Return to navigation page or list derivations

Review Langmuir Adsorption

step inference rule input feed output step validity (as per SymPy)
1
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 3736177473
    \(r_{\rm adsorption}=k_{\rm adsorption} p_A [S]\)
 no validation is available for declarations
2
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 6955192897
    \(r_{\rm desorption}=k_{\rm desorption} [A_{\rm adsorption}]\)
 no validation is available for declarations
3
  • 111104: declare assumption
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an assumption.
  1. 6783009163
    \(r_{\rm adsorption}=r_{\rm desorption}\)
 no validation is available for declarations
4
  • 111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 3736177473
    \(r_{\rm adsorption}=k_{\rm adsorption} p_A [S]\)
  1. 6783009163
    \(r_{\rm adsorption}=r_{\rm desorption}\)
  1. 3507029294
    \(k_{\rm adsorption} p_A [S]=r_{\rm desorption}\)
 valid
5
  • 111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 3507029294
    \(k_{\rm adsorption} p_A [S]=r_{\rm desorption}\)
  1. 6955192897
    \(r_{\rm desorption}=k_{\rm desorption} [A_{\rm adsorption}]\)
  1. 3488423948
    \(k_{\rm adsorption} p_A [S]=k_{\rm desorption} [A_{\rm adsorption}]\)
 LHS diff is pdg0001966 - pdg0006850*pdg0009046*pdg0009067 RHS diff is 0
6
  • 111975: divide both sides by
  • number of inputs: 1; feeds: 1; outputs: 1
  • Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.
  1. 3488423948
    \(k_{\rm adsorption} p_A [S]=k_{\rm desorption} [A_{\rm adsorption}]\)
  1. 8162179726
    \(k_{\rm adsorption} p_A\)
  1. 9562264720
    \([S]=\frac{k_{\rm desorption} [A_{\rm adsorption}]}{k_{\rm adsorption} p_A}\)
 valid
7
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 3599953931
    \([S_0]=[S] + [A_{\rm adsorption}]\)
 no validation is available for declarations
8
  • 111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 9562264720
    \([S]=\frac{k_{\rm desorption} [A_{\rm adsorption}]}{k_{\rm adsorption} p_A}\)
  1. 3599953931
    \([S_0]=[S] + [A_{\rm adsorption}]\)
  1. 4301729661
    \([S_0]=\frac{[A_{\rm adsorption}]}{\left( \frac{k_{\rm adsorption}}{k_{\rm desorption}} \right) p_A} + [A_{\rm adsorption}]\)
 valid
9
  • 111432: factor out X
  • number of inputs: 1; feeds: 1; outputs: 1
  • Factor $#1$ from Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 4301729661
    \([S_0]=\frac{[A_{\rm adsorption}]}{\left( \frac{k_{\rm adsorption}}{k_{\rm desorption}} \right) p_A} + [A_{\rm adsorption}]\)
  1. 1268845856
    \([A_{\rm adsorption}]\)
  1. 2168306601
    \([S_0]=\left(\frac{k_{\rm desorption}}{k_{\rm adsorption}} \frac{1}{p_A} + 1\right)[A_{\rm adsorption}]\)
 valid
10
  • 111975: divide both sides by
  • number of inputs: 1; feeds: 1; outputs: 1
  • Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.
  1. 3488423948
    \(k_{\rm adsorption} p_A [S]=k_{\rm desorption} [A_{\rm adsorption}]\)
  1. 1945487024
    \(p_A [S]\)
  1. 5085809757
    \(\frac{k_{\rm adsorption}}{k_{\rm desorption}}=\frac{[A_{\rm adsorption}]}{p_A [S]}\)
 Algebraic error: LHS diff is pdg0006850 - pdg0006850/pdg0008379, RHS diff is pdg0004940*(pdg0008379 - 1)/(pdg0009046*pdg0009067)
11
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 7924063906
    \(K_{equilibrium}=\frac{k_{\rm adsorption}}{k_{\rm desorption}}\)
 no validation is available for declarations
12
  • 111483: raise both sides to power
  • number of inputs: 1; feeds: 1; outputs: 1
