The following chemical reactions used to be untilized to rapidly produce large amounts of `N_(2)` gas inside an automobile air bag:
`2NaN_(3) rarr 2 Na + 3 N_(2) (g)`
`10 Na + 2 KNO_(3) rarr K_(2) + 5 Na_(2) O + N_(2) (g)`
`K_(2) O+ Na_(2) O + SiO_(2) rarr` Alkaline silicate (glass)
How many grams of `KNO_(3)` are needed to produce enough `N_(2)` to fill a `12.3 L` air baG AT `27^(@)C` and 4 atm.
a. `202 g` b. `81.25 g`
c. `404 g` d. `25.25 g`

Explanation

d. `PV = nRT`
`n_(N_(2)) = (PV)/(RT) = (4 xx 12.3)/(0.082 xx 300) = 2 mol`
2 mol produces `= 3 "mol" N_(2)`
a. 10 mol `Na` produces ` = (3)/(2) xx 10 = 15 "mol" N_(2)`
b. 10 mol `Na = 2 "mol" KNO_(3) -= "mol" N_(2)`
`(15 "mol" N_(2))`
Total mol of `N_(2)` produced `= 15 + 1`
`= 16 "mol" N_(2))`
`:. 16 "mol" N_(2) = 2 "mol" KNO_(3)k (Mw KNO_(3) = 101 g)`
`= 2 xx 101 g KNO_(3)`
`2 "mol" N_(2) = (2 xx 101 xx 2)/(16) = 25.25 g`
`:.` Weight of `KNO_(3) = 25.25 g`