morfosintaxis-lógica aquesta-aquella

cantû aquesta cantçió.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∀&1& y ][ [y] és cantçió ]


no cantû aquesta cantçió.
[ [x] és yo ]-[ [x] no canta [y] ]-[ ∀&1& y ][ [y] és cantçió ]


cantû aquella cantçió.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∃&1& y ][ [y] és cantçió ]


no cantû aquella cantçió.
[ [x] és yo ]-[ [x] no canta [y] ]-[ ∃&1& y ][ [y] és cantçió ]

morfosintaxis-lógica entre y or-entre

estic entre la esquerra y la dreta.
[ [x] és yo ]-[ [x] está entre [a] y [b] ]-[ ∀$1$ a ][ [a] és esquerra ]-[ ∀$1$ b ][ [b] és dreta ]


no estic entre la esquerra y la dreta.
[ [x] és yo ]-[ [x] no está entre [a] y [b] ]-[ ∀$1$ a ][ [a] és esquerra ]-[ ∀$1$ b ][ [b] és dreta ]


estic or-entre la esquerra o la dreta.
[ [x] és yo ]-[ [x] está or-entre [a] o [b] ]-[ ∀$1$ a ][ [a] és esquerra ]-[ ∀$1$ b ][ [b] és dreta ]


no estic or-entre la esquerra o la dreta.
[ [x] és yo ]-[ [x] no está or-entre [a] o [b] ]-[ ∀$1$ a ][ [a] és esquerra ]-[ ∀$1$ b ][ [b] és dreta ]

morfosintaxis-lógica a dins y a fora

estic a dins de casa.
[ [x] és yo ]-[ [x] está a dins de [y] ]-[ [y] és casa ]


no estic a dins de casa.
[ [x] és yo ]-[ [x] no está a dins de [y] ]-[ [y] és casa ]


estic a fora de casa.
[ [x] és yo ]-[ [x] está a fora de [y] ]-[ [y] és casa ]


no estic a fora de casa.
[ [x] és yo ]-[ [x] no está a fora de [y] ]-[ [y] és casa ]

morfosintaxis-lógica les y unes n

cantû les n cantçions.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∀$n$ y ][ [y] és cantçió ]


no cantû les n cantçions.
[ [x] és yo ]-[ [x] no canta [y] ]-[ ∀$n$ y ][ [y] és cantçió ]


cantû unes n cantçions.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∃$n$ y ][ [y] és cantçió ]


no cantû unes n cantçions.
[ [x] és yo ]-[ [x] no canta [y] ]-[ ∃$n$ y ][ [y] és cantçió ]

morfosintaxis-lógica les y unes

cantû les cantçions.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∀$...$ y ][ [y] és cantçió ]


no cantû les cantçions.
[ [x] és yo ]-[ [x] o canta [y] ]-[ ∀$...$ y ][ [y] és cantçió ]


cantû unes cantçions.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∃$...$ y ][ [y] és cantçió ]


no cantû unes cantçions.
[ [x] és yo ]-[ [x] no canta [y] ]-[ ∃$...$ y ][ [y] és cantçió ]

morfosintaxis lógica la y una

cantû la cantçió.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∀$1$ y ][ [y] és cantçió ]


no cantû la cantçió.
[ [x] és yo ]-[ [x] no canta [y] ]-[ ∀$1$ y ][ [y] és cantçió ]


cantû una cantçió.
[ [x] és yo ]-[ [x] canta [y] ]-[ ∃$1$ y ][ [y] és cantçió ]


no cantû una cantçió.
[ [x] és yo ]-[ [x] no canta [y] ]-[ ∃$1$ y ][ [y] és cantçió ]

dual-italiano

yo detzire
tú detzire
él detzire
ella detzire


nosotros detzim-ti
vosotros detziu-ti
ellos ditzen-ti
ellas ditzen-ti

dual-italiano

me gustare.
te gustare.
le gustare.


nos gustare.
os gustare.
les gustare.

dual-italiano

yo estare.
tu estare.
él estare.
ella estare.


nosotros estem-ti.
vosotros esteu-ti.
ellos están-ti.
ellas están-ti.

dual-italiano

yo construyire
tú construyire
él construyire
ella construyire


Nosotros construyim-ti
Vosotros construyiu-ti
ellos construyen-ti
ellas construyen-ti

dual-italiano

yo cantare
tú cantare
él cantare
ella cantare


Nosotros cantem-ti
Vosotros canteu-ti
ellos cantan-ti
ellas cantan-ti

dual-italiano

yo sere.
tu sere.
él sere.
ella sere.


nosotros som-ti.
vosotros sou-ti.
ellos son-ti.
ellas son-ti.

circuits eléctrics: condensadors, resistències y bobines

V(t) = ( a_{1}+...+a_{n} )·q(t)
V(t) = ( (1/a_{1})+...+(1/a_{n}) )^{(-1)}·q(t)


V(t) = ( R_{1}+...+R_{n} )·d_{t}[q(t)]
V(t) = ( (1/R_{1})+...+(1/R_{n}) )^{(-1)}·d_{t}[q(t)]


V(t) = ( L_{1}+...+L_{n} )·d_{tt}^{2}[q(t)]
V(t) = ( (1/L_{1})+...+(1/L_{n}) )^{(-1)}·d_{tt}^{2}[q(t)]


V(t) = ( ∑ a_{i} )·( ∑ (1/a_{k}) )·( ∑ a_{j} )·q(t)
V(t) = ( ( ∑ (1/a_{i}) )·( ∑ a_{k} )·( ∑ (1/a_{j}) ) )^{(-1)}·q(t)


V(t) = ( ∑ R_{i} )·( ∑ (1/R_{k}) )·( ∑ R_{j} )·d_{t}[q(t)]
V(t) = ( ( ∑ (1/R_{i}) )·( ∑ R_{k} )·( ∑ (1/R_{j}) ) )^{(-1)}·d_{t}[q(t)]


V(t) = ( ∑ L_{i} )·( ∑ (1/L_{k}) )·( ∑ L_{j} )·d_{tt}^{2}[q(t)]
V(t) = ( ( ∑ (1/L_{i}) )·( ∑ L_{k} )·( ∑ (1/L_{j}) ) )^{(-1)}·d_{tt}^{2}[q(t)]

circuits eléctrics

en serie:
( V_{1}+...(n)...+V_{n} ) = ( R_{1}+...(n)...+R_{n} )·I_{0}


en paral·lel:
( I_{1}+...(n)...+I_{n} ) = ( (1/R_{1})+...(n)...+(1/R_{n}) )·V_{0}