  • Raise both sides of Eq.~\\ref{eq:#2} to $#1$; yields Eq.~\\ref{eq:#3}.
  1. 7924063906
    \(K_{equilibrium}=\frac{k_{\rm adsorption}}{k_{\rm desorption}}\)
  1. 5516739892
    \(-1\)
  1. 6240546932
    \(\frac{1}{K_{equilibrium}}=\frac{k_{\rm desorption}}{k_{\rm adsorption}}\)
 recognized infrule but not yet supported
13
  • 111634: substitute RHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 6240546932
    \(\frac{1}{K_{equilibrium}}=\frac{k_{\rm desorption}}{k_{\rm adsorption}}\)
  1. 2168306601
    \([S_0]=\left(\frac{k_{\rm desorption}}{k_{\rm adsorption}} \frac{1}{p_A} + 1\right)[A_{\rm adsorption}]\)
  1. 7517073655
    \([S_0]=\left(\frac{1}{K_{\rm equilibrium}} \frac{1}{p_A} + 1\right)[A_{\rm adsorption}]\)
 valid
14
  • 111975: divide both sides by
  • number of inputs: 1; feeds: 1; outputs: 1
  • Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.
  1. 7517073655
    \([S_0]=\left(\frac{1}{K_{\rm equilibrium}} \frac{1}{p_A} + 1\right)[A_{\rm adsorption}]\)
  1. 5426418187
    \([A_{\rm adsorption}]\)
  1. 6457999644
    \(\frac{[S_0]}{[A_{\rm adsorption}]}=\frac{1}{K_{\rm equilibrium}} \frac{1}{p_A} + 1\)
 valid
15
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 2114909846
    \(\theta_A=\frac{[A_{\rm adsorption}]}{[S_0]}\)
 no validation is available for declarations
16
  • 111483: raise both sides to power
  • number of inputs: 1; feeds: 1; outputs: 1
  • Raise both sides of Eq.~\\ref{eq:#2} to $#1$; yields Eq.~\\ref{eq:#3}.
  1. 2114909846
    \(\theta_A=\frac{[A_{\rm adsorption}]}{[S_0]}\)
  1. 7564010952
    \(-1\)
  1. 8131665171
    \(\frac{1}{\theta_A}=\frac{[S_0]}{[A_{\rm adsorption}]}\)
 recognized infrule but not yet supported
17
  • 111634: substitute RHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 6457999644
    \(\frac{[S_0]}{[A_{\rm adsorption}]}=\frac{1}{K_{\rm equilibrium}} \frac{1}{p_A} + 1\)
  1. 8131665171
    \(\frac{1}{\theta_A}=\frac{[S_0]}{[A_{\rm adsorption}]}\)
  1. 7928111771
    \(\frac{1}{\theta_A}=\frac{1}{K_{\rm equilibrium} p_A} + 1\)
 LHS diff is 0 RHS diff is pdg0003037/pdg0004940 - 1 - 1/(pdg0004933*pdg0009046)
18
  • 111886: change variable X to Y
  • number of inputs: 1; feeds: 2; outputs: 1
  • Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.
  1. 7928111771
    \(\frac{1}{\theta_A}=\frac{1}{K_{\rm equilibrium} p_A} + 1\)
  1. 7630953440
    \(\frac{K_{\rm equilibrium} p_A}{K_{\rm equilibrium} p_A}\)
  1. 6346902704
    \(1\)
  1. 7267424860
    \(\frac{1}{\theta_A}=\frac{1+(K_{\rm equilibrium}\ p_A)}{K_{\rm equilibrium}\ p_A}\)
 valid
19
  • 111483: raise both sides to power
  • number of inputs: 1; feeds: 1; outputs: 1
  • Raise both sides of Eq.~\\ref{eq:#2} to $#1$; yields Eq.~\\ref{eq:#3}.
  1. 7267424860
    \(\frac{1}{\theta_A}=\frac{1+(K_{\rm equilibrium}\ p_A)}{K_{\rm equilibrium}\ p_A}\)
  1. 3911081515
    \(-1\)
  1. 4689334676
    \(\theta_A=\frac{K_{\rm equilibrium}\ p_A}{1+K_{\rm equilibrium}\ p_A}\)
 recognized infrule but not yet supported
20
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 4689334676
    \(\theta_A=\frac{K_{\rm equilibrium}\ p_A}{1+K_{\rm equilibrium}\ p_A}\)
 no validation is available for declarations


Hold the mouse over a node to highlight that node and its neighbors. You can zoom in/out. You can pan the image. You can move nodes by clicking and dragging.

Actions: Edit Derivation

Generate Tex file or PDF file
   xor   

Delete Derivation and all associated steps

This does not remove expressions, symbols, and operations.

timing of Neo4j queries: