# 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?

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D am 3 Mai 2022
Beantwortet: Shivansh am 28 Dez. 2023
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.
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### Antworten (1)

Shivansh am 28 Dez. 2023
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.
Hope it helps!
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