R_{k} = n
V_{k} = k
I_{k} = k


I_{0} = ( (n+1)/(2n) )
V_{0} = ( (n(n+1))/2 )




R_{k} = 1
V_{k} = k
I_{k} = k


I_{0} = ( (n+1)/2 )
V_{0} = ( (n+1)/2 )


R_{k} = n
V_{k} = 1
I_{k} = 1


I_{0} = ( 1/n )
V_{0} = n


R_{k} = 1
V_{k} = 1
I_{k} = 1


I_{0} = 1
V_{0} = 1

mecànica clàssica arrel cúbica de la posició

m·d_{t}[x(t)] = a·( x(t) )^{(1/3)}


m·d_{tt}^{2}[x(t)] = (1/3)·a·( x(t) )^{(-1)(2/3)}·d_{t}[x(t)]


m·d_{tt}^{2}[x(t)] = (1/3)·(a^{2}/m)·( x(t) )^{(-1)(1/3)}


( x(t) )^{(1/3)}·d_{tt}^{2}[x(t)] = (1/3)·(a^{2}/m^{2})


d_{t}[x(t)]·d_{tt}^{2}[x(t)] = (1/3)·(a^{3}/m^{3})


(1/2)·d_{t}[x(t)]^{2} = (1/3)·(a^{3}/m^{3})·t


d_{t}[x(t)] = ( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(1/2)}


x(t) = ( (2/3)·(a/m) )^{(3/2)}·t^{(3/2)}


d_{tt}^{2}[x(t)] = (1/2)·( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(-1)(1/2)}


E(t) = ∫ [ (m/2)·( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(-1)(1/2)}·( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(1/2)}) ] d[t]
E(t) = ∫ [ (m/2)·( (2/3)·(a^{3}/m^{3}) ) ] d[t]


E(t) = (1/3)·(a^{3}/m^{2})·t


(m/2)·d_{t}[x(t)]^{2} = (1/3)·(a^{3}/m^{2})·t

mecànica clàssica arrel cuadrada de la posició

m·d_{t}[x(t)] = a·( x(t) )^{(1/2)}


m·d_{tt}^{2}[x(t)] = (1/2)·a·( x(t) )^{(-1)(1/2)}·d_{t}[x(t)]


m·d_{tt}^{2}[x(t)] = (1/2)·(a^{2}/m)


d_{tt}^{2}[x(t)] = (1/2)·(a^{2}/m^{2})


d_{t}[x(t)] = (1/2)·(a^{2}/m^{2})·t


x(t) = (1/4)·(a^{2}/m^{2})·t^{2}


E(t) = ∫ [ ( (1/2)·(a^{2}/m) )·( (1/2)·(a^{2}/m^{2})·t ) ] d[t]


E(t) = (1/8)·(a^{4}/m^{3})·t^{2}


(m/2)·d_{t}[x(t)]^{2} = (1/8)·(a^{4}/m^{3})·t^{2}

bi-hexa-glicerina

H_{4}Hex[C_{6}]_{2n}N_{4n+(-4)}( 4n·C_{m}N_{2m+(-2)}H_{2m+1} ) + ...
... 4n·(NaOH) + e^{-} ==>...
... H_{4}Hex[C_{6}]_{2n}N_{4n+(-4)}(OH)_{4n} + ...
... 4n·( NaC_{m}N_{2m+(-2)}H_{2m+1} )


H_{4}Hex[C_{6}]_{2n}N_{4n+(-4)}(OH)_{4n} + ...
... 4n·( NaC_{m}N_{2m+(-2)}H_{2m+1} ) + e^{+} ==>...
... H_{4}Hex[C_{6}]_{2n}N_{4n+(-4)}( 4n·C_{m}N_{2m+(-2)}H_{2m+1} ) + 4n·(NaOH)


bi-hexa-glicerina-nitrogenada
N-C=C-C=C-N <==> ( 2 destructores & 2 duales )


bi-hexa-glicerina
=C-C=C-C=C-C= <==> ( 4 constructores )


Entalpia de reacción:
[ H_{4}Hex[C_{6}]_{2n}N_{4n+(-4)}( 4n·C_{m}N_{2m+(-2)}H_{2m}H ) ] = 32n
[ 4n·NaOH ] = 12n


[ H_{4}Hex[C_{6}]_{2n}N_{4n+(-4)}(OH)_{4n} ] = 24n
[ 4n·( NaC_{m}N_{2m+(-2)}H_{2m}H ] = 20n


32n+12n = 24n+20n = 44n

cuantificadors lógics

[∀x][ P(x) ] <==> ( P(x_{1} ) ∧...(n)...∧ ( P(x_{n}) )
[∃x][ ¬P(x) ] <==> ( ¬P(x_{1} ) ∨...(n)...∨ ( ¬P(x_{n}) )


[∃x][ P(x) ] <==> ( P(x_{1} ) ∨...(n)...∨ ( P(x_{n}) )
[∀x][ ¬P(x) ] <==> ( ¬P(x_{1} ) ∧...(n)...∧ ( ¬P(x_{n}) )

termodinàmica de gas ideal cúbico positivo-positivo

(PV)^{3} + (kT)·(PV)^{2} + (kT)^{2}(PV) = (kT)^{3}

a^{3}+(-1)·a^{2}+(-1)·a+(-1) = 0
b^{3}+b^{2}+b+(-1) = 0


a = ( x+(1/3) )
b = ( y+(-1)·(1/3) )


( x^{3}+(1/3)·x+(1/27) )+(-1)·( (2/3)·x+(1/9) )+(-1)·( x+(1/3) )+(-1) = 0
( y^{3}+(1/3)·y+(-1)(1/27) )+( (-1)·(2/3)·y+(1/9) )+( y+(-1)(1/3) )+(-1) = 0


( x^{3}+(-1)·(4/3)·x+( (1/27)+(-1)·(1/9)+(-1)·(1/3) )+(-1) = 0
( y^{3}+(2/3)·y+( (-1)(1/27)+(1/9)+(-1)·(1/3) )+(-1) = 0


