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Definition of reaction rate

For a reaction of the form A+B→CA+B→C, the rate can be expressed in terms of the change in concentration of any of its components

in which Δ[A] is the difference between the concentration of A over the time interval t₂ – t₁:

Notice the minus signs in the first two examples above. The concentration of a reactant always decreases with time, so Δ[A]and Δ[A] are both negative. Since negative rates do not make much sense, rates expressed in terms of a reactant concentration are always preceded by a minus sign to make the rate come out positive.

Consider now a reaction in which the coefficients are different:

A+3B→2D

Example 1

For the oxidation of ammonia

4NH3+3O2→2N2+6H2O

it was found that the rate of formation of N₂ was 0.27 mol L^–1 s^–1.

1. 
   At what rate was water being formed?
   
2. 
   At what rate was ammonia being consumed?
   

3 × (0.27 mol L^–1 s^–1) = 0.81 mol L^–1 s^–1.

b) 4 moles of NH₃ are consumed for every 2 moles of N₂ formed, so the rate of disappearance of ammonia is

2 × (0.27 mol L^–1 s^–1) = 0.54 mol L^–1 s^–1.

Instantaneous rates

Thus for the reaction whose progress is plotted here, the actual rate (as measured by the increasing concentration of product) varies continuously, being greatest at time zero. The instantaneous rate of a reaction is given by the slope of a tangent to the concentration-vs.-time curve.

If you do not know calculus, bear in mind that the larger the time interval Δt, the smallerwill be the precision of the instantaneous rate.

Introduction

A+B⟶AB

Figure 1.  The above picture shows a hypthetical reaction profile in which the reactants (red) decrease in concentration as the products increase in concetration (blue).

Looking at Figure 1 above, we can see that the rate can be measured in terms of either reactant (A or B) or either product (C or D). Not all variables are needed to solve for the rate. Therefore, if you have the value for "A" as well as the value for "a" you can solve for the reaction rate. 

You can also notice from Formula 1 above that, the change in reactants over the change in time must have a negative sign in front of them. The reason for this is because the reactants are decreasing as a function of time, the rate would come out to be negative (because it is the reverse rate). Therefore, putting a negative sign in front of the variable will allow for the solution to be a positive rate.

Rate Laws and Rate Constants

Rate=k[A]^s[B]^t

As you can see from equation 2 above, the reaction rate is dependent on the concentration of the reactants as well as the rate constant. However, there are also other factors that can influence the rate of reaction. These factors include temperature and catalysts. When you are able to write a rate law equation for a certain reaction, you can determine the Reaction Order based on the values of s and t. 

Temperature Dependence

Reaction Rate

However, increasing the temperature will not always increase the rate of the reaction. If the temperature of a reaction were to reach a certain point where the reactant will begin to degrade, it will decrease the rate of the reaction.

Rate Constant

k=Ae^−Ea/RT

As you can see from equation 3, the rate constant kk is dependent on the temperature (in Kelvins) and also the Activation energy, E_a(in joules)_. "A" in the equation represents a pre-exponential factor that has the same units as k. Finally, R is the universal gas constant.

Catalysts

Reaction Order

Example 1:

Rate=k[A]^s[B]^t

Reaction Order=s+t

NOTE: The rate of reaction must be a non-negative value. It can be zero and does not need to be an integer. 

As shown in Formula 5, the complete reaction order is equal to the sum of "s" and "t." But what does each of these variables by themself mean? Each variable represents the order of the reaction with respect to the reactant it is placed on. In this certain situation, s is the order of the reaction with respect to [A] and t is the order of the reaction with respect to [B]. 

Here is an example of how you can look at this: If a reaction order with respect to [A] was 2 (s = 2) and [B] was 1 (t = 1), then that basically means that the concentration of reactant A is decreasing by a factor of 2 and the concentration of [B] is decrease by a factor of 1. 

So if you have a reation order of Zero (s + t = 0), this basically means that the concentration of the reactants does not affect the rate of reaction. You could remove or add reactants to the mixture but the rate will not change. 

