1. Convert Units
* Volume (V): 500.0 mL = 0.500 L
* Pressure (P): 780 mmHg = 1.03 atm (using the conversion factor 1 atm = 760 mmHg)
* Temperature (T): 135 °C = 408 K (using the conversion factor K = °C + 273.15)
2. Ideal Gas Law
The ideal gas law is expressed as:
PV = nRT
Where:
* P = Pressure (in atm)
* V = Volume (in L)
* n = Number of moles
* R = Ideal gas constant (0.0821 L·atm/mol·K)
* T = Temperature (in K)
3. Solve for Number of Moles (n)
Rearrange the ideal gas law to solve for n:
n = PV / RT
Substitute the known values:
n = (1.03 atm)(0.500 L) / (0.0821 L·atm/mol·K)(408 K)
n ≈ 0.0155 moles
4. Calculate Number of Molecules
* Avogadro's Number: One mole of any substance contains 6.022 x 10^23 molecules (Avogadro's number).
* Calculate Molecules:
Number of molecules = (0.0155 moles) * (6.022 x 10^23 molecules/mole)
Number of molecules ≈ 9.34 x 10^21 molecules
Therefore, there are approximately 9.34 x 10^21 molecules of N2 gas in the 500.0 mL sample.
