One mole of a gas filled in a container at N.T.P., the number of molecules in 1 cm³ of volume will be

To find the number of molecules in 1 cm³ of a gas at N.T.P. (Normal Temperature and Pressure), we can use the concept of molar volume and Avogadro's number.

First, we recall that at N.T.P., 1 mole of any ideal gas occupies a standard volume of 22.4 liters.
We can convert this volume from liters to cubic centimeters (cm³):
Since 1 liter = 1000 cm³, the molar volume in cm³ is:
$\text{Volume}=22.4\times 1000\text{cm}{3}^{}=22400\text{cm}{3}^{}$

According to Avogadro's hypothesis, 1 mole of any substance contains Avogadro's number of molecules, which is approximately:
$N_A=6.02\times {10}^{23}\text{molecules}$

Therefore, 22400 cm³ of gas contains 6.02 × 10²³ molecules.
To find the number of molecules in 1 cm³ of volume, we divide the total number of molecules by the total volume in cm³:
$\text{Number of molecules in 1 cm}{3}^{}=\frac{6.02\times {10}^{23}}{22400}$

Thus, the correct option matches the expression:
6.02 x 10²³ / 22400