   # Formic acid decomposes at 550 °C according to the equation HCO 2 H(g) → CO 2 (g) + H 2 (g) The reaction follows first-order kinetics. In an experiment, it is determined that 75% of a sample of HCO 2 H has decomposed in 72 seconds. Determine t ½ , for this reaction. ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 14, Problem 53GQ
Textbook Problem
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## Formic acid decomposes at 550 °C according to the equationHCO2H(g) → CO2(g) + H2(g)The reaction follows first-order kinetics. In an experiment, it is determined that 75% of a sample of HCO2H has decomposed in 72 seconds. Determine t½, for this reaction.

Interpretation Introduction

Interpretation:

For the given first order reaction, about 75% of the reactant get decomposed in 72 seconds and the half-life for the reaction has to be determined.

Concept introduction:

In order to establish the plausibility of a mechanism, one must compare the rate law of the rate determining step to the experimentally determined rate law.

Rate determining step: In a chemical reaction the rate determining step is the slowest step. The rate of the reaction depends on the rate of that slowest step.

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Rate constant: The rate constant for a chemical reaction is the proportionality term in the chemical reaction rate law which gives the relationship between the rate and the concentration of the reactant present in the chemical reaction.

Rate order: It is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction. The order of the reaction is directly proportional to the concentration of the reactants.

Half-Life: It is defined as the time required to reduce the concentration of reactant present in the reaction to one half of its initial value.

Activation energy: It is the minimum energy required by the reacting species in order to undergo chemical reaction.

Intermediate species: It is the species formed during the middle of the chemical reaction between the reactant and the desired product.

### Explanation of Solution

Given:

The reaction is a first order reaction.

75% of the given reactant concentration takes 72 s to decompose from its initial concentration.

In order to find the half-life period for the given reaction, the half-period expression for the first-order reaction should be used.

The half-life period for the first order reaction is as follows:

t1/2=ln2k

For the given reaction only the percent decomposition at particular time is given but not the rate constant k hence the following expression should be used in order to calculate the half-life.

[A]t[A]0=12nwhere,[A]t=finialconcentration at time t[A]0=initialconcentration

[A]t[A]0=12n25%100%=12nsince,[A]t=cocentration after given timeȀ

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