( x^{3}+(-1)·(4/3)·x+(-1)·(38/27) = 0
( y^{3}+(2/3)·y+(-1)·(34/27) = 0


T(P,V) = a·( 1/k )·PV


P(T,V) = b·k·( T/V )
V(T,P) = b·k·( T/P )


d_{P}[ T(P,V) ] = a·( 1/k )·V
d_{V}[ T(P,V) ] = a·( 1/k )·P


d_{T}[ P(T,V) ] = b·k·(1/V)
d_{V}[ P(T,V) ] = (-1)·b·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = b·k·(1/P)
d_{P}[ V(T,P) ] = (-1)·b·k·( 1/P^{2} )

termodinàmica del gas cuadrático negativo

(PV)^{2} + (-1)·(kT)·(PV) = (kT)^{2}


T(P,V) = ( ((-1)+5^{(1/2)})/2 )·( 1/k )·PV


P(T,V) = ( (1+5^{(1/2)})/2 )·k·( T/V )
V(T,P) = ( (1+5^{(1/2)})/2 )·k·( T/P )


d_{P}[ T(P,V) ] = ( ((-1)+5^{(1/2)})/2 )·( 1/k )·V
d_{V}[ T(P,V) ] = ( ((-1)+5^{(1/2)})/2 )·( 1/k )·P


d_{T}[ P(T,V) ] = ( (1+5^{(1/2)})/2 )·k·(1/V)
d_{V}[ P(T,V) ] = (-1)·( (1+5^{(1/2)})/2 )·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = ( (1+5^{(1/2)})/2 )·k·(1/P)
d_{P}[ V(T,P) ] = (-1)·( (1+5^{(1/2)})/2 )·k·( 1/P^{2} )

termodinàmica de gas ideal cuadrático positivo

(PV)^{2} + (kT)·(PV) = (kT)^{2}


T(P,V) = ( 1/(2k^{2}) )( kPV+( (kPV)^{2}+4(kPV)^{2} )^{(1/2)} )
T(P,V) = ( 1/(2k^{2}) )( kPV+5^{(1/2)}·kPV )
T(P,V) = ( 1/(2k^{2}) )( (1+5^{(1/2)})·kPV )


T(P,V) = ( (1+5^{(1/2)})/2 )·( 1/k )·PV


P(T,V) = ( 1/(2V^{2}) )( (-1)·kTV+( (kTV)^{2}+4(kTV)^{2} )^{(1/2)} )
P(T,V) = ( 1/(2V^{2}) )( (-1)·kTV+5^{(1/2)}·kTV )
P(T,V) = ( 1/(2V^{2}) )( ((-1)+5^{(1/2)})·kTV )


V(T,V) = ( 1/(2P^{2}) )( (-1)·kTP+( (kTP)^{2}+4(kTP)^{2} )^{(1/2)} )
V(T,V) = ( 1/(2P^{2}) )( (-1)·kTP+5^{(1/2)}·kTP )
V(T,V) = ( 1/(2P^{2}) )( ((-1)+5^{(1/2)})·kTP )


P(T,V) = ( ((-1)+5^{(1/2)})/2 )·k·( T/V )
V(T,P) = ( ((-1)+5^{(1/2)})/2 )·k·( T/P )


d_{P}[ T(P,V) ] = ( (1+5^{(1/2)})/2 )·( 1/k )·V
d_{V}[ T(P,V) ] = ( (1+5^{(1/2)})/2 )·( 1/k )·P


d_{T}[ P(T,V) ] = ( ((-1)+5^{(1/2)})/2 )·k·(1/V)
d_{V}[ P(T,V) ] = (-1)·( ((-1)+5^{(1/2)})/2 )·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = ( ((-1)+5^{(1/2)})/2 )·k·(1/P)
d_{P}[ V(T,P) ] = (-1)·( ((-1)+5^{(1/2)})/2 )·k·( 1/P^{2} )

termodinàmica de gas ideal

PV = kT


T(P,V) =  (1/k)·PV


P(T,V) =  k·( T/V )
V(T,P) =  k·( T/P )


d_{P}[ T(P,V) ] = (1/k)·V
d_{V}[ T(P,V) ] = (1/k)·P


d_{T}[ P(T,V) ] = k·(1/V)
d_{V}[ P(T,V) ] = (-1)·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = k·(1/P)
d_{P}[ V(T,P) ] = (-1)·k·( 1/P^{2} )

partición de números enteros en base dos-seis

pm+8 = (6+2)+(m+...(p)...+m)


pm+10 = (6+2+2)+(m+...(p)...+m)


pm+12 = (6+2+2+2)+(m+...(p)...+m)
pm+12 = (6+6)+(m+...(p)...+m)


pm+14 = (6+2+2+2+2)+(m+...(p)...+m)
pm+14 = (6+6+2)+(m+...(p)...+m)


pm+16 = (6+2+2+2+2+2)+(m+...(p)...+m)
pm+16 = (6+6+2+2)+(m+...(p)...+m)


pm+18 = (6+2+2+2+2+2+2)+(m+...(p)...+m)
pm+18 = (6+6+2+2+2)+(m+...(p)...+m)
pm+18 = (6+6+6)+(m+...(p)...+m)


P( pm+(6k) ) = ( (6k)/6 )
P( pm+(6k+2) ) = ( ((6k+2)+(-2))/6 )
P( pm+(6k+4) ) = ( ((6k+4)+(-4))/6 )

partición de números enteros en base tres-seis

pm+9 = (6+3)+(m+...(p)...+m)


pm+12 = (6+3+3)+(m+...(p)...+m)
pm+12 = (6+6)+(m+...(p)...+m)


pm+15 = (6+3+3+3)+(m+...(p)...+m)
pm+15 = (6+6+3)+(m+...(p)...+m)


pm+18 = (6+3+3+3+3)+(m+...(p)...+m)
pm+18 = (6+6+3+3)+(m+...(p)...+m)
pm+18 = (6+6+6)+(m+...(p)...+m)


P( pm+(6k) ) = ( (6k)/6 )
P( pm+(6k+3) ) = ( ((6k+3)+(-3))/6 )

partición de números enteros en base dos-cuatro

pm+6 = (4+2)+(m+...(p)...+m)


pm+8 = (4+2+2)+(m+...(p)...+m)
pm+8 = (4+4)+(m+...(p)...+m)


pm+10 = (4+2+2+2)+(m+...(p)...+m)
pm+10 = (4+4+2)+(m+...(p)...+m)


pm+12 = (4+2+2+2+2)+(m+...(p)...+m)
pm+12 = (4+4+2+2)+(m+...(p)...+m)
pm+12 = (4+4+4)+(m+...(p)...+m)


