{ "cells": [ { "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 : 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 : 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: Feb. 5, 2023" ] }, { "cell_type": "markdown", "id": "7ba9c24d-102a-4571-8207-c5766525774f", "metadata": {}, "source": [ "![Temporarily suspending the Laws of Physics](../../docs/impossible_1.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "# Extend the sys.path variable, to contain the project's root directory\n", "import set_path\n", "set_path.add_ancestor_dir_to_syspath(2) # The number of levels to go up \n", " # to reach the project's home, from the folder containing this notebook" ] }, { "cell_type": "code", "execution_count": 2, "id": "01bae555-3dcf-42c1-bddc-9477a37f49f8", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_data import ReactionData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "from src.modules.numerical.numerical import Numerical as num\n", "\n", "import numpy as np\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": [ { "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_1\"],\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": {}, "outputs": [], "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 = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\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", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "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": [ "![Energy levels always going down](../../docs/impossible_1b.jpg)" ] }, { "cell_type": "markdown", "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", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'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", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "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" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc(conc=initial_conc, snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 8, "id": "50ddd8e3-58c6-41f8-b874-ddc9a1d64d30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 800.0\n", "50 total step(s) taken\n", "From time 0 to 0.009, in 36 substeps of 0.00025 (each 1/4 of full step)\n", "From time 0.009 to 0.05, in 41 FULL steps of 0.001\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(time_step=0.001, stop_time=0.05,\n", " dynamic_substeps=4, rel_fast_threshold=80.)\n", "\n", "dynamics.explain_time_advance()\n", "\n", "# dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 9, "id": "fbf24a85-b152-4b24-b350-00bed12e7bb9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 200.0\n", "50 total step(s) taken\n", "From time 0 to 0.009, in 36 substeps of 0.00025 (each 1/4 of full step)\n", "From time 0.009 to 0.05, in 41 FULL steps of 0.001\n", "From time 0.05 to 0.13, in 64 substeps of 0.00125 (each 1/4 of full step)\n", "From time 0.13 to 0.3, in 34 FULL steps of 0.005\n" ] } ], "source": [ "dynamics.single_compartment_react(time_step=0.005, stop_time=0.3,\n", " dynamic_substeps=4, rel_fast_threshold=100.)\n", "\n", "dynamics.explain_time_advance()\n", "\n", "#dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 10, "id": "938b9678-900a-4d6b-8cac-68d62545b09e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 120.0\n", "170 total step(s) taken\n", "From time 0 to 0.009, in 36 substeps of 0.00025 (each 1/4 of full step)\n", "From time 0.009 to 0.05, in 41 FULL steps of 0.001\n", "From time 0.05 to 0.13, in 64 substeps of 0.00125 (each 1/4 of full step)\n", "From time 0.13 to 0.3, in 34 FULL steps of 0.005\n", "From time 0.3 to 0.31, in 4 substeps of 0.0025 (each 1/4 of full step)\n", "From time 0.31 to 2, in 169 FULL steps of 0.01\n" ] } ], "source": [ "dynamics.single_compartment_react(time_step=0.01, stop_time=2.,\n", " dynamic_substeps=4, rel_fast_threshold=120.)\n", "\n", "dynamics.explain_time_advance()\n", "\n", "#dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "cbf6c9c7-8cec-400f-9e70-49ff1a9f485c", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 11, "id": "68172367-1929-4eb2-9350-864eebebb7e1", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves()" ] }, { "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": 12, "id": "f13381bb-d635-4667-b28c-99497370bf27", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 33.81 ; [A] = 21.43\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", "B <-> C\n", "Final concentrations: [C] = 44.76 ; [B] = 33.81\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", "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": 12, "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 `A` at the end time, and contributions to its change (\"Delta A\") from _individual_ reactions affecting `A`, as available from the diagnostic data:" ] }, { "cell_type": "code", "execution_count": 13, "id": "d3ef9936-020b-4ab3-b762-8a6cffb963b6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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TIMEDelta ADelta BDelta Creactionsubsteptime_subdivisiondelta_timecaption
3471.99-0.9142860.9142860.00010.01
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" ], "text/plain": [ " TIME Delta A Delta B Delta C reaction substep time_subdivision \\\n", "347 1.99 -0.914286 0.914286 0.0 0 0 1 \n", "\n", " delta_time caption \n", "347 0.01 " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_data(rxn_index=0, tail=1)" ] }, { "cell_type": "code", "execution_count": 14, "id": "1004ce75-b71b-4982-a68d-aa65cf8fcb1b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: C <-> A\n" ] }, { "data": { "text/html": [ "
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TIMEDelta ADelta BDelta Creactionsubsteptime_subdivisiondelta_timecaption
2781.990.9142860.0-0.9142862010.01
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" ], "text/plain": [ " TIME Delta A Delta B Delta C reaction substep time_subdivision \\\n", "278 1.99 0.914286 0.0 -0.914286 2 0 1 \n", "\n", " delta_time caption \n", "278 0.01 " ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_data(rxn_index=2, tail=1)" ] }, { "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 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": "1d51c42b-fcc0-47c8-9b84-122416b82f4a", "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": 15, "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 = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 16, "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": 17, "id": "4d98c72b-986e-4122-9b2e-c4592b68d6fb", "metadata": {}, "outputs": [], "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": 18, "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 = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 19, "id": "1e4e5e85-1407-440c-ba9c-dff59843b5ac", "metadata": {}, "outputs": [], "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": 20, "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 = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 18 / Delta_G = 4,441.69 / K = 0.166667) | 1st order in all reactants & products\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": 21, "id": "197dd1e8-9c3e-435a-8bb4-9b8f8cbda54b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 150.0\n", "250 total step(s) taken\n", "From time 0 to 0.009, in 36 substeps of 0.00025 (each 1/4 of full step)\n", "From time 0.009 to 0.05, in 41 FULL steps of 0.001\n", "From time 0.05 to 0.13, in 64 substeps of 0.00125 (each 1/4 of full step)\n", "From time 0.13 to 0.3, in 34 FULL steps of 0.005\n", "From time 0.3 to 0.31, in 4 substeps of 0.0025 (each 1/4 of full step)\n", "From time 0.31 to 2, in 169 FULL steps of 0.01\n", "From time 2 to 2.02, in 12 substeps of 0.002 (each 1/4 of full step)\n", "From time 2.02 to 4, in 247 FULL steps of 0.008\n" ] } ], "source": [ "dynamics.single_compartment_react(time_step=0.008, stop_time=4.,\n", " dynamic_substeps=4, rel_fast_threshold=120.)\n", "\n", "dynamics.explain_time_advance()\n", "\n", "#dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 22, "id": "f06b91e6-730f-40cc-9566-cef4b16cb169", "metadata": {}, "outputs": [], "source": [ "fig0 = dynamics.plot_curves(suppress=True) # Prepare, but don't show, the main plot" ] }, { "cell_type": "code", "execution_count": 23, "id": "8d6ccc03-3e48-4142-bdbf-ca6d6fe6fda0", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "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": 24, "id": "5dcb9571-340a-48a0-8711-f4d7ed6dcc0c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 30 ; [A] = 10\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: 9.469e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "B <-> C\n", "Final concentrations: [C] = 60 ; [B] = 30\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: 3.551e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "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: 0.16666696258266173\n", "Discrepancy between the two values: 4.735e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 24, "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": 25, "id": "51b6568d-dbbb-4655-9f41-0b1ecc5a18da", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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