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"cell_type": "markdown",
"id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f",
"metadata": {},
"source": [
"## Violating the Laws of Physics for Fun and Insight!\n",
"### A cascade of reactions `A <-> B <-> C` , mostly in the forward direction\n",
"### [PART 1](#impossible_1_part1) : the above, together with a PHYSICALLY-IMPOSSIBLE \"closing\" of the cycle with :\n",
"#### `C <-> A`, *ALSO* mostly in the forward direction _(never mind the laws of thermodymics)!_\n",
"### [PART 2](#impossible_1_part2) : restoring the law of physics (by letting `C <-> A` adjust its kinetics based on the energy difference.)\n",
"\n",
"All 1st-order kinetics. \n",
"\n",
"LAST REVISED: May 5, 2024"
]
},
{
"cell_type": "markdown",
"id": "7ba9c24d-102a-4571-8207-c5766525774f",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "1d51c42b-fcc0-47c8-9b84-122416b82f4a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "248cf329",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"from experiments.get_notebook_info import get_notebook_basename\n",
"\n",
"from src.modules.chemicals.chem_data import ChemData as chem\n",
"from src.modules.reactions.reaction_dynamics import ReactionDynamics\n",
"\n",
"import plotly.express as px\n",
"import plotly.graph_objects as go\n",
"from src.modules.visualization.graphic_log import GraphicLog"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e",
"metadata": {
"tags": []
},
"outputs": [
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"name": "stdout",
"output_type": "stream",
"text": [
"-> Output will be LOGGED into the file 'impossible_1.log.htm'\n"
]
}
],
"source": [
"# Initialize the HTML logging\n",
"log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n",
"\n",
"# Set up the use of some specified graphic (Vue) components\n",
"GraphicLog.config(filename=log_file,\n",
" components=[\"vue_cytoscape_2\"],\n",
" extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")"
]
},
{
"cell_type": "markdown",
"id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf",
"metadata": {},
"source": [
"### Initialize the system"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "32edd4eb-556d-40d3-8f25-8e515b5beaae",
"metadata": {},
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"data": {
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"1"
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},
"execution_count": 4,
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"output_type": "execute_result"
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"source": [
"# Initialize the system\n",
"chem_data = chem(names=[\"A\", \"B\", \"C\"])\n",
"\n",
"# Reaction A <-> B, mostly in forward direction (favored energetically)\n",
"# Note: all reactions in this experiment have 1st-order kinetics for all species\n",
"chem_data.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=9., reverse_rate=3.)\n",
"\n",
"# Reaction B <-> C, also favored energetically\n",
"chem_data.add_reaction(reactants=\"B\", products=\"C\",\n",
" forward_rate=8., reverse_rate=4.)"
]
},
{
"cell_type": "markdown",
"id": "faa20450-8753-4d19-ad1c-0cad77e6d165",
"metadata": {},
"source": [
"# Part 1 - \"Turning off the Laws of Physics\"!"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "95927c4b-8c13-462e-85f6-5d6db3006da2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 3 (at temp. 25 C)\n",
"0: A <-> B (kF = 9 / kR = 3 / delta_G = -2,723.4 / K = 3) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n",
"2: C <-> A (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A', 'C'}\n",
"[GRAPHIC ELEMENT SENT TO LOG FILE `impossible_1.log.htm`]\n"
]
}
],
"source": [
"# LET'S VIOLATE THE LAWS OF PHYSICS!\n",
"# Reaction C <-> A, also mostly in forward direction - MAGICALLY GOING \"UPSTREAM\" from C, to the higher-energy level of \"A\"\n",
"chem_data.add_reaction(reactants=\"C\" , products=\"A\",\n",
" forward_rate=3., reverse_rate=2.) # PHYSICALLY IMPOSSIBLE! Future versions of Life123 may flag this!\n",
"\n",
"chem_data.describe_reactions()\n",
"\n",
"# Send the plot of the reaction network to the HTML log file\n",
"chem_data.plot_reaction_network(\"vue_cytoscape_2\")"
]
},
{
"cell_type": "markdown",
"id": "15abbc56-c39d-4bb9-b1f1-d3b9911c7749",
"metadata": {},
"source": [
"# Notice the absurdity of the energy levels always going down, throughout the cycle (like in an Escher painting!)"
