thermochemical equation

(noun)

A special equation type, denoting the overall change in energy.

Related Terms

Examples of thermochemical equation in the following topics:

  • Thermochemical Equations

    • Thermochemical equations are chemical equations which include the enthalpy change of the reaction, $\Delta H_{rxn}$ .
    • A thermochemical equation is a balanced stoichiometric chemical equation which includes the enthalpy change.
    • The equation takes the form:
    • The equation takes the form:
    • Therefore, all thermochemical equations must be stoichiometrically balanced.

  • Pressure and Free Energy

    • Therefore, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure.

  • Inconsistent and Dependent Systems

    • In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
    • The equations of a linear system are independent if none of the equations can be derived algebraically from the others.
    • When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.
    • For example, the equations
    • Adding the first two equations together gives 3x + 2y = 2, which can be subtracted from the third equation to yield 0 = 1.

  • Solving Systems Graphically

    • A simple way to solve a system of equations is to look for the intersecting point or points of the equations.
    • A system of equations (also known as simultaneous equations) is a set of equations with multiple variables, solved when the values of all variables simultaneously satisfy all of the equations.
    • Once you have converted the equations into slope-intercept form, you can graph the equations.
    • To determine the solutions of the set of equations, identify the points of intersection between the graphed equations.
    • This graph shows a system of equations with two variables and only one set of answers that satisfies both equations.

  • Parametric Equations

    • Parametric equations are a set of equations in which the coordinates (e.g., $x$ and $y$) are expressed in terms of a single third parameter.
    • Converting a set of parametric equations to a single equation involves eliminating the variable from the simultaneous equations.
    • If one of these equations can be solved for $t$, the expression obtained can be substituted into the other equation to obtain an equation involving $x$ and $y$ only.
    • In some cases there is no single equation in closed form that is equivalent to the parametric equations.
    • One example of a sketch defined by parametric equations.

  • Linear Equations

    • A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.
    • A common form of a linear equation in the two variables $x$ and $y$ is:
    • The parametric form of a linear equation involves two simultaneous equations in terms of a variable parameter $t$, with the following values:
    • Linear differential equations are differential equations that have solutions which can be added together to form other solutions.
    • Linear differential equations are of the form:

  • Solving Differential Equations

    • Differential equations are solved by finding the function for which the equation holds true.
    • A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself to its derivatives of various orders.
    • As you can see, such an equation relates a function $f(x)$ to its derivative.
    • Solving the differential equation means solving for the function $f(x)$.
    • The "order" of a differential equation depends on the derivative of the highest order in the equation.

  • The Substitution Method

    • The substitution method is a way of solving a system of equations by expressing the equations in terms of only one variable.
    • The substitution method for solving systems of equations is a way to simplify the system of equations by expressing one variable in terms of another, thus removing one variable from an equation.
    • When the resulting simplified equation has only one variable to work with, the equation becomes solvable.
    • Note that now this equation only has one variable (y).
    • We can then simplify this equation and solve for y:

  • Solving Systems of Equations in Three Variables

    • In mathematics, simultaneous equations are a set of equations containing multiple variables.
    • This is a set of linear equations, also known as a linear system of equations, in three variables:
    • Now subtract two times the first equation from the third equation to get
    • Next, subtract two times the third equation from the second equation and simplify:
    • Finally, subtract the third and second equation from the first equation to get

  • Introduction to Systems of Equations

    • A system of equations consists of two or more equations with two or more variables, where any solution must satisfy all of the equations in the system at the same time.
    • A system of linear equations consists of two or more linear equations made up of two or more variables, such that all equations in the system are considered simultaneously.
    • The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
    • We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations.
    • Note that a system of linear equations may contain more than two equations, and more than two variables.