Введение
В химической кинетике уравнение скорости (также известное как закон скорости или эмпирическое дифференциальное уравнение скорости) является эмпирическим дифференциальным математическим выражением для скорости реакции в зависимости от концентраций химических видов и постоянных параметров (обычно коэффициентов скорости и частных порядков реакции). Для многих реакций начальная скорость описывается степенным законом, таким как
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as
where [\mathrm{A}] and [\mathrm{B}] are the molar concentrations of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M). The exponents x and y are the partial orders of reaction for \mathrm{A} and \mathrm{B} and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. If the reaction takes place in a closed system at constant temperature and volume, without a build up of reaction intermediates, the reaction rate is defined as
where νi is the stoichiometric coefficient for chemical Xi, with a negative sign for a reactant. The initial reaction rate has some functional dependence on the concentrations of the reactants,
and this dependence is known as the rate equation or rate law. This law generally cannot be deduced from the chemical equation and must be determined by experiment. The constant k is called the rate constant. The exponents, which can be fractional,
In a dilute solution, an elementary reaction (one having a single step with a single transition state) is empirically found to obey the law of mass action. This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. The differential rate equation for an elementary reaction using product notation is:
Where:
is the rate of change of reactant concentration with respect to time. k is the rate constant of the reaction. represents the concentrations of the reactants, raised to the powers of their stoichiometric coefficients and multiplied together.
где [\mathrm{A}] и [\mathrm{B}] – молярные концентрации веществ \mathrm{A} и \mathrm{B}, обычно выражаемые в молях на литр (молярность, M). Показатели x и y – частные порядки реакции по отношению к \mathrm{A} и \mathrm{B}, а общий порядок реакции равен сумме этих показателей. Эти показатели часто являются положительными целыми числами, но могут быть и нулем, дробными или отрицательными. Порядок реакции – это число, которое количественно определяет степень влияния концентраций реагентов на скорость химической реакции. Иными словами, порядок реакции – это показатель степени, в которую возводится концентрация конкретного реагента. Если реакция протекает в замкнутой системе при постоянной температуре и объеме, без накопления промежуточных продуктов, скорость реакции определяется как
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as
where [\mathrm{A}] and [\mathrm{B}] are the molar concentrations of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M). The exponents x and y are the partial orders of reaction for \mathrm{A} and \mathrm{B} and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. If the reaction takes place in a closed system at constant temperature and volume, without a build up of reaction intermediates, the reaction rate is defined as
where νi is the stoichiometric coefficient for chemical Xi, with a negative sign for a reactant. The initial reaction rate has some functional dependence on the concentrations of the reactants,
and this dependence is known as the rate equation or rate law. This law generally cannot be deduced from the chemical equation and must be determined by experiment. The constant k is called the rate constant. The exponents, which can be fractional,
In a dilute solution, an elementary reaction (one having a single step with a single transition state) is empirically found to obey the law of mass action. This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. The differential rate equation for an elementary reaction using product notation is:
Where:
is the rate of change of reactant concentration with respect to time. k is the rate constant of the reaction. represents the concentrations of the reactants, raised to the powers of their stoichiometric coefficients and multiplied together.
где νi – стехиометрический коэффициент для химического вещества Xi, со знаком минус для реагента. Начальная скорость реакции функционально зависит от концентраций реагентов,
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as
where [\mathrm{A}] and [\mathrm{B}] are the molar concentrations of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M). The exponents x and y are the partial orders of reaction for \mathrm{A} and \mathrm{B} and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. If the reaction takes place in a closed system at constant temperature and volume, without a build up of reaction intermediates, the reaction rate is defined as
where νi is the stoichiometric coefficient for chemical Xi, with a negative sign for a reactant. The initial reaction rate has some functional dependence on the concentrations of the reactants,
and this dependence is known as the rate equation or rate law. This law generally cannot be deduced from the chemical equation and must be determined by experiment. The constant k is called the rate constant. The exponents, which can be fractional,
In a dilute solution, an elementary reaction (one having a single step with a single transition state) is empirically found to obey the law of mass action. This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. The differential rate equation for an elementary reaction using product notation is:
Where:
is the rate of change of reactant concentration with respect to time. k is the rate constant of the reaction. represents the concentrations of the reactants, raised to the powers of their stoichiometric coefficients and multiplied together.