Table 1. The table below displays numerous values and equations utilized when observing chemical kinetics for numerous reactions types
	Zero-Order	First-Order	Second-Order
Rate Law	Rate= k	Rate= k[A]	Rate= k[A]2
Integrated Rate Law	[A]t= −kt+[A]0	ln[A]t= −kt+ln[A]0	1[A]t=−kt+1[A]0
Units of Rate Constant (k):	molL−1s−1	s−1	Lmol−1s−1
Linear Plot to Determine (k):	[A] versus time	ln[A] versus time	versus time
Relationship of Rate Constant to the Slope of Straight Line:	slope= −k	slope= −k	slope= k
Half-life:

Sample Problems

2. TRUE or FALSE: Changes in the temperature or the introduction of a catalyst will affect the rate constant of a reaction

For sample problems 3-6, use Formula 6 to answer the questions

H2O⟶2H2+O2(6)(6)H2O⟶2H2+O2

*Assume the reaction occurs at constant temperature

3. For the given reaction above, state the rate law.

4. State the overall order of the reaction.

5. Find the rate, given k = 1.14 x 10^-2 and [H₂O] = 2.04M

6. Find the half-life of the reaction.

Answers

2. FALSE. The rate constant is not dependant on the presence of a catalyst. Catalysts, however, can effect the total rate of a reaction.

3.  Rate= k[H₂O] Rate= k[H₂O]

4. First - Order

5. 2.33 x 10^-2 s^-1

6. 29.7 s

3.3. A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and formulae, wherein the reactant entities are given on the left-hand side and the product entities on the right-hand side.^[1] The coefficients next to the symbols and formulae of entities are the absolute values of the stoichiometric numbers. The first chemical equation was diagrammed by Jean Beguin in 1615.^[2]

A chemical equation consists of the chemical formulas of the reactants (the starting substances) and the chemical formula of the products (substances formed in the chemical reaction). The two are separated by an arrow symbol ({\displaystyle \rightarrow }, usually read as "yields") and each individual substance's chemical formula is separated from others by a plus sign.

As an example, the equation for the reaction of hydrochloric acid with sodium can be denoted:

2 HCl +2 Na →2 NaCl + H 2

This equation would be read as "two HCl plus two Na yields two NaCl and H two." But, for equations involving complex chemicals, rather than reading the letter and its subscript, the chemical formulas are read using IUPAC nomenclature. Using IUPAC nomenclature, this equation would be read as "hydrochloric acid plus sodium yields sodium chloride andhydrogen gas."

This equation indicates that sodium and HCl react to form NaCl and H₂. It also indicates that two sodium molecules are required for every two hydrochloric acid molecules and the reaction will form two sodium chloride molecules and one diatomic molecule of hydrogen gas molecule for every two hydrochloric acid and two sodium molecules that react. Thestoichiometric coefficients (the numbers in front of the chemical formulas) result from the law of conservation of mass and the law of conservation of charge

In order to write a correct chemical equation, we must balance all of the atoms on the left side of thereaction with the atoms on the right side. Let's look at another example. If you use a gas stove to cook your dinner, chances are that your stove burns natural gas, which is primarily methane. Methane (CH₄) is a molecule that contains four hydrogen atoms bonded to one carbon atom. When you lightthe stove, you are supplying the activation energy to start the reaction of methane with oxygen in the air. During this reaction, chemical bonds break and re-form and the products that are produced are carbon dioxide and water vapor (and, of course, light and heat that you see as the flame). The unbalanced chemical equation would be written:

Although we have discussed balancing equations in terms of numbers of atoms and molecules, keep in mind that we never talk about a single atom (or molecule) when we use chemical equations. This is because single atoms (and molecules) are so tiny that they are difficult to isolate. Chemical equations are discussed in relation to the number of moles of reactants and products used or produced (see our The Mole module). Because the mole refers to a standard number of atoms (or molecules), the term can simply be substituted into chemical equations. Thus, the balanced methane equation above can also be interpreted as reading, "one mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water."

Lewis Theory

Lewis Acids and Bases

1. 
   An acid is a substance that accepts a lone pair of electrons.
   
2. 
   A base is a substance that donates a lone pair electrons.
   

This reaction shows a Lewis base (NH₃) donating an electron pair to a Lewis acid (H⁺) to form an adduct (NH₄⁺).