help me understand this chem question please

[deeentist79]

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a detonator explodes
Pb(N3)2 -----------> Pb + 3N2,
The reaction creates 14.3 L of N2 gas at standard temperature and pressure, how much metallic lead is produced. R= 0.082.

Now i know using PV=nRT, we find the moles of N2 gas, that comes out to be 2/3 mol.
What i dont understand is how did they deduce that since 2/3 moles of N2 are produced, 2/9 moles of Pb are produced??/😕😕

The answer is 44.1 g of Pb.

Can some please explain the stoichiometry?

 

[chanberg]

the way i always remember how to do it is

find moles = pv=nrt
N = 0.638 moles of N2 gas
you want pb soo

0.638 x (whatyouwant) / (whatyouhave) x (mw of pb) = 44.1 grams
what we want is = 1 mole of Pb
what we have is = 3 moles of N2