и эта зависимость известна как уравнение скорости или закон скорости. Этот закон, как правило, нельзя вывести из химического уравнения и должен быть определен экспериментально. Константа k называется константой скорости. Показатели, которые могут быть дробными,
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as
where [\mathrm{A}] and [\mathrm{B}] are the molar concentrations of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M). The exponents x and y are the partial orders of reaction for \mathrm{A} and \mathrm{B} and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. If the reaction takes place in a closed system at constant temperature and volume, without a build up of reaction intermediates, the reaction rate is defined as
where νi is the stoichiometric coefficient for chemical Xi, with a negative sign for a reactant. The initial reaction rate has some functional dependence on the concentrations of the reactants,
and this dependence is known as the rate equation or rate law. This law generally cannot be deduced from the chemical equation and must be determined by experiment. The constant k is called the rate constant. The exponents, which can be fractional,
In a dilute solution, an elementary reaction (one having a single step with a single transition state) is empirically found to obey the law of mass action. This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. The differential rate equation for an elementary reaction using product notation is:
Where:
is the rate of change of reactant concentration with respect to time. k is the rate constant of the reaction. represents the concentrations of the reactants, raised to the powers of their stoichiometric coefficients and multiplied together.
В разбавленном растворе элементарная реакция (состоящая из одной стадии с одним переходным состоянием) эмпирически подчиняется закону действующих масс. Это предсказывает, что скорость зависит только от концентраций реагентов, возведенных в степени, равные их стехиометрическим коэффициентам. Дифференциальное уравнение скорости для элементарной реакции с использованием произведения концентраций:
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as
where [\mathrm{A}] and [\mathrm{B}] are the molar concentrations of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M). The exponents x and y are the partial orders of reaction for \mathrm{A} and \mathrm{B} and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. If the reaction takes place in a closed system at constant temperature and volume, without a build up of reaction intermediates, the reaction rate is defined as
where νi is the stoichiometric coefficient for chemical Xi, with a negative sign for a reactant. The initial reaction rate has some functional dependence on the concentrations of the reactants,
and this dependence is known as the rate equation or rate law. This law generally cannot be deduced from the chemical equation and must be determined by experiment. The constant k is called the rate constant. The exponents, which can be fractional,
In a dilute solution, an elementary reaction (one having a single step with a single transition state) is empirically found to obey the law of mass action. This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. The differential rate equation for an elementary reaction using product notation is:
Where:
is the rate of change of reactant concentration with respect to time. k is the rate constant of the reaction. represents the concentrations of the reactants, raised to the powers of their stoichiometric coefficients and multiplied together.
Где:
– скорость изменения концентрации реагента во времени. k – константа скорости реакции. – концентрации реагентов, возведенные в степень их стехиометрических коэффициентов и перемноженные.
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as
where [\mathrm{A}] and [\mathrm{B}] are the molar concentrations of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M). The exponents x and y are the partial orders of reaction for \mathrm{A} and \mathrm{B} and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the reactants. In other words, the order of reaction is the exponent to which the concentration of a particular reactant is raised. If the reaction takes place in a closed system at constant temperature and volume, without a build up of reaction intermediates, the reaction rate is defined as
where νi is the stoichiometric coefficient for chemical Xi, with a negative sign for a reactant. The initial reaction rate has some functional dependence on the concentrations of the reactants,
and this dependence is known as the rate equation or rate law. This law generally cannot be deduced from the chemical equation and must be determined by experiment. The constant k is called the rate constant. The exponents, which can be fractional,
In a dilute solution, an elementary reaction (one having a single step with a single transition state) is empirically found to obey the law of mass action. This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. The differential rate equation for an elementary reaction using product notation is:
Where:
is the rate of change of reactant concentration with respect to time. k is the rate constant of the reaction. represents the concentrations of the reactants, raised to the powers of their stoichiometric coefficients and multiplied together.