]
},
{
"cell_type": "markdown",
"id": "1c04542a-aba7-466a-9ee8-a2f550c6ced2",
"metadata": {},
"source": [
""
]
},
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"id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7",
"metadata": {},
"source": [
"### Set the initial concentrations of all the chemicals"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "e4ff6a84-f5d5-4645-9c56-d9e981c108df",
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"data": {
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"{'A': 100.0, 'B': 0.0, 'C': 0.0}"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"initial_conc = {\"A\": 100., \"B\": 0., \"C\": 0.} \n",
"initial_conc"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf",
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"name": "stdout",
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"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 100.0\n",
" Species 1 (B). Conc: 0.0\n",
" Species 2 (C). Conc: 0.0\n",
"Set of chemicals involved in reactions: {'B', 'A', 'C'}\n"
]
}
],
"source": [
"dynamics = ReactionDynamics(chem_data=chem_data)\n",
"dynamics.set_conc(conc=initial_conc, snapshot=True)\n",
"dynamics.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 8,
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"200 total step(s) taken\n"
]
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],
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"dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"dynamics.single_compartment_react(initial_step=0.01, target_end_time=2.0,\n",
" variable_steps=False) # To avoid extra complexity, we're sticking to simple fixed-time steps"
]
},
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",
"text/html": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "fbf24a85-b152-4b24-b350-00bed12e7bb9",
"metadata": {},
"outputs": [],
"source": [
"# dynamics.explain_time_advance()\n",
"\n",
"# dynamics.get_history()"
]
},
{
"cell_type": "markdown",
"id": "225e1cd9-8c48-4ed4-8510-268476bae0c0",
"metadata": {},
"source": [
"### It might look like an equilibrium has been reached. But NOT! Verify the LACK of final equilibrium state:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "5dcb9571-340a-48a0-8711-f4d7ed6dcc0c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 21.43 ; [B] = 33.81\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.57778\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 3.0\n",
"Discrepancy between the two values: 47.41 %\n",
"Reaction is NOT in equilibrium (not within 1% tolerance)\n",
"\n",
"1: B <-> C\n",
"Final concentrations: [B] = 33.81 ; [C] = 44.76\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.32394\n",
" Formula used: [C] / [B]\n",
"2. Ratio of forward/reverse reaction rates: 2.0\n",
"Discrepancy between the two values: 33.8 %\n",
"Reaction is NOT in equilibrium (not within 1% tolerance)\n",
"\n",
"2: C <-> A\n",
"Final concentrations: [A] = 21.43 ; [C] = 44.76\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.478723\n",
" Formula used: [A] / [C]\n",
"2. Ratio of forward/reverse reaction rates: 1.5\n",
"Discrepancy between the two values: 68.09 %\n",
"Reaction is NOT in equilibrium (not within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"{False: [0, 1, 2]}"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "markdown",
"id": "f74cae99-4f86-4ce7-ad51-fff15ecdfa56",
"metadata": {},
"source": [
"## Not surprisingly, none of the reactions of this physically-impossible hypothetical system are in equilibrium\n",
"### Even though the concentrations don't change, it's NOT from equilibrium in the reactions - but rather from a balancing out of consuming and replenishing across reactions. \n",
"#### Consider, for example, the concentrations of the chemical `A` at the end time, and contributions to its change (\"Delta A\") from the _individual_ reactions affecting `A`, as available from the diagnostic data:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "d3ef9936-020b-4ab3-b762-8a6cffb963b6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reaction: A <-> B\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" START_TIME | \n",
" Delta A | \n",
" Delta B | \n",
" Delta C | \n",
" time_step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 197 | \n",
" 1.97 | \n",
" -0.914286 | \n",
" 0.914286 | \n",
" 0.0 | \n",
" 0.01 | \n",
" | \n",
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\n",
" \n",
" | 198 | \n",
" 1.98 | \n",
" -0.914286 | \n",
" 0.914286 | \n",
" 0.0 | \n",
" 0.01 | \n",
" | \n",
"
\n",
" \n",
" | 199 | \n",
" 1.99 | \n",
" -0.914286 | \n",
" 0.914286 | \n",
" 0.0 | \n",
" 0.01 | \n",
" | \n",
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\n",
" \n",
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\n",
