How many molecule are present in 12 L of liquid `C Cl_(4)`? The density of the liquid is 1.59 g `cm^(-3)`?

Options

A. `7.44 xx 10^(26)`
B. `0.744 xx 10^(26)`
C. `1.59 xx 10^(26)`
D. `15.9 xx 10^(26)`

Explanation

To solve the question of how many molecules are present in 12 L of liquid CCl₄, given its density, we can follow these steps:

### Step 1: Convert Volume from Liters to Cubic Centimeters
1 liter is equal to 1000 cubic centimeters (cm³). Therefore, to convert 12 liters to cubic centimeters:
\[ \text{Volume} = 12 \, \text{L} \times 1000 \, \text{cm}^3/\text{L} = 12000 \, \text{cm}^3 \]

### Step 2: Calculate the Mass of CCl₄
Using the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
We can rearrange this to find the mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Given that the density of CCl₄ is 1.59 g/cm³, we can calculate the mass:
\[ \text{Mass} = 1.59 \, \text{g/cm}^3 \times 12000 \, \text{cm}^3 = 19080 \, \text{g} \]

### Step 3: Calculate the Molar Mass of CCl₄
The molar mass of CCl₄ can be calculated by adding the atomic masses of its constituent atoms:
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Chlorine (Cl) = 35.5 g/mol
- Since there are 4 chlorine atoms in CCl₄:
\[ \text{Molar mass of CCl}_4 = 12 + 4 \times 35.5 = 12 + 142 = 154 \, \text{g/mol} \]

### Step 4: Calculate the Number of Moles of CCl₄
Using the mass we calculated and the molar mass:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{19080 \, \text{g}}{154 \, \text{g/mol}} \approx 123.90 \, \text{moles} \]

### Step 5: Calculate the Number of Molecules
Using Avogadro's number (approximately \(6.023 \times 10^{23}\) molecules/mol):
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of molecules} = 123.90 \, \text{moles} \times 6.023 \times 10^{23} \, \text{molecules/mol} \approx 744 \times 10^{23} \, \text{molecules} \]
This can also be expressed as:
\[ 0.744 \times 10^{26} \, \text{molecules} \]

### Final Answer
The number of molecules present in 12 L of liquid CCl₄ is approximately \(0.744 \times 10^{26}\) molecules.

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