`N_(2)` gas is present in one litre flask at a pressure of `7.6 xx 10^(-10)` mm of Hg. The number of `N_(2)` gas molecules in the flask at 0°C are

Answer

To find the number of nitrogen gas (N₂) molecules in a 1-liter flask at a pressure of \(7.6 \times 10^{-10}\) mm of Hg and a temperature of 0°C, we can use the Ideal Gas Law, which is given by the equation:

\[ PV = nRT \]

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

### Step 1: Convert the pressure from mm of Hg to atm
The pressure in mm of Hg needs to be converted to atm. The conversion factor is:
\[ 1 \text{ atm} = 760 \text{ mm of Hg} \]

Thus, we can convert the pressure:
\[ P = \frac{7.6 \times 10^{-10} \text{ mm of Hg}}{760 \text{ mm of Hg/atm}} = 1.0 \times 10^{-12} \text{ atm} \]

### Step 2: Convert the temperature from Celsius to Kelvin
To convert the temperature from Celsius to Kelvin:
\[ T = 0°C + 273 = 273 \text{ K} \]

### Step 3: Substitute values into the Ideal Gas Law to find the number of moles (n)
We can rearrange the Ideal Gas Law to solve for \(n\):
\[ n = \frac{PV}{RT} \]
Substituting the values we have:
\[ n = \frac{(1.0 \times 10^{-12} \text{ atm}) \times (1 \text{ L})}{(0.0821 \text{ L·atm/(K·mol)}) \times (273 \text{ K})} \]

Calculating the denominator:
\[ 0.0821 \times 273 \approx 22.4143 \text{ L·atm/(K·mol)} \]

Now substituting back:
\[ n = \frac{1.0 \times 10^{-12}}{22.4143} \approx 4.46 \times 10^{-14} \text{ moles} \]

### Step 4: Convert moles to molecules
To find the number of molecules, we use Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol):
\[ \text{Number of molecules} = n \times N_A \]
Where \(N_A\) is Avogadro's number.

Calculating the number of molecules:
\[ \text{Number of molecules} = (4.46 \times 10^{-14} \text{ moles}) \times (6.022 \times 10^{23} \text{ molecules/mol}) \approx 2.69 \times 10^{10} \text{ molecules} \]

### Final Answer
The number of nitrogen gas molecules in the flask at 0°C is approximately \(2.69 \times 10^{10}\) molecules.

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