P( pm+(4k) ) = ( (4k)/4 )
P( pm+(4k+2) ) = ( ((4k+2)+(-2))/4 )

partición de números enteros en base cuatro

pm+5 = (4+1)+(m+...(p)...+m)


pm+6 = (4+1+1)+(m+...(p)...+m)


pm+7 = (4+1+1+1)+(m+...(p)...+m)


pm+8 = (4+1+1+1+1)+(m+...(p)...+m)
pm+8 = (4+4)+(m+...(p)...+m)


pm+9 = (4+1+1+1+1+1)+(m+...(p)...+m)
pm+9 = (4+4+1)+(m+...(p)...+m)


pm+10 = (4+1+1+1+1+1+1)+(m+...(p)...+m)
pm+10 = (4+4+1+1)+(m+...(p)...+m)


pm+11 = (4+1+1+1+1+1+1+1)+(m+...(p)...+m)
pm+11 = (4+4+1+1+1)+(m+...(p)...+m)


pm+12 = (4+1+1+1+1+1+1+1+1)+(m+...(p)...+m)
pm+12 = (4+4+1+1+1+1)+(m+...(p)...+m)
pm+12 = (4+4+4)+(m+...(p)...+m)


P( pm+(4k) ) = ( (4k)/4 )
P( pm+(4k+1) ) = ( ((4k+1)+(-1))/4 )
P( pm+(4k+2) ) = ( ((4k+2)+(-2))/4 )
P( pm+(4k+3) ) = ( ((4k+3)+(-3))/4 )

partición de números enteros en base tres

pm+4 = (3+1)+(m+...(p)...+m)


pm+5 = (3+1+1)+(m+...(p)...+m)


pm+6 = (3+1+1+1)+(m+...(p)...+m)
pm+6 = (3+3)+(m+...(p)...+m)


pm+7 = (3+1+1+1+1)+(m+...(p)...+m)
pm+7 = (3+3+1)+(m+...(p)...+m)


pm+8 = (3+1+1+1+1+1)+(m+...(p)...+m)
pm+8 = (3+3+1+1)+(m+...(p)...+m)


pm+9 = (3+1+1+1+1+1+1)+(m+...(p)...+m)
pm+9 = (3+3+1+1+1)+(m+...(p)...+m)
pm+9 = (3+3+3)+(m+...(p)...+m)


P( pm+(3k) ) = ( (3k)/3 )
P( pm+(3k+1) ) = ( ((3k+1)+(-1))/3 )
P( pm+(3k+2) ) = ( ((3k+2)+(-2))/3 )

partición de números enteros en base dos

pm+3 = (2+1)+(m+...(p)...+m)


pm+4 = (2+1+1)+(m+...(p)...+m)
pm+4 = (2+2)+(m+...(p)...+m)


pm+5 = (2+1+1+1)+(m+...(p)...+m)
pm+5 = (2+2+1)+(m+...(p)...+m)


pm+6 = (2+1+1+1+1)+(m+...(p)...+m)
pm+6 = (2+2+1+1)+(m+...(p)...+m)
pm+6 = (2+2+2)+(m+...(p)...+m)


pm+7 = (2+1+1+1+1+1)+(m+...(p)...+m)
pm+7 = (2+2+1+1+1)+(m+...(p)...+m)
pm+7 = (2+2+2+1)+(m+...(p)...+m)


pm+8 = (2+1+1+1+1+1+1)+(m+...(p)...+m)
pm+8 = (2+2+1+1+1+1)+(m+...(p)...+m)
pm+8 = (2+2+2+1+1)+(m+...(p)...+m)
pm+8 = (2+2+2+2)+(m+...(p)...+m)


P( pm+(2k) ) = ( (2k)/2 )
P( pm+(2k+1) ) = ( ((2k+1)+(-1))/2 )


Problema:


Sigui pm+7 = 13 ==>


2·3+7 = (2+1+1+1+1+1)+(3+3)
2·3+7 = (2+2+1+1+1)+(3+3)
2·3+7 = (2+2+2+1)+(3+3)


2·3+7 = (2+1+1+1+1+1)+(2+2+2)
2·3+7 = (2+2+1+1+1)+(2+2+2)
2·3+7 = (2+2+2+1)+(2+2+2)


6·1+7 = (2+1+1+1+1+1)+6
6·1+7 = (2+2+1+1+1)+6
6·1+7 = (2+2+2+1)+6


6·1+7 = (2+1+1+1+1+1)+(1+1+1+1+1+1)
6·1+7 = (2+2+1+1+1)+(1+1+1+1+1+1)
6·1+7 = (2+2+2+1)+(1+1+1+1+1+1)


Problema:


Sigui pm+5 = 11 ==>


2·3+5 = (2+1+1+1)+(3+3)
2·3+5 = (2+2+1)+(3+3)


2·3+5 = (2+1+1+1)+(2+2+2)
2·3+5 = (2+2+1)+(2+2+2)


6·1+5 = (2+1+1+1)+6
6·1+5 = (2+2+1)+6


6·1+5 = (2+1+1+1)+(1+1+1+1+1+1)
6·1+5 = (2+2+1)+(1+1+1+1+1+1)

particiones de un número entero

n = 1+...(n)...+1


m+(1+...(q+1)...+1) = m+(q+1)


P_{1}(n) = (n+(-1))


m+(2+...(q+1)...+2) = m+(q+1)·2


Si n=2k ==> P_{2}(n) = k+(-1) = ( (n+(-2))/2 )
Si n=2k+1 ==> P_{2}(n) = k = ( (n+(-1))/2 )


m+(3+...(q+1)...+3) = m+(q+1)·3


Si n=3k ==> P_{3}(n) = k+(-1) = ( (n+(-3))/3 )
Si n=3k+1 ==> P_{3}(n) = k = ( (n+(-1))/3 )
Si n=3k+2 ==> P_{3}(n) = k = ( (n+(-2))/3 )


m+(4+...(q+1)...+4) = m+(q+1)·4


Si n=4k ==> P_{4}(n) = k+(-1) = ( (n+(-4))/4 )
Si n=4k+1 ==> P_{4}(n) = k = ( (n+(-1))/4 )
Si n=4k+2 ==> P_{4}(n) = k = ( (n+(-2))/4 )
Si n=4k+3 ==> P_{4}(n) = k = ( (n+(-3))/4 )


m+(5+...(q+1)...+5) = m+(q+1)·5


Si n=5k ==> P_{5}(n) = k+(-2) = ( (n+(-5))/5 )
Si n=5k+1 ==> P_{5}(n) = k+(-2) = ( (n+(-1))/5 )
Si n=5k+2 ==> P_{5}(n) = k+(-1) = ( (n+(-2))/5 )
Si n=5k+3 ==> P_{5}(n) = k+(-1) = ( (n+(-3))/5 )
Si n=5k+4 ==> P_{5}(n) = k+(-1) = ( (n+(-4))/5 )




(2+...(p+2)...+2)+(1+...(q+2)...+1) = (p+2)·2+(q+2)


