/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 59 \(75 \%\) of a first-order react... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

\(75 \%\) of a first-order reaction was completed in \(32 \mathrm{~min}\). When was \(50 \%\) of the reaction completed? (a) \(24 \mathrm{~min}\) (b) \(16 \mathrm{~min}\) (c) \(8 \mathrm{~min}\) (d) \(64 \mathrm{~min}\)

Short Answer

Expert verified
The first-order reaction was 50% completed in 32 minutes.

Step by step solution

01

Understand the Nature of a First-Order Reaction

First-order reactions have a constant half-life, regardless of the concentration of the reactants. This means that the time taken for the concentration of a reactant to fall to half its initial value is always the same.
02

Identify Given Information and What is Being Asked

It is given that 75% of the reaction is completed in 32 minutes. We are asked to find the time when 50% of the reaction is completed.
03

Calculate the Time for 50% Completion

Since the reaction is first-order, the time taken to go from 100% to 50% (which is the half-life of the reaction) is the same as the time taken to go from 50% to 25%. This is because each 'half-life' period will result in the concentration halving. If 75% completion corresponds to having 25% left and it takes 32 minutes, then one half-life has passed. Therefore, in one half-life (which is the time to go from 100% to 50%), the reaction would take 32 minutes.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Kinetics
At its core, chemical kinetics is the study of how fast chemical reactions occur. It's a central part of understanding chemistry, providing insights into reaction mechanisms and the factors that influence the speed of reactions. For students diving into chemical kinetics, it's crucial to comprehend how various variables—such as temperature, concentration of reactants, and the presence of catalysts—can affect the reaction rate.

A first-order reaction, one of the basic reaction types in kinetics, is characterized by its reaction rate being directly proportional to the concentration of only one reactant. What makes this reaction type fascinating is its consistent half-life, which remains unchanged regardless of the initial concentration of the reactant. This property is incredibly useful in calculations and predictions regarding the reaction progress.

In educational settings like NEET chemistry preparation, grasping chemical kinetics is imperative as it lays the groundwork for more complex topics and practical applications in fields such as pharmacology and environmental science.
Reaction Rate
Understanding the reaction rate is essential for mastery in chemistry and succeeding in competitive exams like NEET. Reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. Simplified, it's how quickly a reaction proceeds. For first-order reactions, the rule of thumb is straightforward—the rate is directly proportional to the concentration of one reactant.

To practically apply this knowledge, assume we're observing a colored chemical dissipate in a solution. The faster the color fades, the higher the reaction rate. In a first-order reaction, this fading would occur at a rate that, mathematically, is expressed as -\frac{{d[A]}}{{dt}} = k[A], where \([A]\) is the concentration of the reactant, \(t\) is time, and \(k\) is the rate constant.

For NEET aspirants, understanding how to use half-life, which for a first-order reaction is constant and independent of concentration, is a powerful tool for solving problems efficiently.
NEET Chemistry Preparation
Preparing for competitive exams like the National Eligibility cum Entrance Test (NEET) demands a strong foundation in chemistry concepts. One must be well-versed in topics like chemical kinetics and the nature of different reactions to crack the chemistry section.

Focused practice on reaction rates and calculations involving half-life can significantly enhance your performance in the exam. Remember, for first-order reactions, the half-life is a consistent value—a critical point that simplifies complex problems.

For instance, when dealing with exercises related to the half-life of a reaction, it's essential to apply logical reasoning and mathematical skills. These problems are structured to test both your conceptual understanding and problem-solving approach—a balance NEET aims to assess in prospective medical students.

Regular revisions, solving past papers, and an in-depth grasp of the basic principles, like the steps demonstrated for the first-order reaction half-life problem, are strategies that can lead to success in NEET chemistry.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A substance reacts according to first-order kinetics. The rate constant for the reaction is \(1 \times 10^{-2} \mathrm{sec}^{1} .\) Its initial concentration is IM. Its initial rate is: (a) \(2 \times 10^{2} \mathrm{Ms}^{-1}\) (b) \(1 \times 10^{2} \mathrm{Ms}^{-1}\) (c) \(1 \times 10^{-2} \mathrm{Ms}^{-1}\) (d) \(2 \times 10^{-2} \mathrm{Ms}^{-1}\)

Which of the following relation is correct for a first order reaction? \((k=\) rate constant; \(\mathrm{r}=\) rate of reaction; \(\mathrm{C}=\) conc. of reactant) (a) \(k=\mathrm{r} \times \mathrm{C}^{2}\) (b) \(k=\mathrm{r} \mathrm{x}\) (c) \(k=\mathrm{C} / r\) (d) \(k=\mathrm{r} / \mathrm{C}\)

For a zero-order reaction, the plot of concentration vs time is linear with: (a) +ve slope and zero intercept (b) - ve slope and zero intercept (c) +ve slope and non-zero intercept (d) - ve slope and non-zero intercept

Which of the following statements is correct? (1) Order of a reaction can be known from experimental results and not from the stoichiometry of a reaction. (2) Molecularity a reaction refers to (i) each of the elementary steps in (an overall mechanism of) a complex reaction or (ii) a single step reaction. (3) Overall molecularity of a reaction may be determined in a manner similar to overall order of reaction. (4) Overall order of a reaction \(\mathrm{A}^{\mathrm{m}}+\mathrm{B}^{\mathrm{n}} \longrightarrow \mathrm{AB}_{\mathrm{x}}\) is \(\mathrm{m}+\mathrm{n}\) Select the correct answer using the following codes: (a) 2 and 3 (b) 1,3 and 4 (c) 2,3 and 4 (d) 1,2 and 3

For the first-order reaction half-life is \(14 \mathrm{~s}\). The time required for the initial concentration to reduce to \(1 / 8\) th of its value is: (a) \(21 \mathrm{~s}\) (b) \(32 \mathrm{~s}\) (c) \(42 \mathrm{~s}\) (d) \(142 \mathrm{~s}\)

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.