What is a 2 order reaction?

Second order reactions can be defined as chemical reactions wherein the sum of the exponents in the corresponding rate law of the chemical reaction is equal to two. The rate of such a reaction can be written either as r = k[A]2, or as r = k[A][B].

byjus.com - Second Order Reaction - Definition and Derivation for Rate Law ... - Byju's

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Second Order Reaction

What is a Second Order Reaction?

From the rate law equations given above, it can be understood that second order reactions are chemical reactions which depend on either the concentrations of two first-order reactants or the concentration of one-second order reactants. Since second order reactions can be of the two types described above, the rate of these reactions can be generalized as follows:

r = k[A]x[B]y

Where the sum of x and y (which corresponds to the order of the chemical reaction in question) equals two.

Examples of Second Order Reactions

A few examples of second order reactions are given below:

(egin{array}{l}H^{+} + OH^{-} ightarrow H_{2}Oend{array} )

(egin{array}{l}C + O_{2} ightarrow CO + Oend{array} )

The two examples given above are the second order reactions depending on the concentration of two separate first order reactants.

(egin{array}{l}2NO_{2} ightarrow 2NO + O_{2}end{array} )

(egin{array}{l}2HI ightarrow I_{2} + H_{2}end{array} )

These reactions involve one second order reactant yielding the product.

Differential and Integrated Rate Equation for Second Order Reactions

Considering the scenario where one second order reactant forms a given product in a chemical reaction, the differential rate law equation can be written as follows:

(egin{array}{l}frac{-d[R]}{dt} = k[R]^{2}end{array} )

In order to obtain the integrated rate equation, this differential form must be rearranged as follows:

(egin{array}{l}frac{d[R]}{[R]^{2}} = -k dtend{array} )

Now, integrating on both sides in consideration of the change in the concentration of reactant between time 0 and time t, the following equation is attained.

(egin{array}{l}int_{[R]_{0}}^{[R]_{t}} frac{d[R]}{[R]^{2}} = -k int_{0}^{t} dtend{array} )

From the power rule of integration, we have:

(egin{array}{l}int frac{dx}{x^{2}} = -frac{1}{x} + Cend{array} )

Where C is the constant of Integration. Now, using this power rule in the previous equation, the following equation can be attained.

(egin{array}{l}frac{1}{[R]_{t}} – frac{1}{[R]_{0}} = ktend{array} )

Which is the required integrated rate expression of second order reactions.

Graph of a Second Order Reaction

Generalizing [R] t as [R] and rearranging the integrated rate law equation of reactions of the second order, the following reaction is obtained.

(egin{array}{l}frac{1}{[R]} = kt + frac{1}{[R]_{0}}end{array} )

Plotting a straight line (y=mx + c) corresponding to this equation (y = 1/[R] , x = t , m = k , c = 1/[R] 0 ) It can be observed that the slope of the straight line is equal to the value of the rate constant, k.

Half-Life of Second-Order Reactions

The half-life of a chemical reaction is the time taken for half of the initial amount of reactant to undergo the reaction. Therefore, while attempting to calculate the half-life of a reaction, the following substitutions must be made:

(egin{array}{l}[R] = frac{[R]_{0}}{2}end{array} )

And,

(egin{array}{l}t = t_{1/2}end{array} )

Now, substituting these values in the integral form of the rate equation of second order reactions, we get:

(egin{array}{l}frac{1}{frac{[R]_{0}}{2}} – frac{1}{[R]_{0}} = kt_{1/2}end{array} )

Therefore, the required equation for the half life of second order reactions can be written as follows.

(egin{array}{l}t_{1/2} = frac{1}{k[R]_{0}}end{array} )

This equation for the half life implies that the half life is inversely proportional to the concentration of the reactants. To learn more about the second-order reaction from the experts you can register to BYJU’S.

How do you check k-means performance?

We need to calculate SSE to evaluate K-Means clustering using Elbow Criterion. The idea of the Elbow Criterion method is to choose the k (no of cluster) at which the SSE decreases abruptly. The SSE is defined as the sum of the squared distance between each member of the cluster and its centroid.

stackoverflow.com - Scikit K-means clustering performance measure - Stack Overflow

I'm trying to do a clustering with K-means method but I would like to measure the performance of my clustering. I'm not an expert but I am eager to learn more about clustering.