Si n=2k ==> P_{1,2}(n) = k+(-2) = ( (n+(-4))/2 )
Si n=2k+1 ==> P_{1,2}(n) = k+(-2) = ( (n+(-5))/2 )


(3+...(p+2)...+3)+(1+...(q+2)...+1) = (p+2)·3+(q+2)


Si n=3k ==> P_{1,3}(n) = k+(-2) = ( (n+(-6))/3 )
Si n=3k+1 ==> P_{1,3}(n) = k+(-2) = ( (n+(-7))/3 )
Si n=3k+2 ==> P_{1,3}(n) = k+(-1) = ( (n+(-5))/3 )


(4+...(p+2)...+4)+(1+...(q+2)...+1) = (p+2)·4+(q+2)


Si n=4k ==> P_{1,4}(n) = k+(-2) = ( (n+(-8))/4 )
Si n=4k+1 ==> P_{1,4}(n) = k+(-2) = ( (n+(-9))/4 )
Si n=4k+2 ==> P_{1,4}(n) = k+(-1) = ( (n+(-6))/4 )
Si n=4k+3 ==> P_{1,4}(n) = k+(-1) = ( (n+(-7))/4 )


(5+...(p+2)...+5)+(1+...(q+2)...+1) = (p+2)·5+(q+2)


Si n=5k ==> P_{1,5}(n) = k+(-2) = ( (n+(-10))/5 )
Si n=5k+1 ==> P_{1,5}(n) = k+(-2) = ( (n+(-11))/5 )
Si n=5k+2 ==> P_{1,5}(n) = k+(-1) = ( (n+(-7))/5 )
Si n=5k+3 ==> P_{1,5}(n) = k+(-1) = ( (n+(-8))/5 )
Si n=5k+4 ==> P_{1,5}(n) = k+(-1) = ( (n+(-9))/5 )






2 = 1+1


3 = 1+1+1
3 = 2+1


4 = 1+1+1+1
4 = 3+1
4 = 2+(1+1)
4 = 2+2


5 = 1+1+1+1+1
5 = 4+1
5 = 3+(1+1)
5 = 2+(1+1+1)
5 = 3+2
5 = 1+(2+2)


6 = 1+1+1+1+1+1
6 = 5+1
6 = 4+(1+1)
6 = 3+(1+1+1)
6 = 2+(1+1+1+1)
6 = 4+2
6 = 2+(2+2)
6 = 3+3
6 = (1+1)+(2+2)


7 = 1+1+1+1+1+1+1
7 = 6+1
7 = 5+(1+1)
7 = 4+(1+1+1)
7 = 3+(1+1+1+1)
7 = 2+(1+1+1+1+1)
7 = 5+2
7 = 3+(2+2)
7 = 1+(2+2+2)
7 = 4+3
7 = 1+(3+3)
7 = (1+1+1)+(2+2)


8 = 1+1+1+1+1+1+1+1
8 = 7+1
8 = 6+(1+1)
8 = 5+(1+1+1)
8 = 4+(1+1+1+1)
8 = 3+(1+1+1+1+1)
8 = 2+(1+1+1+1+1+1)
8 = 6+2
8 = 4+(2+2)
8 = 2+(2+2+2)
8 = 5+3
8 = 2+(3+3)
8 = 4+4
8 = (1+1+1+1)+(2+2)
8 = (1+1)+(2+2+2)
8 = (1+1)+(3+3)


9= 1+1+1+1+1+1+1+1+1
9 = 8+1
9 = 7+(1+1)
9 = 6+(1+1+1)
9 = 5+(1+1+1+1)
9 = 4+(1+1+1+1+1)
9 = 3+(1+1+1+1+1+1)
9 = 2+(1+1+1+1+1+1+1)
9 = 7+2
9 = 5+(2+2)
9 = 3+(2+2+2)
9 = 1+(2+2+2+2)
9 = 6+3
9 = 3+(3+3)
9 = 5+4
9 = 1+(4+4)
9 = (1+1+1+1+1)+(2+2)
9 = (1+1+1)+(2+2+2)
9 = (1+1+1)+(3+3)


10 = 1+1+1+1+1+1+1+1+1+1
10 = 9+1
10 = 8+(1+1)
10 = 7+(1+1+1)
10 = 6+(1+1+1+1)
10 = 5+(1+1+1+1+1)
10 = 4+(1+1+1+1+1+1)
10 = 3+(1+1+1+1+1+1+1)
10 = 2+(1+1+1+1+1+1+1+1)
10 = 8+2
10 = 6+(2+2)
10 = 4+(2+2+2)
10 = 2+(2+2+2+2)
10 = 7+3
10 = 4+(3+3)
10 = 1+(3+3+3)
10 = 6+4
10 = 2+(4+4)
10 = 5+5
10 = (1+1+1+1+1+1)+(2+2)
10 = (1+1+1+1)+(2+2+2)
10 = (1+1)+(2+2+2+2)
10 = (1+1+1+1)+(3+3)
10 = (1+1)+(4+4)

oxigeno gas noble

Hidrógeno
{
[01]
[00]
valencia = 1
}


Helio
{
[11]
[00]
valencia = 0


[01]
[01]
valencia = 2
}


Eka-Hidrógeno
{
[10]
[00]-[00][00][00]
valencia = 1
}


Eka-Helio ( oxigeno )
{
[11]
[00]-[00][00][00]
valencia = 0


[01]
[01]-[00][00][00]
valencia = 2
}

química valencias y spines de metales

grup
{
[01]-[00][00][00]-[00][00][00][00][00]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 1
}


grup
{
[01]-[00][00][00]-[00][00][00][00][00]
[01]-[00][00][00]-[00][00][00][00][00]
valencia = 2
}


grup
{
[00]-[01][01][01]-[00][00][00][00][00]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 3
}


grup
{
[01]-[01][01][01]-[00][00][00][00][00]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 4
}


Metales:


grup
{
[00]-[00][00][00]-[01][01][01][01][01]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 5
}


grup
{
[01]-[00][00][00]-[01][01][01][01][01]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 6
}


grup
{
[01]-[00][00][00]-[01][01][01][01][01]
[01]-[00][00][00]-[00][00][00][00][00]
valencia = 7
}


grup
{
[00]-[01][01][01]-[01][01][01][01][01]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 8
}


grup
{
[01]-[01][01][01]-[01][01][01][01][01]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 9
}


grup
{
[00]-[00][00][00]-[11][11][11][11][11]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 0


[11]-[01][01][01]-[01][01][01][01][01]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 8


