Answer : The mass of
required is, 166.4 grams.
Explanation :
First we have to calculate the moles of nitrogen gas.
Using ideal gas equation:
![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
where,
P = Pressure of
gas = 1.00 atm
V = Volume of
gas = 113 L
n = number of moles
= ?
R = Gas constant = ![0.0821L.atm/mol.K](https://tex.z-dn.net/?f=0.0821L.atm%2Fmol.K)
T = Temperature of
gas = ![85^oC=273+85=358K](https://tex.z-dn.net/?f=85%5EoC%3D273%2B85%3D358K)
Putting values in above equation, we get:
![1.00atm\times 113L=n\times (0.0821L.atm/mol.K)\times 358K](https://tex.z-dn.net/?f=1.00atm%5Ctimes%20113L%3Dn%5Ctimes%20%280.0821L.atm%2Fmol.K%29%5Ctimes%20358K)
![n=3.84mol](https://tex.z-dn.net/?f=n%3D3.84mol)
Now we have to calculate the moles of sodium azide.
The balanced chemical reaction is,
![2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)](https://tex.z-dn.net/?f=2NaN_3%28s%29%5Crightarrow%202Na%28s%29%2B3N_2%28g%29)
From the balanced reaction we conclude that
As, 3 mole of
produced from 2 mole of ![NaN_3](https://tex.z-dn.net/?f=NaN_3)
So, 3.84 moles of
produced from
moles of ![NaN_3](https://tex.z-dn.net/?f=NaN_3)
Now we have to calculate the mass of ![NaN_3](https://tex.z-dn.net/?f=NaN_3)
![\text{ Mass of }NaN_3=\text{ Moles of }NaN_3\times \text{ Molar mass of }NaN_3](https://tex.z-dn.net/?f=%5Ctext%7B%20Mass%20of%20%7DNaN_3%3D%5Ctext%7B%20Moles%20of%20%7DNaN_3%5Ctimes%20%5Ctext%7B%20Molar%20mass%20of%20%7DNaN_3)
Molar mass of
= 65 g/mole
![\text{ Mass of }NaN_3=(2.56moles)\times (65g/mole)=166.4g](https://tex.z-dn.net/?f=%5Ctext%7B%20Mass%20of%20%7DNaN_3%3D%282.56moles%29%5Ctimes%20%2865g%2Fmole%29%3D166.4g)
Therefore, the mass of
required is, 166.4 grams.