of molecules in a volume of \(1.12 \times 10^{-7}\) cc. We can set up a proportion based on the volumes:
\[ \text{Number of molecules in } 1.12 \times 10^{-7} \text{ cc} = \left( \frac{1.12 \times 10^{-7} \text{ cc}}{22400 \text{ cc}} \right) \times (6 \times 10^{23} \text{ molecules}) \]

### Step 4: Calculate the number of molecules
Now we can substitute the values into the equation:
\[ \text{Number of molecules} = \left( \frac{1.12 \times 10^{-7}}{22400} \right) \times (6 \times 10^{23}) \]

Calculating the fraction:
\[ \frac{1.12 \times 10^{-7}}{22400} = \frac{1.12}{22400} \times 10^{-7} = 5 \times 10^{-12} \]

Now multiplying by Avogadro's number:
\[ \text{Number of molecules} = 5 \times 10^{-12} \times 6 \times 10^{23} = 30 \times 10^{11} = 3 \times 10^{12} \]

### Final Answer
Thus, the number of molecules in \(1.12 \times 10^{-7}\) cc of gas at STP is \(3 \times 10^{12}\) molecules.

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