This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
from https://arxiv.org/pdf/2210.12150.pdf
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
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10 | divide both sides by |
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LHS diff is pdg6850 - pdg6850/pdg8379 RHS diff is pdg4940*(pdg8379 - 1)/(pdg9046*pdg9067) |
3488423948:
5085809757: |
3488423948:
5085809757: |
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11 | declare initial expr |
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no validation is available for declarations |
7924063906:
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7924063906:
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definition of equilibrium |
6 | divide both sides by |
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valid |
3488423948:
9562264720: |
3488423948:
9562264720: |
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16 | raise both sides to power |
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no check is performed |
2114909846:
8131665171: |
2114909846:
8131665171: |
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12 | raise both sides to power |
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no check is performed |
7924063906:
6240546932: |
7924063906:
6240546932: |
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18 | change variable X to Y |
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valid |
7928111771:
7267424860: |
7928111771:
7267424860: |
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14 | divide both sides by |
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valid |
7517073655:
6457999644: |
7517073655:
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17 | substitute RHS of expr 1 into expr 2 |
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valid |
8131665171:
6457999644: 7928111771: |
8131665171:
6457999644: 7928111771: |
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19 | raise both sides to power |
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no check is performed |
7267424860:
4689334676: |
7267424860:
4689334676: |
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3 | declare assumption |
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no validation is available for declarations |
6783009163:
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6783009163:
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5 | substitute LHS of expr 1 into expr 2 |
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valid |
6955192897:
3507029294: 3488423948: |
6955192897:
3507029294: 3488423948: |
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15 | declare initial expr |
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no validation is available for declarations |
2114909846:
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2114909846:
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4 | substitute LHS of expr 1 into expr 2 |
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valid |
3736177473:
inconsistent dimensions 6783009163: 3507029294: |
3736177473:
N/A 6783009163: 3507029294: |
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2 | declare initial expr |
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no validation is available for declarations |
6955192897:
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6955192897:
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20 | declare final expr |
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no validation is available for declarations |
4689334676:
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4689334676:
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7 | declare initial expr |
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no validation is available for declarations |
3599953931:
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3599953931:
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The concentration of all sites by summing the concentration of free sites [S] and occupied sites |
8 | substitute LHS of expr 1 into expr 2 |
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valid |
9562264720:
3599953931: 4301729661: |
9562264720:
3599953931: 4301729661: |
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9 | factor out X |
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valid |
4301729661:
2168306601: |
4301729661:
2168306601: |
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13 | substitute RHS of expr 1 into expr 2 |
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valid |
6240546932:
2168306601: 7517073655: |
6240546932:
2168306601: 7517073655: |
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1 | declare initial expr |
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no validation is available for declarations |
3736177473:
inconsistent dimensions |
3736177473:
N/A |
symbol ID | category | latex | scope | dimension | name | value | Used in derivations | references | |
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3037 | variable |
[S_0]
\([S_0]\) |
real |
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total number of sites | 7 | |||
4940 | variable |
[A_{\rm adsorption}]
\([A_{\rm adsorption}]\) |
real |
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surface concentration of A in molecules per square meter | 13 | |||
1791 | variable |
\theta_A
\(\theta_A\) |
real | dimensionless | the fraction of the surface sites covered with A | 5 | |||
6687 | variable |
r_{\rm adsorption}
\(r_{\rm adsorption}\) |
real |
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rate of adsorption | 2 | |||
6850 | variable |
k_{\rm adsorption}
\(k_{\rm adsorption}\) |
real | dimensionless | constant of forward adsorption reaction | 10 | |||
1966 | variable |
r_{\rm desorption}
\(r_{\rm desorption}\) |
real |
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rate of desorption | 3 | |||
9067 | variable |
[S]
\([S]\) |
real |
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concentration of free sites in number per square meter | 7 | |||
4933 | variable |
K_{\rm equilibrium}
\(K_{\rm equilibrium}\) |
real | dimensionless | constant for equilibrium when rate of adsorption equals the rate of desorption | 8 | |||
9046 | variable |
p_A
\(p_A\) |
real | dimensionless | partial pressure of A over the surface | 15 | |||
8379 | variable |
k_{\rm desorption}
\(k_{\rm desorption}\) |
real | dimensionless | constant of backward desorption reaction | 8 |