[01]-[01][01][01]-[01][01][01][01][01]
[01]-[00][00][00]-[00][00][00][00][00]
valencia = 10
}


grup
{
[00]-[11][11][11]-[01][01][01][01][01]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 5


[11]-[01][01][01]-[01][01][01][01][01]
[01]-[00][00][00]-[00][00][00][00][00]
valencia = 9


[00]-[01][01][01]-[01][01][01][01][01]
[00]-[01][01][01]-[00][00][00][00][00]
valencia = 11
}


grup
{
[01]-[11][11][11]-[01][01][01][01][01]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 6


[01]-[01][01][01]-[01][01][01][01][01]
[00]-[01][01][01]-[00][00][00][00][00]
valencia = 12
}


grup
{
[00]-[01][01][01]-[11][11][11][11][11]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 3


[00]-[01][01][01]-[01][01][01][01][01]
[00]-[00][00][00]-[01][01][01][01][01]
valencia = 13
}


grup
{
[01]-[01][01][01]-[11][11][11][11][11]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 4


[01]-[01][01][01]-[01][01][01][01][01]
[00]-[00][00][00]-[01][01][01][01][01]
valencia = 14
}


grup
{
[11]-[01][01][01]-[11][11][11][11][11]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 3


[01]-[01][01][01]-[11][11][11][11][11]
[01]-[00][00][00]-[00][00][00][00][00]
valencia = 5


[01]-[01][01][01]-[01][01][01][01][01]
[01]-[00][00][00]-[01][01][01][01][01]
valencia = 15
}


grup
{
[00]-[11][11][11]-[11][11][11][11][11]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 0


[00]-[01][01][01]-[11][11][11][11][11]
[00]-[01][01][01]-[00][00][00][00][00]
valencia = 6


[00]-[11][11][11]-[01][01][01][01][01]
[00]-[00][00][00]-[01][01][01][01][01]
valencia = 10


[00]-[01][01][01]-[01][01][01][01][01]
[00]-[01][01][01]-[01][01][01][01][01]
valencia = 16
}


grup
{
[01]-[11][11][11]-[11][11][11][11][11]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 1


[01]-[01][01][01]-[11][11][11][11][11]
[00]-[01][01][01]-[00][00][00][00][00]
valencia = 7


[01]-[11][11][11]-[01][01][01][01][01]
[00]-[00][00][00]-[01][01][01][01][01]
valencia = 11


[01]-[01][01][01]-[01][01][01][01][01]
[00]-[01][01][01]-[01][01][01][01][01]
valencia = 17
}


grup
{
[11]-[11][11][11]-[11][11][11][11][11]
[00]-[00][00][00]-[00][00][00][00][00]
valencia = 0


[01]-[11][11][11]-[11][11][11][11][11]
[01]-[00][00][00]-[00][00][00][00][00]
valencia = 2


[11]-[01][01][01]-[11][11][11][11][11]
[00]-[01][01][01]-[00][00][00][00][00]
valencia = 6


[11]-[11][11][11]-[01][01][01][01][01]
[00]-[00][00][00]-[01][01][01][01][01]
valencia = 10


[11]-[01][01][01]-[01][01][01][01][01]
[00]-[01][01][01]-[01][01][01][01][01]
valencia = 16


[01]-[01][01][01]-[11][11][11][11][11]
[01]-[01][01][01]-[00][00][00][00][00]
valencia = 8


[01]-[11][11][11]-[01][01][01][01][01]
[01]-[00][00][00]-[01][01][01][01][01]
valencia = 12


[01]-[01][01][01]-[01][01][01][01][01]
[01]-[01][01][01]-[01][01][01][01][01]
valencia = 18
}

