Fucking Chemistry

Automotive airbags have little capsules filled with sodium azide. Upon collision, the capsule breaks and the chemical decomposes, generating the exact amount of gas needed to fill the airbag. Describe how the ideal gas law could be used to determine how much of the powdered substance must be placed into the explosive capsule, how big to make the airbag, and how much pressure the airbag should be designed to withhold.

\def \I #1{#1}
\def \A #1#2{#2 {#1}}
\def \Set #1#2{\def #2 {\A{#1}}}
\def \Infix #1#2#3{#3 {#1 {#2}}}
\def \DefI #1#2{\def #1 {\Infix #2} \def #2}

\def \L #1#2{#1}
\def \R #1#2{#2}
\def \T #1{#1 \L}
\def \F #1{#1 \R}
\def \PBool #1{#1 {True} {False}}
\def \Not #1{#1 \F \T}
\def \And #1#2{#1 {#2} \F}
\def \Or #1#2{#1 \T {#2}}
\def \Xor #1#2{#1 {#2 \Not} {#2}}
\def \EqB #1#2{#1 {#2} {#2 \Not}}
\def \Maj #1#2{#1 {#2 \Or} {#2 \And}}
\def \CompB #1#2#3#4#5{
    #1 {
        #2 \I {#4} {#3}
    }{
        #2 \I {#5} {#4}
    }
}

\def \P #1#2#3#4{#3 {#4 {#1}} {#4 {#2}}}
\def \N #1#2{\T}
\DefI \. \PairP #1#2#3{#3 {\P{#1}{#2}}}
\Set \N \Nil
\def \List {\Nil \.}
\def \Left #1{#1 \L}
\def \Right #1{#1 \R}
\def \Null #1{#1 \L {\L \F}}
\def \Lone #1{#1 \L \Null}
\def \Last #1{\Lone {#1} \I {#1 \R} {#1 \L \Last}}

\List \T \Set \NegOne
\List \F \Set \0
\List \F \. \T \Set \1
\def \ShiftR #1{\Lone {#1} \I {\A {#1}} {#1 \L}}
\DefI \NB \NBP #1#2{
    \Lone {#1} \And {\EqB {#2} {#1 \R}} \I
    {\A {#1}}
    {\PairP {#1} {#2}}
}
\def \PBin #1{
    \Null {#1} \I
    {}
    {#1 \L \PBin #1 \R \I 1 0}
}

\DefI \= \EqIP #1#2{
    #1 \R \EqB {#2 \R} \And {
        \Lone {#1} \And {\Lone {#2}} \Or {
            \Lone {#1} \Not \And {\Lone {#2} \Not} \And
            {\ShiftR {#1} \= {\ShiftR {#2}}}
        }
    }
}
\DefI \CompI \CompIP #1#2#3#4#5{
    \Lone {#1} \And {\Lone {#2}} \I {
        #1 \R \CompB {#2 \R} {#5} {#4} {#3}
    }{
        \ShiftR {#2} {\ShiftR {#1} \CompIP}
        {#3}
        {#1 \R \CompB {#2 \R} {#3} {#4} {#5}}
        {#5}
    }
}
\def \< #1#2{\CompI {#1} {#2} \F \F \T}

\def \AddC #1#2#3{
    \Lone {#1} \And {\EqB{#3} {#1 \R}} \I {
        \A {#2}
    }{
        \Lone {#2} \And {\EqB{#3} {#2 \R}} \I {
            \A {#1}
        }{
            \Maj {#3} {#1 \R} {#2 \R}
            {\ShiftR {#2} {\ShiftR {#1} \AddC}}
            \NB
            {\Xor {#3} {#1 \R} \Xor {#2 \R}}
        }
    }
}
\def \+ #1#2{#2 \AddC {#1} \R}

\1 \+ \1 \Set \2
\2 \+ \1 \Set \3
\3 \+ \1 \Set \4
\4 \+ \1 \Set \5
\5 \+ \1 \Set \6
\6 \+ \1 \Set \7
\7 \+ \1 \Set \8
\8 \+ \1 \Set \9
\9 \+ \1 \Set \Ten

\def \OComp #1{
    \Null {#1} \I {
        \Nil
    }{
        #1 \L \OComp \. {#1 \R \Not}
    }
}
\def \Neg #1{\OComp{#1} \+ \1}
\def \- #1#2{#2 \OComp \AddC {#1} \L}

\DefI \* \TimesP #1#2{
    \Lone {#1} \I {
        #1 \R \I {\Neg {#2}}{\0}
    }{
        #1 \R \I {
            #1 \L \TimesP {#2} \NB \F \+ {\A {#2}}
        }{
            #1 \L \TimesP {#2} \NB \F
        }
    }
}

\def \QRPos #1#2{
    \Lone {#1} \I {
        #1 \R \I {
            \NegOne \. {\- {#2} \1}
        }{
            \0 \. \0
        }
    }{
        \ShiftR {#1} \QRPos {#2} \Set \PrevQR
        \PrevQR \Right \NB {#1 \R} \Set \NewR
        \NewR \< {\A {#2}} \I {
            \PrevQR \Left \NB \F \. \NewR
        }{
            \PrevQR \Left \NB \T \. {\NewR \- {\A {#2}}}
        }
    }
}
\DefI \QR \QRP #1#2{
    \Last {#2} \I {
        \Neg {#2} {\Neg {#1} \QRPos} \Set \PrevQR
        \PrevQR \Left \. {\PrevQR \Right \Neg}
    }{
        \= {#2} \0 \I {
            \OhShi
        }{
            \QRPos {#1} {#2}
        }
    }
}
\def \/ #1#2{\QR {#1} {#2} \Left}
\def \Mod #1#2{\QR {#1} {#2} \Right}

\def \Fact #1{
    \< {#1} \2 \I {
        \1
    }{
        \- {#1} \1 \Fact \* {\A {#1}}
    }
}

\DefI \At \AtP #1#2{
    \= {#2} \0 \I {
        #1 \R
    }{
        \- {#2} \1 {#1 \L \AtP}
    }
}

\List {\A9}\.{\A8}\.{\A7}\.{\A6}\.{\A5}\.{\A4}\.{\A3}\.{\A2}\.{\A1}\.{\A0} \Set \Digits
\def \PDecQR #1{
    #1 \L \Lone \I {
    }{
        #1 \L \PDecPos
    }
    \Digits \At {#1 \R} \I
}
\def \PDecPos #1{
    \Ten {\QRPos {#1}} \PDecQR
}
\def \PDec #1{
    \< {#1} \0 \I {
        - \Neg {#1} \PDecPos
    }{
        \PDecPos {#1}
    }
}
\Fact \5