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

To solve the problem of how many grams of \( KNO_3 \) are needed to produce enough \( N_2 \) to fill a 12.3 L airbag at 27°C and 4 atm, we can follow these steps:

### Step 1: Calculate the number of moles of \( N_2 \)

We can use the Ideal Gas Law, which is given by the formula:

\[
PV = nRT
...