química valencias y spines

Litio: Li
grup
{
[01]-[00][00][00]
[00]-[00][00][00]
valencia = 1
}


Berilio: Be
grup
{
[01]-[00][00][00]
[01]-[00][00][00]
valencia = 2
}


Boro: B
grup
{
[00]-[01][01][01]
[00]-[00][00][00]
valencia = 3
}


Carbono: C
grup
{
[01]-[01][01][01]
[00]-[00][00][00]
valencia = 4
}


Nitrogeno: N
grup
{
[11]-[01][01][01]
[00]-[00][00][00]
valencia = 3


[01]-[01][01][01]
[01]-[00][00][00]
valencia = 5
}


Eka-azufre: Ea
grup
{
[00]-[11][11][11]
[00]-[00][00][00]
valencia = 0


[11]-[01][01][01]
[01]-[00][00][00]
valencia = 4


[00]-[01][01][01]
[00]-[01][01][01]
valencia = 6
}


Fluor: F
grup
{
[01]-[11][11][11]
[00]-[00][00][00]
valencia = 1


[01]-[01][01][01]
[00]-[01][01][01]
valencia = 7
}


Oxigeno: O
grup
{
[11]-[11][11][11]
[00]-[00][00][00]
valencia = 0


[01]-[11][11][11]
[01]-[00][00][00]
valencia = 2


[11]-[01][01][01]
[00]-[01][01][01]
valencia = 6


[01]-[01][01][01]
[01]-[01][01][01]
valencia = 8
}

tri-hidróxido hiper-nítrico

H_{3}N + 3·H_{2}O + e^{+} ==> N(OH)_{3} + 3·H_{2}


N(OH)_{3} + 3·H_{2} + e^{-} ==> H_{3}N + 3·H_{2}O


Entalpia de reacción:
[ H_{3}N ] = 6
[ 3·H_{2}O ] = 9


[ N(OH)_{3} ] = 9
[ 3·H_{2} ] = 6


6+9 = 9+6 = 15

bi-hidróxido nítrico

H_{3}N + 2·H_{2}O + e^{+} ==> HN(OH)_{2} + 2·H_{2}


HN(OH)_{2} + 2·H_{2} + e^{-} ==> H_{3}N + 2·H_{2}O


Entalpia de reacción:
[ H_{3}N ] = 5
[ 2·H_{2}O ] = 6


[ HN(OH)_{2} ] = 7
[ 2·H_{2} ] = 4


5+6 = 7+4 = 11

mono-hidróxido nitroso

H_{3}N + H_{2}O + e^{+} ==> H_{2}N(OH) + H_{2}


H_{2}N(OH) + H_{2} + e^{-} ==> H_{3}N + H_{2}O


Entalpia de reacción:
[ H_{3}N ] = 4
[ H_{2}O ] = 3


[ H_{2}N(OH) ] = 5
[ H_{2} ] = 2


4+3 = 5+2 = 7

oxidación del hidro-nitrógeno

2·H_{3}N + O_{2} + e^{+} ==> 2·HNO + 2·H_{2}


2·HNO + 2·H_{2} + e^{-} ==> 2·H_{3}N + O_{2}


Entalpia de reacción:
[ 2·H_{3}N ] = 10
[ O_{2} ] = 4


[ 2·HNO ] = 10
[ 2·H_{2} ] = 4


10+4 = 10+4 = 14

oxidación del hidro-fosfuro

H_{5}P + O_{2} + e^{+} ==> HPO_{2} + 2·H_{2}


HPO_{2} + 2·H_{2} + e^{-} ==> H_{5}P + O_{2}


Entalpia de reacción:
[ H_{5}P ] = 9
[ O_{2} ] = 4


[ HPO_{2} ] = 9
[ 2·H_{2} ] = 4


9+4 = 9+4 = 13

hidro-oxo-fosfuro de carbono

HP(C_{2n}O)_{2} + e^{+} ==> HPO_{2} + 2n·C_{2}


HPO_{2} + 2n·C_{2} + e^{-} ==> HP(C_{2n}O)_{2}


Entalpia de reacción:
[ HP(C_{2n}O)_{2} ] = 16n+9


[ HPO_{2} ] = 9
[ 2n·C_{2} ] = 16n


16n+9 = 9+16n = 16n+9

hidro-oxo-fosfuro de nitrógeno

HP(N_{2n}O)_{2} + e^{+} ==> HPO_{2} + 2n·N_{2}


HPO_{2} + 2n·N_{2} + e^{-} ==> HP(N_{2n}O)_{2}


Entalpia de reacción:
[ HP(N_{2n}O)_{2} ] = 12n+9


[ HPO_{2} ] = 9
[ 2n·N_{2} ] = 12n


12n+9 = 9+12n = 12n+9

construcción de hidro-nitruros por inducción sobre el hidro-bi-nitrogeno

N_{2n}H_{4} + N_{2}H_{4} + e^{+} ==> N_{2(n+1)}H_{4} + 2·H_{2}


N_{2(n+1)}H_{4} + 2·H_{2} + e^{-} ==> N_{2n}H_{4} + N_{2}H_{4}


Entalpia de reacción:
[ N_{2n}H_{4} ] = 8
[ N_{2}H_{4} ] = 8


[ N_{2(n+1)}H_{4} ] = 12
[ 2·H_{2} ] = 4


8+8 = 12+4 = 16

oxidación de hidro-nitruros

N_{2n}H_{4} + n·O_{2} + e^{+} ==> n·N_{2}O_{2} + 2·H_{2}


n·N_{2}O_{2} + 2·H_{2} + e^{-} ==> N_{2n}H_{4} + n·O_{2}


Entalpia de reacción:
[ N_{2n}H_{4} ] = 6n+4
[ n·O_{2} ] = 4n


[ n·N_{2}O_{2} ] = 10n
[ 2·H_{2} ] = 4


(6n+4)+4n = 10n+4 = 10n+4

oxidación del hidro-bi-nitrogeno

N_{2}H_{4} + O_{2} + e^{+} ==> N_{2}O_{2} + 2·H_{2}


N_{2}O_{2} + 2·H_{2} + e^{-} ==> N_{2}H_{4} + O_{2}


Entalpia de reacción:
[ N_{2}H_{4} ] = 10
[ O_{2} ] = 4


[ N_{2}O_{2} ] = 10
[ 2·H_{2} ] = 4


10+4 = 10+4 = 14

construcción de hidrocarburos por inducción sobre el metano

C_{n}H_{2n+2} + CH_{4} + e^{+} ==> C_{n+1}H_{2(n+1)+2} + H_{2}


C_{n+1}H_{2(n+1)+2} + H_{2} + e^{-} ==> C_{n}H_{2n+2} + CH_{4}


Entalpia de reacción:
[ C_{n}H_{2n+2} ] = 5
[ CH_{4} ] = 5


[ C_{n+1}H_{2(n+1)+2} ] = 8
[ H_{2} ] = 2


5+5 = 8+2 = 10

hidrocarburo nitrogenado carbonizado

[∀n][ n >] 2 ] ==>


2·C_{n}N_{2n+(-2)}H_{2n+2} + (n+(-1))·C_{2} + e^{+} ==> ...
... 2·C_{n}N_{2n+(-2)}C_{n+(-1)}H_{2n+2}


2·C_{n}N_{2n+(-2)}C_{n+(-1)}H_{2n+2} + e^{-} ==> ...
... 2·C_{n}N_{2n+(-2)}H_{2n+2} + (n+(-1))·C_{2}


Entalpia de reacción:
[ 2·C_{n}N_{2n+(-2)}H_{2n+2} ] = 12n+(-12)
[ (n+(-1))·C_{2} ] = 8n+(-8)


[ 2·C_{n}N_{2n+(-2)}C_{n+(-1)}H_{2n+2} ] = 20n+(-20)


(12n+(-12))+(8n+(-8)) = 20n+(-20)

glicerina derivada de un aceite

[∀n][ n >] 2 ] ==>


H_{2}C_{n}N_{2n+(-2)}( 2n·C_{m}N_{2m+(-2)}H_{2m+1} ) + 2n·(NaOH)} + e^{-} ==> ...
... H_{2}C_{n}N_{2n+(-2)}(OH)_{2n} + 2n·( NaC_{m}N_{2m+(-2)}H_{2m+1} )


oleo + hidróxido de sodio + energía ==> glicerina + hidro-palmitato de sodio


H_{2}C_{n}N_{2n+(-2)}(OH)_{2n} + 2n·( NaC_{m}N_{2m+(-2)}H_{2m+1} ) + e^{+} ==> ...
... H_{2}C_{n}N_{2n+(-2)}( 2n·C_{m}N_{2m+(-2)}H_{2m+1} ) + 2n·(NaOH)}


Entalpia de reacción:
[ H_{2}C_{n}N_{2n+(-2)}( 2n·C_{m}N_{2m+(-2)}H_{2m+1} ) ] = 12n
[ 2n·NaOH ] = 6n


[ H_{2}C_{n}N_{2n+(-2)}(OH)_{2n} ] = 8n
[ 2n·NaC_{m}H_{2m+1} ] = 10n


12n+6n = 8n+10n = 18n

aceite de un hidrocarburo nitrogenado

[∀n][ n >] 2 ] ==>


C_{n}N_{2n+(-2)}H_{2n+2} + 2n·C_{m}N_{2m+(-2)}H_{2m+2} + e^{+} ==> ...
... H_{2}C_{n}N_{2n+(-2)}( 2n·C_{m}N_{2m+(-2)}H_{2m+1} ) + 2n·H_{2}


