Respuesta :
Answer : The number of molecules present in nitrogen gas are, [tex]3.48\times 10^{13}[/tex]
Explanation :
First we have to calculate the moles of nitrogen gas by using ideal gas equation.
[tex]PV=nRT[/tex]
where,
P = Pressure of [tex]N_2[/tex] gas = [tex]1.00\times 10^{-6}mmHg=1.32\times 10^{-9}atm[/tex] (1 atm = 760 mmHg)
V = Volume of [tex]N_2[/tex] gas = 985 mL = 0.982 L (1 L = 1000 mL)
n = number of moles [tex]N_2[/tex] = ?
R = Gas constant = [tex]0.0821L.atm/mol.K[/tex]
T = Temperature of [tex]N_2[/tex] gas = [tex]0.0^oC=273+0.0=273K[/tex]
Now put all the given values in above equation, we get:
[tex](1.32\times 10^{-9}atm)\times 0.982L=n\times (0.0821L.atm/mol.K)\times 273K[/tex]
[tex]n=5.78\times 10^{-11}mol[/tex]
Now we have to calculate the number of molecules present in nitrogen gas.
As we know that 1 mole of substance contains [tex]6.022\times 10^{23}[/tex] number of molecules.
As, 1 mole of [tex]N_2[/tex] gas contains [tex]6.022\times 10^{23}[/tex] number of molecules
So, [tex]5.78\times 10^{-11}[/tex] mole of [tex]N_2[/tex] gas contains [tex](5.78\times 10^{-11})\times (6.022\times 10^{23})=3.48\times 10^{13}[/tex] number of molecules
Therefore, the number of molecules present in nitrogen gas are, [tex]3.48\times 10^{13}[/tex]
