The volume of a gas at 0°C and 700 mm pressure is 760 cc. The number of molecules present in this volume is:

Options

A. `1.88 xx 10^(22)`
B. `6.022 xx 10^(23)`
C. `18.8 xx 10^(23)`
D. `18.8 xx 10^(23)`

Answer

To find the number of molecules present in a given volume of gas under specific conditions, we can use the Ideal Gas Law, which is expressed as:

\[ PV = nRT \]

Where:
- \( P \) = Pressure (in atm)
- \( V \) = Volume (in liters)
- \( n \) = Number of moles
- \( R \) = Ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = Temperature (in Kelvin)

### Step-by-Step Solution:

1. **Convert Pressure from mmHg to atm**:
\[ P = \frac{700 \text{ mmHg}}{760 \text{ mmHg/atm}} = 0.9211 \text{ atm} \]

2. **Convert Volume from cc to liters**:
\[ V = 760 \text{ cc} = 760 \text{ mL} = \frac{760}{1000} \text{ L} = 0.760 \text{ L} \]

3. **Convert Temperature from Celsius to Kelvin**:
\[ T = 0°C + 273 = 273 \text{ K} \]

4. **Use the Ideal Gas Law to find the number of moles \( n \)**:
\[ n = \frac{PV}{RT} \]
Substituting the values:
\[ n = \frac{(0.9211 \text{ atm}) \times (0.760 \text{ L})}{(0.0821 \text{ L·atm/(K·mol)}) \times (273 \text{ K})} \]

5. **Calculate \( n \)**:
\[ n = \frac{0.700 \text{ atm·L}}{22.413 \text{ L·atm/(K·mol)}} \approx 0.03123 \text{ moles} \]

6. **Calculate the number of molecules**:
The number of molecules \( N \) can be calculated using Avogadro's number \( N_A \):
\[ N = n \times N_A \]
Where \( N_A = 6.022 \times 10^{23} \text{ molecules/mol} \):
\[ N = 0.03123 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.88 \times 10^{22} \text{ molecules} \]

### Final Answer:
The number of molecules present in the volume is approximately \( 1.88 \times 10^{22} \) molecules.

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