Here is my code :

import pandas as pd from sklearn import datasets #loading the dataset iris = datasets.load_iris() df = pd.DataFrame(iris.data) #K-Means from sklearn import cluster k_means = cluster.KMeans(n_clusters=3) k_means.fit(df) #K-means training y_pred = k_means.predict(df) #We store the K-means results in a dataframe pred = pd.DataFrame(y_pred) pred.columns = ['Species'] #we merge this dataframe with df prediction = pd.concat([df,pred], axis = 1) #We store the clusters clus0 = prediction.loc[prediction.Species == 0] clus1 = prediction.loc[prediction.Species == 1] clus2 = prediction.loc[prediction.Species == 2] k_list = [clus0.values, clus1.values,clus2.values] Now that I have my KMeans and my three clusters stored, I'm trying to use the Dunn Index to measure the performance of my clustering (we seek the greater index) For that purpose I import the jqm_cvi package (available here)

from jqmcvi import base base.dunn(k_list)

My question is : does any clustering internal evaluation already exist in Scikit Learn (except from silhouette_score) ? Or in another well known library ?

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What is a 2 order reaction?

Is it OK to snap strangers?

What are the four types of social media content?

Second Order Reaction

Table of Contents

What is a Second Order Reaction?

r = k[A]x[B]y

Examples of Second Order Reactions

A few examples of second order reactions are given below:

(egin{array}{l}H^{+} + OH^{-} ightarrow H_{2}Oend{array} )

(egin{array}{l}C + O_{2} ightarrow CO + Oend{array} )

(egin{array}{l}2NO_{2} ightarrow 2NO + O_{2}end{array} )

(egin{array}{l}2HI ightarrow I_{2} + H_{2}end{array} )

These reactions involve one second order reactant yielding the product.

Differential and Integrated Rate Equation for Second Order Reactions

(egin{array}{l}frac{-d[R]}{dt} = k[R]^{2}end{array} )

(egin{array}{l}frac{d[R]}{[R]^{2}} = -k dtend{array} )

(egin{array}{l}int_{[R]_{0}}^{[R]_{t}} frac{d[R]}{[R]^{2}} = -k int_{0}^{t} dtend{array} )

From the power rule of integration, we have:

(egin{array}{l}int frac{dx}{x^{2}} = -frac{1}{x} + Cend{array} )

(egin{array}{l}frac{1}{[R]_{t}} – frac{1}{[R]_{0}} = ktend{array} )

Which is the required integrated rate expression of second order reactions.

Graph of a Second Order Reaction

(egin{array}{l}frac{1}{[R]} = kt + frac{1}{[R]_{0}}end{array} )

Half-Life of Second-Order Reactions

(egin{array}{l}[R] = frac{[R]_{0}}{2}end{array} )

And,

(egin{array}{l}t = t_{1/2}end{array} )

(egin{array}{l}frac{1}{frac{[R]_{0}}{2}} – frac{1}{[R]_{0}} = kt_{1/2}end{array} )

(egin{array}{l}t_{1/2} = frac{1}{k[R]_{0}}end{array} )

Other important links:

What are the best media jobs?

How many views is viral TikTok?

How do you check k-means performance?

Here is my code :

from jqmcvi import base base.dunn(k_list)

My question is : does any clustering internal evaluation already exist in Scikit Learn (except from silhouette_score) ? Or in another well known library ?

What is the fastest song to reach 100 million views?

How many followers do you need to call yourself an influencer?

Can you make money with 5000 Instagram followers?

Which content is most popular on Instagram?

(egin{array}{l}H^{+} + OH^{-} ightarrow H_{2}Oend{array} )

(egin{array}{l}C + O_{2} ightarrow CO + Oend{array} )

(egin{array}{l}2NO_{2} ightarrow 2NO + O_{2}end{array} )

(egin{array}{l}2HI ightarrow I_{2} + H_{2}end{array} )

(egin{array}{l}frac{-d[R]}{dt} = k[R]^{2}end{array} )

(egin{array}{l}frac{d[R]}{[R]^{2}} = -k dtend{array} )

(egin{array}{l}int_{[R]_{0}}^{[R]_{t}} frac{d[R]}{[R]^{2}} = -k int_{0}^{t} dtend{array} )

(egin{array}{l}int frac{dx}{x^{2}} = -frac{1}{x} + Cend{array} )

(egin{array}{l}frac{1}{[R]_{t}} – frac{1}{[R]_{0}} = ktend{array} )

(egin{array}{l}frac{1}{[R]} = kt + frac{1}{[R]_{0}}end{array} )

(egin{array}{l}[R] = frac{[R]_{0}}{2}end{array} )

(egin{array}{l}t = t_{1/2}end{array} )

(egin{array}{l}frac{1}{frac{[R]_{0}}{2}} – frac{1}{[R]_{0}} = kt_{1/2}end{array} )

(egin{array}{l}t_{1/2} = frac{1}{k[R]_{0}}end{array} )