Solution : For a first order reaction, the rate of the reaction doubled as the concentration of the reactant is doubled because the rate is directly proportional to the concentration of the reactants. Show
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The factors that affect the reaction rate of a chemical reaction, which may determine whether a desired product is formed. In this section, we will show you how to quantitatively determine the reaction rate. Rate LawsTypically, reaction rates decrease with time because reactant concentrations decrease as reactants are converted to products. Reaction rates generally increase when reactant concentrations are increased. This section examines mathematical expressions called rate laws, which describe the relationships between reactant rates and reactant concentrations. Rate laws are mathematical descriptions of experimentally verifiable data. Rate laws may be written from either of two different but related perspectives. A differential rate law expresses the reaction rate in terms of changes in the concentration of one or more reactants (Δ[R]) over a specific time interval (Δt). In contrast, an integrated rate law describes the reaction rate in terms of the initial concentration ([R]0) and the measured concentration of one or more reactants ([R]) after a given amount of time (t); integrated rate laws are discussed in more detail later. The integrated rate law is derived by using calculus to integrate the differential rate law. Whether using a differential rate law or integrated rate law, always make sure that the rate law gives the proper units for the reaction rate, usually moles per liter per second (M/s). Reaction OrdersFor a reaction with the general equation: \[aA + bB \rightarrow cC + dD \label{14.3.1} \] the experimentally determined rate law usually has the following form: \[\text{rate} = k[A]^m[B]^n \label{14.3.2}\] The proportionality constant (k) is called the rate constant, and its value is characteristic of the reaction and the reaction conditions. A given reaction has a particular rate constant value under a given set of conditions, such as temperature, pressure, and solvent; varying the temperature or the solvent usually changes the value of the rate constant. The numerical value of k, however, does not change as the reaction progresses under a given set of conditions. The reaction rate thus depends on the rate constant for the given set of reaction conditions and the concentration of A and B raised to the powers m and n, respectively. The values of m and n are derived from experimental measurements of the changes in reactant concentrations over time and indicate the reaction order, the degree to which the reaction rate depends on the concentration of each reactant; m and n need not be integers. For example, Equation \(\ref{14.3.2}\) tells us that Equation \(\ref{14.3.1}\) is mth order in reactant A and nth order in reactant B. It is important to remember that n and m are not related to the stoichiometric coefficients a and b in the balanced chemical equation and must be determined experimentally. The overall reaction order is the sum of all the exponents in the rate law: m + n. Note Under a given set of conditions, the value of the rate constant does not change as the reaction progresses. Although differential rate laws are generally used to describe what is occurring on a molecular level during a reaction, integrated rate laws are used to determine the reaction order and the value of the rate constant from experimental measurements. (Click the link for a presentation of the general forms for integrated rate laws.)  These reactions are important in maintaining steady levels of NO. The following table lists kinetics data for the reaction of NO with O2 at 25°C: \[2NO(g) + O_2(g) \rightarrow 2NO_2(g)\] Determine the rate law for the reaction and calculate the rate constant. Experiment[NO]0 (M)[O2]0 (M)Initial Rate (M/s)10.02350.01257.98 × 10−320.02350.025015.9 × 10−330.04700.012532.0 × 10−340.04700.025063.5 × 10−3Given: balanced chemical equation, initial concentrations, and initial rates Asked for: rate law and rate constant Strategy:
Solution A Comparing Experiments 1 and 2 shows that as [O2] is doubled at a constant value of [NO2], the reaction rate approximately doubles. Thus the reaction rate is proportional to [O2]1, so the reaction is first order in O2. Comparing Experiments 1 and 3 shows that the reaction rate essentially quadruples when [NO] is doubled and [O2] is held constant. That is, the reaction rate is proportional to [NO]2, which indicates that the reaction is second order in NO. Using these relationships, we can write the rate law for the reaction: rate = k[NO]2[O2] B The data in any row can be used to calculate the rate constant. Using Experiment 1, for example, gives \[k=\dfrac{\textrm{rate}}{[\mathrm{NO}]^2[\mathrm{O_2}]}=\dfrac{7.98\times10^{-3}\textrm{ M/s}}{(0.0235\textrm{ M})^2(0.0125\textrm{ M})}=1.16\times10^3\;\mathrm{ M^{-2}\cdot s^{-1}}\] Alternatively, using Experiment 2 gives \[k=\dfrac{\textrm{rate}}{[\mathrm{NO}]^2[\mathrm{O_2}]}=\dfrac{15.9\times10^{-3}\textrm{ M/s}}{(0.0235\textrm{ M})^2(0.0250\textrm{ M})}=1.15\times10^3\;\mathrm{ M^{-2}\cdot s^{-1}}\] The difference is minor and associated with significant digits and likely experimental error in making the table. The overall reaction order \((m + n) = 3\), so this is a third-order reaction whose rate is determined by three reactants. The units of the rate constant become more complex as the overall reaction order increases. Exercise \(\PageIndex{2}\) The peroxydisulfate ion (S2O82−) is a potent oxidizing agent that reacts rapidly with iodide ion in water: \[S_2O^{2−}_{8(aq)} + 3I^−_{(aq)} \rightarrow 2SO^{2−}_{4(aq)} + I^−_{3(aq)}\] The following table lists kinetics data for this reaction at 25°C. Determine the rate law and calculate the rate constant. Experiment[S2O82−]0 (M)[I−]0 (M)Initial Rate (M/s)10.270.382.0520.400.383.0630.400.221.76Answer rate = k[S2O82−][I−]; k = 20 M−1·s−1 Initial Rates and Rate Law Expressions: https://youtu.be/VZl5dipsCEQ SummaryThe rate law for a reaction is a mathematical relationship between the reaction rate and the concentrations of species in solution. Rate laws can be expressed either as a differential rate law, describing the change in reactant or product concentrations as a function of time, or as an integrated rate law, describing the actual concentrations of reactants or products as a function of time. The rate constant (k) of a rate law is a constant of proportionality between the reaction rate and the reactant concentration. The exponent to which a concentration is raised in a rate law indicates the reaction order, the degree to which the reaction rate depends on the concentration of a particular reactant. 14.3: Effect of Concentration on Reaction Rates: The Rate Law is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. Why does doubling the concentration double the reaction rate?By doubling the reactant concentration, you would be actually quadrupling the reaction rate since 2 squared is 4. If it was a first-order reaction, rate is proportional to the first power, so doubling the reactant concentration doubles the reaction rate since 2 to the power of 1 is still 2.
When the concentration of a reactant A is doubled the rate of reaction increased by a factor of 4 the order of reaction with respect to A is?<br> In the question, since rate is directly proportional to the conc. Of reactant, hence the reaction is of first order.
When the concentration of A is doubled the rate is also doubled What is the order of reaction with respect to that reactant A?If the rate doubles when the concentration of reactant is doubled, the reaction is the first-order. If the rate becomes 4-fold times (quadruples) when the concentration of the reactant is doubled, the reaction is the second-order and similarly, the third, the fourth, and the higher orders.
When the concentration of A is doubled the rate increases by a factor of?If the concentration of A is doubled, the reaction rate doubles; if the concentration of A is increased by a factor of 10, the reaction rate increases by a factor of 10, and so forth.
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