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"
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"text/plain": [
" START_TIME Delta A Delta B Delta C time_step caption\n",
"197 1.97 -0.914286 0.914286 0.0 0.01 \n",
"198 1.98 -0.914286 0.914286 0.0 0.01 \n",
"199 1.99 -0.914286 0.914286 0.0 0.01 "
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.get_diagnostic_rxn_data(rxn_index=0, tail=3)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "1004ce75-b71b-4982-a68d-aa65cf8fcb1b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reaction: C <-> A\n"
]
},
{
"data": {
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"\n",
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\n",
" \n",
" \n",
" | \n",
" START_TIME | \n",
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" Delta B | \n",
" Delta C | \n",
" time_step | \n",
" caption | \n",
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\n",
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" START_TIME Delta A Delta B Delta C time_step caption\n",
"197 1.97 0.914286 0.0 -0.914286 0.01 \n",
"198 1.98 0.914286 0.0 -0.914286 0.01 \n",
"199 1.99 0.914286 0.0 -0.914286 0.01 "
]
},
"execution_count": 13,
"metadata": {},
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],
"source": [
"dynamics.get_diagnostic_rxn_data(rxn_index=2, tail=3)"
]
},
{
"cell_type": "markdown",
"id": "f5b83b4d-f9be-4bd7-955f-803daa0bb658",
"metadata": {},
"source": [
"### Looking at the last row from each of the 2 dataframes above, one case see that, at every reaction cycle, [A] gets reduced by some quantity (0.914286) by the reaction `A <-> B`, while simultaneously getting increased by the SAME amount by the (fictional) reaction `C <-> A`. \n",
"### Hence, the concentration of A remains constant - but none of the reactions is in equilibrium!"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "562234fc-6f35-4ad4-ab89-13efa748baa7",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "d8cdc411-7b4d-4241-a218-9737f6cd2e0a",
"metadata": {},
"source": [
"# PART 2 - Let's restore the Laws of Physics!"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "e743e6a7-a8b1-4aba-b7db-4d7c61277a65",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 3 (at temp. 25 C)\n",
"0: A <-> B (kF = 9 / kR = 3 / delta_G = -2,723.4 / K = 3) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n",
"2: C <-> A (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A', 'C'}\n"
]
}
],
"source": [
"chem_data.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "f37675c8-827b-4c3d-bd55-93f776cc4989",
"metadata": {},
"outputs": [],
"source": [
"dynamics.clear_reactions() # Let's start over with the reactions (without affecting the data from the reactions)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "4d98c72b-986e-4122-9b2e-c4592b68d6fb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# For the reactions A <-> B, and B <-> C, everything is being restored to the way it was before\n",
"chem_data.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=9., reverse_rate=3.)\n",
"\n",
"# Reaction , also favored energetically\n",
"chem_data.add_reaction(reactants=\"B\", products=\"C\",\n",
" forward_rate=8., reverse_rate=4.)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "593bbaa1-bdf4-4bfd-a1ce-d0c843ca43f1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: A <-> B (kF = 9 / kR = 3 / delta_G = -2,723.4 / K = 3) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A', 'C'}\n"
]
}
],
"source": [
"chem_data.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "1e4e5e85-1407-440c-ba9c-dff59843b5ac",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# But for the reaction C <-> A, this time we'll \"bend the knee\" to the laws of thermodynamics!\n",
"# We'll use the same forward rate as before, but we'll let the reverse rate be picked by the system, \n",
"# based of thermodynamic data consistent with the previous 2 reactions : i.e. an energy difference of -(-2,723.41 - 1,718.28) = +4,441.69 (reflecting the \n",
"# \"going uphill energetically\" from C to A\n",
"chem_data.add_reaction(reactants=\"C\", products=\"A\",\n",
" forward_rate=3., delta_G=4441.69) # Notice the positive Delta G: we're going from \"C\", to the higher-energy level of \"A\""
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "707863ca-48d6-41b2-ad44-8fbce297cb4d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 3 (at temp. 25 C)\n",
"0: A <-> B (kF = 9 / kR = 3 / delta_G = -2,723.4 / K = 3) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n",
"2: C <-> A (kF = 3 / kR = 18 / delta_G = 4,441.7 / K = 0.16667) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A', 'C'}\n"
]
}
],
"source": [
"chem_data.describe_reactions()"
]
},
{
"cell_type": "markdown",
"id": "2fefd29d-ae6a-4eda-8a8f-81625a99bd30",
