Answer:
At RTP (room temperature and pressure), one mole of any ideal gas occupies a volume of 24.45 dm³. Therefore, we can use the following steps to calculate the number of molecules of nitrogen dioxide in 3 dm³ at RTP:
Calculate the number of moles of nitrogen dioxide in 3 dm³ using the ideal gas law:
PV = nRT
Where:
P = pressure = 1 atm (at standard pressure)
V = volume = 3 dm³
n = number of moles (unknown)
R = gas constant = 0.0821 L atm/(mol K)
T = temperature = 298 K (at standard temperature)
n = PV/RT
n = (1 atm)(3 dm³)/(0.0821 L atm/(mol K) x 298 K)
n = 0.122 mol
Calculate the number of molecules of nitrogen dioxide in 0.122 mol using Avogadro's number:
1 mol of any substance contains 6.022 x 10^23 molecules (Avogadro's number)
Therefore, the number of molecules in 0.122 mol of nitrogen dioxide is:
6.022 x 10^23 molecules/mol x 0.122 mol = 7.35 x 10^22 molecules
Therefore, there are 7.35 x 10^22 molecules of nitrogen dioxide in 3 dm³ at RTP.
Step-by-step explanation: