Social Media Means
Photo by DS stories Pexels Logo Photo: DS stories

What is K in first order?

'k' is the rate constant of the first-order reaction, whose units are s- 1.

byjus.com - First-Order Reactions (Chemical Kinetics) - Free Study Material - Byju's
Who is the father of 4p?
Who is the father of 4p?

Edmund Jerome McCarthy Edmund Jerome McCarthy (February 20, 1928 – December 3, 2015) was an American marketing professor and author. He proposed...

Read More »
Last updated Sep 29, 2022
Can you run an ultra While Pregnant?
Can you run an ultra While Pregnant?

For women who can regularly run marathon and ultramarathon distances prior to pregnancy, running them in a non-competitive way during pregnancy...

Read More »
Last updated Jul 24, 2019

First-Order Reactions

Introduction

A first-order reaction is one in which the rate of reaction is proportional to the concentration of the reactant. To put it another way, doubling the concentration doubles the reaction rate. A first-order reaction can have one or two reactants, as in the case of the decomposition reaction.

Table of Content

What is a First-Order Reaction?

A first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants. Thus, the order of these reactions is equal to 1.

Examples of First-Order Reactions

SO 2 Cl 2 → Cl 2 + SO 2

Cl → Cl + SO 2N 2 O 5 → O 2 + 4NO 2 O → O + 4NO 2H 2 O 2 → 2H 2 O + O 2

Differential Rate Law for a First-Order Reaction

A differential rate law can be employed to describe a chemical reaction at a molecular level. The differential rate expression for a first-order reaction can be written as:

Rate = -d[A]/dt = k[A]1 = k[A]

Where,

‘k’ is the rate constant of the first-order reaction, whose units are s -1 .

. ‘[A]’ denotes the concentration of the first-order reactant ‘A’.

d[A]/dt denotes the change in the concentration of the first-order reactant ‘A’ in the time interval ‘dt’.

Integrated Rate Law for a First-Order Reaction

Integrated rate expressions can be used to experimentally calculate the value of the rate constant of a reaction. To obtain the integral form of the rate expression for a first-order reaction, the differential rate law for the first-order reaction must be rearranged as follows.

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

(egin{array}{l}Rightarrow frac{d[A]}{[A]} = -kdtend{array} )

Integrating both sides of the equation, the following expression is obtained.

(egin{array}{l}int_{[A]_0}^{[A]}frac{d[A]}{[A]} = -int_{t_0}^{t}kdtend{array} )

Which can be rewritten as:

(egin{array}{l}int_{[A]_0}^{[A]}frac{1}{[A]}d[A] = -int_{t_0}^{t}kdtend{array} )

Since

(egin{array}{l}intfrac{1}{x} = ln(x) end{array} )

ln[A] – ln[A] 0 = -kt

What attracts Gen Z?
What attracts Gen Z?

Provide clear career paths, mentorship programs, and training to help attract Gen Z to your company. These programs can prove to Gen Z candidates...

Read More »
Last updated Oct 25, 2022
What is the hottest job in 2022?
What is the hottest job in 2022?

List of Hottest Job in 2022 Health workers. Jobs in the health sector still dominate the jobs that are most needed in the future such as nurses,...

Read More »
Last updated Sep 28, 2022

ln[A] = -kt + ln[A] 0 (or) ln[A] = ln[A] 0 – kt Raising each side of the equation to the exponent ‘e’ (since eln(x) = x), the equation is transformed as follows:

(egin{array}{l}e^{ln[A]} = e^{ln[A]_0 – kt}end{array} )

Therefore,

(egin{array}{l}[A] = [A]_0 e^{-kt}end{array} )

This expression is the integrated form of the first-order rate law.

Graphical Representation of a First-Order Reaction

The concentration v/s time graph for a first-order reaction is provided below.

For first-order reactions, the equation ln[A] = -kt + ln[A] 0 is similar to that of a straight line (y = mx + c) with slope -k. This line can be graphically plotted as follows. Thus, the graph for ln[A] v/s t for a first-order reaction is a straight line with slope -k.

Half-Life of a First-Order Reaction

The half-life of a chemical reaction (denoted by ‘t 1/2 ’) is the time taken for the initial concentration of the reactant(s) to reach half of its original value. Therefore,

At t = t 1/2 , [A] = [A] 0 /2

Where [A] denotes the concentration of the reactant and [A] 0 denotes the initial concentration of the reactant. Substituting the value of A = [A] 0 /2 and t = t 1/2 in the equation [A] = [A] 0 e-kt:

(egin{array}{l}frac{[A]_0}{2} = [A]_0 e^{-kt_{1/2}}end{array} )

(egin{array}{l}Rightarrow frac{1}{2} = e^{-kt_{1/2}}end{array} )

Taking the natural logarithm of both sides of the equation to eliminate ‘e’, the following equation is obtained.

(egin{array}{l}ln(frac{1}{2}) = -kt_{1/2}end{array} )

(egin{array}{l}Rightarrow t_{1/2} = frac{0.693}{k}end{array} )

Thus, the half-life of a first-order reaction is equal to 0.693/k (where ‘k’ denotes the rate constant, whose units are s-1). Frequently Asked Questions – FAQs What is the definition of a first-order reaction? A first-order reaction can be defined as a chemical reaction for which the reaction rate is entirely dependent on the concentration of only one reactant. In such reactions, if the concentration of the first-order reactant is doubled, then the reaction rate is also doubled. Similarly, if the first-order reactant concentration is increased five-fold, it will be accompanied by a 500% increase in the reaction rate. What are the differential rate law and the integrated rate law for a first-order reaction? The differential rate law for a first-order reaction can be expressed as follows: Rate = -d[A]/dt = k[A] The integrated rate equation for a first-order reaction is: [A] = [A] 0 e-kt [A] = [A] Where, [A] is the current concentration of the first-order reactant

[A] 0 is the initial concentration of the first-order reactant

Is Google pay a payment gateway?
Is Google pay a payment gateway?

Yes, Google Pay API supports onboarding ecommerce platforms. Payment processor, gateway, or ecommerce platform partners that host a checkout page...

Read More »
Last updated Nov 11, 2018
What to do with $100000 for a year?
What to do with $100000 for a year?

Investing 100k In Real Estate. Many seasoned investors will argue that the best investment for 100K is in real estate. ... Individual Stocks....

Read More »
Last updated Mar 17, 2020

is the initial concentration of the first-order reactant t is the time elapsed since the reaction began

k is the rate constant of the first-order reaction

e is Euler’s number (which is the base of the natural logarithm) What is the relationship between the half-life and the rate constant for a first-order reaction? The half-life of a chemical reaction is the time required for the concentration of the reactants to reach half of their initial value. For first-order reactions, the relationship between the reaction half-life and the reaction rate constant is given by the expression: t 1/2 = 0.693/k Where ‘t 1/2 ’ denotes the half-life of the reaction and ‘k’ denotes the rate constant. What are the units of the rate constant for a first-order reaction? For first-order reactions, the rate constant is expressed in s1 (reciprocal seconds). The units of the rate constant can be determined using the following expression: Units of k = M(1-n).s-1 (where ‘n’ is the order of the reaction) Since the reaction order of a first-order reaction is equal to 1, the equation is transformed as follows: Units of k = M(1-1).s-1 = s-1 For a first-order reaction, if a graph is plotted with ln[A] on the Y-axis and time on the X-axis, what will it look like? The graph will be a straight line with a slope of -k. To learn more about first-order reactions and other important concepts in chemical kinetics, register with BYJU’S and download the mobile application on your smartphone.

byjus.com - First-Order Reactions (Chemical Kinetics) - Free Study Material - Byju's
How do I overcome social media anxiety?
How do I overcome social media anxiety?

If it's making you feel more anxious, limiting your own exposure to social media intake in a structured way can be helpful. One example could be...

Read More »
Last updated Aug 16, 2019
Can I retire on a million dollars?
Can I retire on a million dollars?

One common rule of thumb is to withdraw 4% from retirement funds each year. Four percent of $1 million provides $40,000 each year for retirement...

Read More »
Last updated Jul 4, 2022
How can I earn real money fast?
How can I earn real money fast?

How to make money online Pick up freelance work online. ... Test websites and apps. ... Pick up tasks on Amazon's Mechanical Turk. ... Take surveys...

Read More »
Last updated Mar 11, 2019
How do I get started in social work?
How do I get started in social work?

Becoming a social worker in seven common steps: Complete a Bachelor's Degree in Social Work or a Related Field. Pursue a Master's Degree in Social...

Read More »
Last updated May 23, 2021