H_{2}C_{n}N_{2n+(-2)}( 2n·C_{m}N_{2m+(-2)}H_{2m+1} ) + 2n·H_{2} + e^{-} ==> ...
... C_{n}N_{2n+(-2)}H_{2n+2} + 2n·C_{m}N_{2m+(-2)}H_{2m+2}


Entalpia de reacción:
[ C_{n}N_{2n+(-2)}H_{2n+2} ] = 6n
[ 2n·C_{m}N_{2m+(-2)}H_{2m+2} ] = 10n


[ H_{2}C_{n}N_{2n+(-2)}( 2n·C_{m}N_{2m+(-2)}H_{2m+1} )  ] = 12n
[ 2n·H_{2}  ] = 4n


6n+10n = 12n+4n = 16n

hidrocarburo nitrogenado

[∀n][ n >] 2 ] ==>


C_{n}H_{2n+2} + (n+(-1))·N_{2} + e^{+} ==> C_{n}N_{2n+(-2)}H_{2n+2}


C_{n}N_{2n+(-2)}H_{2n+2} + e^{-} ==> C_{n}H_{2n+2} + (n+(-1))·N_{2}


Entalpia de reacción:
[ C_{n}H_{2n+2} ] = 4n
[ (n+(-1))·N_{2} ] = 6n+(-6)


[ C_{n}N_{2n+(-2)}H_{2n+2} ] = 10n+(-6)


4n+(6n+(-6)) = 10n+(-6) = 10n+(-6)

hidrocarburos alcanos combustión

C_{n}H_{2n+2} + n·O_{2} + e^{+} ==> n·CO_{2} + (n+1)·H_{2}


n·CO_{2} + (n+1)·H_{2} + e^{-} ==> C_{n}H_{2n+2} + n·O_{2}


Entalpia de reacción:
[ C_{n}H_{2n+2} ] = 6n+2
[ n·O_{2} ] = 4n


[ n·CO_{2} ] = 8n
[ (n+1)·H_{2} ] = 2n+2


(6n+2)+4n = 8n+(2n+2) = 10n+2

carburo de dos hidrógenos octogonal

Oct[C_{8}]H_{2} + O_{2} + e^{+} ==> C_{8}O_{2} + H_{2}


C_{8}O_{2} + H_{2} + e^{-} ==> Oct[C_{8}]H_{2} + O_{2}


Entalpia de reacción:
[ Oct[C_{8}]H_{2} ] = 10
[ O_{2} ] = 4


[ C_{8}O_{2} ] = 12
[ H_{2} ] = 2


10+4 = 12+2 = 14

carburo de dos hidrógenos hexagonal

Hex[C_{6}]H_{2} + O_{2} + e^{+} ==> C_{6}O_{2} + H_{2}


C_{6}O_{2} + H_{2} + e^{-} ==> Hex[C_{6}]H_{2} + O_{2}


Entalpia de reacción:
[ Hex[C_{6}]H_{2} ] = 10
[ O_{2} ] = 4


[ C_{6}O_{2} ] = 12
[ H_{2} ] = 2


10+4 = 12+2 = 14

bi-metano octogonal combustión

Oct[C_{8}]H_{8} + 4·O_{2} + e^{+} ==> 4·C_{2}O_{2} + 4·H_{2}


4·C_{2}O_{2} + 4·H_{2} + e^{-} ==> Oct[C_{8}]H_{8} + 4·O_{2}


Entalpia de reacción:
[ Oct[C_{8}]H_{8} ] = 40
[ 4·O_{2} ] = 16


[ 4·C_{2}O_{2} ] = 48
[ 4·H_{2} ] = 8


40+16 = 48+8 = 56

hiper-nitrat de ferro 3

hiper-nitrat de Ferro 3:


2·N(OH)_{3} + Fe_{2} + e^{-} ==> 2·HNFe + 3·H_{2}O_{2}
2·HNFe + 3·H_{2}O_{2} + e^{+} ==> 2·N(OH)_{3} + Fe_{2}


Entalpia de reacción:
[ 2·HN(OH)_{3} ] = 18
[ Fe_{2} ] = 6
[ 2·NFe ] = 12
[ 3·H_{2}O_{2} ] = 12


18+6 = 12+12 = 24

nitrit de liti y nitrat de berili

nitrit de liti:


2·H_{2}N(OH) + Li_{2} + e^{-} ==> 2·H_{2}NLi + H_{2}O_{2}
2·H_{2}NLi + H_{2}O_{2} + e^{+} ==> 2·H_{2}N(OH) + Li_{2}


Entalpia de reacción:
[ 2·H_{2}N(OH) ] = 10
[ Li_{2} ] = 2
[ 2·H_{2}NLi ] = 8
[ H_{2}O_{2} ] = 4


10+2 = 8+4 = 12


nitrat de Berili:


2·HN(OH)_{2} + Be_{2} + e^{-} ==> 2·HNBe + 2·H_{2}O_{2}
2·HNBe + 2·H_{2}O_{2} + e^{+} ==> 2·HN(OH)_{2} + Be_{2}


Entalpia de reacción:
[ 2·HN(OH)_{2} ] = 14
[ Be_{2} ] = 4
[ 2·HNBe ] = 10
[ 2·H_{2}O_{2} ] = 8


14+4 = 10+8 = 18

metano hexagonal combustión

Hex[C_{6}]H_{4} + 2·O_{2} + e^{+} ==> 2·C_{3}O_{2} + 2·H_{2}


2·C_{3}O_{2} + 2·H_{2} + e^{-} ==> Hex[C_{6}]H_{4} + 2·O_{2}


Entalpia de reacción:
[ Hex[C_{6}]H_{4} ] = 20
[ 2·O_{2} ] = 8


[ 2·C_{3}O_{2} ] = 24
[ 2·H_{2} ] = 4


20+8 = 24+4 = 28

agua

2·H_{2} + O_{2} + e^{+} ==> 2·H_{2}O


2·H_{2}O + e^{-} ==> 2·H_{2} + O_{2}


Entalpia de reacción:
[ 2·H_{2} ] = 4
[ O_{2} ] = 4


[ 2·H_{2}O ] = 8


4+4 = 8

metano combustión

CH_{4} + O_{2} + e^{+} ==> CO_{2} + 2·H_{2}


CO_{2} + 2·H_{2} + e^{-} ==> CH_{4} + O_{2}


Entalpia de reacción:
[ CH_{4} ] = 8
[ O_{2} ] = 4


[ CO_{2} ] = 8
[ 2·H_{2} ] = 4


8+4 = 12