Нулевой порядок
Для реакций нулевого порядка скорость реакции не зависит от концентрации реагента, поэтому изменение его концентрации не оказывает влияния на скорость реакции. Таким образом, концентрация изменяется линейно во времени. Это может происходить, когда существует лимитирующий фактор, ограничивающий число молекул реагента, способных реагировать одновременно, например, если реакция требует контакта с ферментом или каталитической поверхностью. Многие ферментативно-катализируемые реакции являются реакциями нулевого порядка, при условии, что концентрация реагента значительно превышает концентрацию фермента, контролирующего скорость, что приводит к насыщению фермента. Например, биологическое окисление этанола до ацетальдегида ферментом печеночной алкогольдегидрогеназой (LADH) является реакцией нулевого порядка по этанолу. Аналогично, реакции с гетерогенным катализом могут быть реакциями нулевого порядка, если каталитическая поверхность насыщена. Например, разложение фосфина (PH3) на горячей вольфрамовой поверхности при высоком давлении является реакцией нулевого порядка по фосфину, который разлагается с постоянной скоростью.
Отрицательный порядок
Скорость реакции может иметь отрицательный частичный порядок по отношению к веществу. Например, превращение озона (O3) в кислород описывается уравнением скорости при избытке кислорода. Это соответствует второму порядку по озону и порядку (−1) по кислороду. Когда частичный порядок отрицателен, общий порядок реакции обычно считается неопределённым. В приведённом выше примере, например, реакция не описывается как реакция первого порядка, несмотря на то, что сумма частичных порядков равна единице, поскольку уравнение скорости более сложное, чем для простой реакции первого порядка.
Обобщение простого примера
Если концентрация в момент времени t = 0 отличается от указанной выше, то вышеприведенные упрощения становятся недействительными, и необходимо решать систему дифференциальных уравнений. Однако эту систему также можно решить точно, что приводит к следующим обобщенным выражениям: когда равновесная постоянная близка к единице, а скорости реакций очень велики, например, при конформационном анализе молекул, для определения констант скорости требуются другие методы, такие как, например, полный анализ формы спектральных линий в ЯМР-спектроскопии.
When the equilibrium constant is close to unity and the reaction rates very fast for instance in conformational analysis of molecules, other methods are required for the determination of rate constants for instance by complete lineshape analysis in NMR spectroscopy.
Параллельные или конкурирующие реакции
Когда вещество одновременно вступает в реакции с образованием двух различных продуктов, говорят, что происходит параллельная или конкурирующая реакция.
Одна реакция первого порядка и одна реакция второго порядка
Это может происходить при изучении бимолекулярной реакции, когда одновременно протекает гидролиз (который можно рассматривать как реакцию псевдо-первого порядка): гидролиз затрудняет изучение кинетики реакции, поскольку часть реагента расходуется в параллельной реакции. Например, A реагирует с R с образованием продукта C, но одновременно реакция гидролиза потребляет некоторое количество A с образованием B, побочного продукта: A + H2O → B и A + R → C. Уравнения скорости: и , где – псевдо-константа первого порядка. Интегрированное уравнение скорости для основного продукта [C] имеет вид , что эквивалентно соотношению между концентрацией B и концентрацией C: . Интегрированные уравнения были получены аналитически, но в процессе выводили, что поэтому предыдущее уравнение для [C] применимо только для низких концентраций [C] по сравнению с начальной концентрацией [A]0.
The integrated equations were analytically obtained but during the process it was assumed that Therefore, previous equation for [C] can only be used for low concentrations of [C] compared to [A]0