How would I go about calculating and plotting the concentration profiles of four molecules in the nitrogen cycle as a function of temperature and pH?

I am attempting to replicate the nitirogen cylce and calculate and plot the concentration of the molecules involved based on the reactions described in the image, as a function of temperature (T=298K) and neautral pH.

Answer 1

[Shivansh]

Hi D,

I understand that you want to implement nitrogen cycle and plot the concentration of the molecules involved based on the reactions in the image in MATLAB.

I am assuming that you know the value of rate constants(k) at the provided temperature and neutral pH.

You can use the below MATLAB code to visualise the concentration of different molecules in nitrogen cycle.

nitrogen_cycle_simulation();

function nitrogen_cycle_simulation()
    % Constants (these would need to be determined experimentally or from literature)
    k1 = 1; % Example rate constant values
    k2 = 1;
    k3 = 1;
    k4 = 1;
    k5 = 1;
    % Initial concentrations
    NH3_0 = 1; % Molar
    NH4_0 = 0; % Molar
    NO2_0 = 0; % Molar
    NO3_0 = 0; % Molar
    N2_0  = 0; % Molar
    initial_conditions = [NH3_0, NH4_0, NO2_0, NO3_0, N2_0];
    % Time span
    tspan = [0, 100]; % Arbitrary time span
    % Solve the system of ODEs
    [T, Y] = ode45(@(t, y) rate_equations(t, y, k1, k2, k3, k4, k5), tspan, initial_conditions);
    % Plot the results
    figure;
    plot(T, Y);
    xlabel('Time');
    ylabel('Concentration');
    legend('NH3', 'NH4+', 'NO2-', 'NO3-', 'N2');
end

function dydt = rate_equations(t, y, k1, k2, k3, k4, k5)
    NH3 = y(1);
    NH4 = y(2);
    NO2 = y(3);
    NO3 = y(4);
    N2  = y(5);
    dNH3_dt = -k1 * NH3 + k2 * NH4;
    dNH4_dt = k1 * NH3 - k2 * NH4 - k3 * NH4;
    dNO2_dt = k3 * NH4 - k4 * NO2;
    dNO3_dt = k4 * NO2 - k5 * NO3;
    dN2_dt  = k5 * NO3; 
    dydt = [dNH3_dt; dNH4_dt; dNO2_dt; dNO3_dt; dN2_dt];
end

Output of the script:

You can set the rate constants and initial concentration of the molecules with respect to your problem. The above script sets up a system of differential equation based on the equations provided and solves them over a defined time span using “ode45” solver.

You can learn more about the “plot” function in MATLAB using the following documentation:

https://www.mathworks.com/help/matlab/ref/plot.html.

You can learn more about the “ode45” function in MATLAB using the following documentation:

https://in.mathworks.com/help/matlab/ref/ode45.html.

Hope it helps!