"metadata": {},
"source": [
"# Notice how, now that we're again following the laws of thermodynamics, the last reaction is mostly IN REVERSE (low K < 1), as it ought to be! \n",
"#### (considering how energetically unfavorable it is)"
]
},
{
"cell_type": "markdown",
"id": "6f42feb3-f556-486b-bb8a-29a482ff4d2a",
"metadata": {},
"source": [
"### Now, let's continue with this \"legit\" set of reactions, from where we left off in our fantasy world at time t=2:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "197dd1e8-9c3e-435a-8bb4-9b8f8cbda54b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"400 total step(s) taken\n"
]
}
],
"source": [
"dynamics.single_compartment_react(initial_step=0.005, target_end_time=4.0,\n",
" variable_steps=False)\n",
"\n",
"#dynamics.explain_time_advance()\n",
"\n",
"#dynamics.get_history()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "f06b91e6-730f-40cc-9566-cef4b16cb169",
"metadata": {},
"outputs": [],
"source": [
"fig0 = dynamics.plot_history() # Prepare, but don't show, the main plot"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "8d6ccc03-3e48-4142-bdbf-ca6d6fe6fda0",
"metadata": {},
"outputs": [
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Add a second plot, with a vertical gray line at t=2\n",
"fig1 = px.line(x=[2,2], y=[0,100], color_discrete_sequence = ['gray'])\n",
"\n",
"# Combine the plots, and display them\n",
"all_fig = go.Figure(data=fig0.data + fig1.data, layout = fig0.layout) # Note that the + is concatenating lists\n",
"all_fig.update_layout(title=\"On the left of vertical gray line: FICTIONAL world; on the right: REAL world!\")\n",
"all_fig.show()"
]
},
{
"cell_type": "markdown",
"id": "2e79b987-135d-416d-baa3-797a5d0b56be",
"metadata": {},
"source": [
"### Notice how [A] drops at time t=2, when we re-enact the Laws of Physics, because A no longer receives the extra boost from the previous mostly-forward (and thus physically-impossible given the unfavorable energy levels!) reaction `C <-> A`. \n",
"### Back to the real world, that (energetically unfavored) reaction now mostly goes IN REVERSE; hence, the boost in [C] as well"
]
},
{
"cell_type": "markdown",
"id": "c81944df-c125-4099-a81f-efc7ae0f9a6e",
"metadata": {},
"source": [
"### Now, we have a REAL equilibrium!"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "f13381bb-d635-4667-b28c-99497370bf27",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 10 ; [B] = 30\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 3.0\n",
"Discrepancy between the two values: 0.0001018 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"1: B <-> C\n",
"Final concentrations: [B] = 30 ; [C] = 60\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2\n",
" Formula used: [C] / [B]\n",
"2. Ratio of forward/reverse reaction rates: 2.0\n",
"Discrepancy between the two values: 3.817e-05 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"2: C <-> A\n",
"Final concentrations: [A] = 10 ; [C] = 60\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.166667\n",
" Formula used: [A] / [C]\n",
"2. Ratio of forward/reverse reaction rates: 0.16666698478459493\n",
"Discrepancy between the two values: 5.09e-05 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "markdown",
"id": "605b7936-546b-4b0c-bf33-cc5007e5343c",
"metadata": {},
"source": [
"### The fact that individual reactions are now in actual, real equilibrium, can be easily seen from the last rows in the diagnostic data. Notice all the delta-concentration values at the final times are virtually zero:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "51b6568d-dbbb-4655-9f41-0b1ecc5a18da",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reaction: A <-> B\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" START_TIME | \n",
" Delta A | \n",
" Delta B | \n",
" Delta C | \n",
" time_step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 599 | \n",
" 3.995 | \n",
" -4.580895e-07 | \n",
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" START_TIME Delta A Delta B Delta C time_step caption\n",
"599 3.995 -4.580895e-07 4.580895e-07 0.0 0.005 "
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.get_diagnostic_rxn_data(rxn_index=0, tail=1)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "5bab7263-f7f4-47e9-878a-fdbba3e8108c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reaction: B <-> C\n"
]
},
{
"data": {
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"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" START_TIME | \n",
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" Delta B | \n",
" Delta C | \n",
" time_step | \n",
" caption | \n",
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\n",
" \n",
" \n",
" \n",
" | 599 | \n",
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