One-bin reaction `2A + 5B <-> 4C + 3D`, with 1st-order kinetics for each species, taken to equilibrium¶

Diffusion not applicable (just 1 bin)

TAGS : "reactions 1D", "under-the-hood"¶

In [1]:

LAST_REVISED = "June 6, 2025"
LIFE123_VERSION = "1.0.0rc6"        # Library version this experiment is based on

In [2]:

#import set_path                    # Using MyBinder?  Uncomment this before running the next cell!

In [3]:

#import sys
#sys.path.append("C:/some_path/my_env_or_install")   # CHANGE to the folder containing your venv or libraries installation!
# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try:  import set_path   

from experiments.get_notebook_info import get_notebook_basename

from life123 import BioSim1D, ChemData, check_version

from life123 import HtmlLog as log
from life123 import GraphicLog

In [4]:

check_version(LIFE123_VERSION)

OK

In [ ]:

In [5]:

# Initialize the HTML logging
log_file = get_notebook_basename() + ".log.htm"    # Use the notebook base filename for the log file

# Set up the use of some specified graphic (Vue) components
GraphicLog.config(filename=log_file,
                  components=["vue_cytoscape_2"],
                  extra_js="https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js")

-> Output will be LOGGED into the file 'reaction_6.log.htm'

In [6]:

# Initialize the system; NOTE: Diffusion not applicable (just 1 bin)
chem_data = ChemData(names=["A", "B", "C", "D"], plot_colors=['navy', 'cyan', 'red', 'orange'])    

bio = BioSim1D(n_bins=1, chem_data=chem_data)

bio.set_all_uniform_concentrations( [4., 7., 5., 2.] )

bio.describe_state()

SYSTEM STATE at Time t = 0:
1 bins and 4 chemical species

Out[6]:

	Species	Diff rate	Bin 0
0	A	None	4.0
1	B	None	7.0
2	C	None	5.0
3	D	None	2.0

In [7]:

# Specify the reaction
reactions = bio.get_reactions()

# Reaction 2A + 5B <-> 4C + 3D , with 1st-order kinetics for each species
reactions.add_reaction(reactants=[(2,"A",1) , (5,"B",1)], products=[(4,"C",1) , (3,"D",1)],
                       forward_rate=5., reverse_rate=2.)

reactions.describe_reactions()

Number of reactions: 1 (at temp. 25 C)
0: 2 A + 5 B <-> 4 C + 3 D  (kF = 5 / kR = 2 / delta_G = -2,271.4 / K = 2.5) | 1st order in all reactants & products
Set of chemicals involved in the above reactions: {"D" (orange), "C" (red), "A" (navy), "B" (cyan)}

In [8]:

# Send a header and a plot to the HTML log file
log.write("Reaction 2 A + 5 B <-> 4 C + 3 D",
          style=log.h2)
reactions.plot_reaction_network("vue_cytoscape_2")

Reaction 2 A + 5 B  4 C + 3 D
[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_6.log.htm`]

In [ ]:

In [9]:

# Let's enable history - by default for all chemicals and all bins
bio.enable_history(take_snapshot=True, caption="Initial state")

History enabled for bins None and chemicals None (None means 'all')

In [10]:

bio.get_bin_history(bin_address=0)

Out[10]:

	SYSTEM TIME	A	B	C	D	caption
0	0.0	4.0	7.0	5.0	2.0	Initial state

In [ ]:

First step¶

In [11]:

bio.get_reaction_handler().enable_diagnostics()   # To save diagnostic information for the simulation run, below

In [12]:

# First step
bio.react(time_step=0.001, n_steps=1)
bio.describe_state()

System Time is now: 0.001
SYSTEM STATE at Time t = 0.001:
1 bins and 4 chemical species

Out[12]:

	Species	Diff rate	Bin 0
0	A	None	3.76
1	B	None	6.40
2	C	None	5.48
3	D	None	2.36

Early in the reaction : [A] = 3.76 , [B] = 6.4 , [C] = 5.48 , [D] = 2.36

In [13]:

bio.get_bin_history(bin_address=0)

Out[13]:

	SYSTEM TIME	A	B	C	D	caption
0	0.000	4.00	7.0	5.00	2.00	Initial state
1	0.001	3.76	6.4	5.48	2.36

In [ ]:

Numerous more steps ¶

In [14]:

# Numerous more steps
bio.react(time_step=0.001, n_steps=40)

bio.describe_state()

System Time is now: 0.041
SYSTEM STATE at Time t = 0.041:
1 bins and 4 chemical species

Out[14]:

	Species	Diff rate	Bin 0
0	A	None	2.802846
1	B	None	4.007114
2	C	None	7.394309
3	D	None	3.795732

Consistent with the 5/2 ratio of forward/reverse rates (and the 1st order reactions), the systems settles in the following equilibrium:
[A] = 2.80284552 , [B] = 4.00711381 , [C] = 7.39430896 , [D] = 3.79573172

In [15]:

# Verify that the reaction has reached equilibrium
bio.get_reaction_handler().is_in_equilibrium(rxn_index=0, conc=bio.bin_snapshot(bin_address = 0))

