1. Use the Ideal Gas Law:
The ideal gas law states: PV = nRT
Where:
* P = Pressure (atm)
* V = Volume (L)
* n = Number of moles
* R = Ideal gas constant (0.0821 L·atm/mol·K)
* T = Temperature (K)
2. Solve for the number of moles (n):
* n = PV / RT
* n = (1 atm * 1.00 L) / (0.0821 L·atm/mol·K * 298 K)
* n ≈ 0.0409 moles
3. Convert moles to molecules:
* Avogadro's number tells us that 1 mole contains 6.022 x 10²³ molecules.
* Number of molecules = n * Avogadro's number
* Number of molecules ≈ 0.0409 moles * 6.022 x 10²³ molecules/mole
* Number of molecules ≈ 2.46 x 10²² molecules
Therefore, there are approximately 2.46 x 10²² nitrogen molecules in 1.00 L of gas at 1 atm and 298 K.