2 A + 5 B <-> 4 C + 3 D
Current concentrations: [A] = 2.803 ; [B] = 4.007 ; [C] = 7.394 ; [D] = 3.796
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.49898
    Formula used:  ([C][D]) / ([A][B])
2. Ratio of forward/reverse reaction rates: 2.5
Discrepancy between the two values: 0.04092 %
Reaction IS in equilibrium (within 1% tolerance)

Out[15]:

True

In [16]:

df = bio.get_bin_history(bin_address=0)
df

Out[16]:

	SYSTEM TIME	A	B	C	D	caption
0	0.000	4.000000	7.000000	5.000000	2.000000	Initial state
1	0.001	3.760000	6.400000	5.480000	2.360000
2	0.002	3.571091	5.927728	5.857818	2.643363
3	0.003	3.421344	5.553360	6.157312	2.867984
4	0.004	3.301981	5.254952	6.396039	3.047029
5	0.005	3.206419	5.016047	6.587162	3.190372
6	0.006	3.129645	4.824113	6.740709	3.305532
7	0.007	3.067794	4.669486	6.864411	3.398309
8	0.008	3.017854	4.544634	6.964293	3.473220
9	0.009	2.977457	4.443643	7.045085	3.533814
10	0.010	2.944734	4.361834	7.110532	3.582899
11	0.011	2.918195	4.295487	7.163611	3.622708
12	0.012	2.896651	4.241627	7.206699	3.655024
13	0.013	2.879148	4.197870	7.241704	3.681278
14	0.014	2.864920	4.162300	7.270160	3.702620
15	0.015	2.853348	4.133370	7.293304	3.719978
16	0.016	2.843932	4.109831	7.312135	3.734101
17	0.017	2.836269	4.090672	7.327463	3.745597
18	0.018	2.830029	4.075073	7.339942	3.754956
19	0.019	2.824948	4.062370	7.350104	3.762578
20	0.020	2.820809	4.052024	7.358381	3.768786
21	0.021	2.817438	4.043596	7.365123	3.773843
22	0.022	2.814692	4.036729	7.370617	3.777962
23	0.023	2.812454	4.031135	7.375092	3.781319
24	0.024	2.810630	4.026576	7.378739	3.784054
25	0.025	2.809144	4.022861	7.381711	3.786283
26	0.026	2.807933	4.019834	7.384133	3.788100
27	0.027	2.806947	4.017366	7.386107	3.789580
28	0.028	2.806142	4.015355	7.387716	3.790787
29	0.029	2.805487	4.013717	7.389027	3.791770
30	0.030	2.804952	4.012381	7.390095	3.792572
31	0.031	2.804517	4.011292	7.390966	3.793225
32	0.032	2.804162	4.010405	7.391676	3.793757
33	0.033	2.803872	4.009681	7.392255	3.794191
34	0.034	2.803637	4.009092	7.392727	3.794545
35	0.035	2.803444	4.008611	7.393111	3.794833
36	0.036	2.803288	4.008219	7.393424	3.795068
37	0.037	2.803160	4.007900	7.393680	3.795260
38	0.038	2.803056	4.007640	7.393888	3.795416
39	0.039	2.802971	4.007428	7.394058	3.795543
40	0.040	2.802902	4.007255	7.394196	3.795647
41	0.041	2.802846	4.007114	7.394309	3.795732

A and B get depleted, while C and D get produced.

2A + 5B <-> 4C + 3D

Let's verify that the stoichiometry is being respected¶

In [17]:

# We'll check the first two arrays of concentrations, from the run's history
arr0 = bio.get_reaction_handler().get_historical_concentrations(row=0, df=df)
arr1 = bio.get_reaction_handler().get_historical_concentrations(row=1, df=df)
arr0, arr1

Out[17]:

(array([4., 7., 5., 2.], dtype=float32),
 array([3.76, 6.4 , 5.48, 2.36], dtype=float32))

In [18]:

# Check that the changes in the first reaction step conform to the stoichiometry
bio.get_reaction_handler().get_diagnostics().stoichiometry_checker(rxn_index=0, 
                                                                   conc_arr_before = arr0, 
                                                                   conc_arr_after = arr1)

Out[18]:

True

In [19]:

arr1 - arr0

Out[19]:

array([-0.24000001, -0.5999999 ,  0.48000002,  0.3599999 ], dtype=float32)

Indeed, the change in [A] is -2 x 0.12, and the change in [B] is -5 X 0.12,
while the change in [C] is 4 x 0.12, and the change in [D] is 3 X 0.12

In [20]:

(arr1 - arr0) / 0.12    # 0.12 is the "moles of reactions" change

Out[20]:

array([-2.0000002, -4.9999995,  4.0000005,  2.9999993], dtype=float32)

In [ ]:

Plots of changes of concentration with time¶

In [21]:

bio.plot_history_single_bin(bin_address=0, 
                            title_prefix="Reaction `2A + 5B <-> 4C + 3D`")

In [ ]:

One-bin reaction 2A + 5B <-> 4C + 3D, with 1st-order kinetics for each species, taken to equilibrium¶

TAGS : "reactions 1D", "under-the-hood"¶

First step¶

Numerous more steps¶

Equilibrium¶

Let's verify that the stoichiometry is being respected¶

Plots of changes of concentration with time¶

One-bin reaction `2A + 5B <-> 4C + 3D`, with 1st-order kinetics for each species, taken to equilibrium¶

Numerous more steps ¶

Equilibrium ¶