Examples of Nernst equation in the following topics:
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- The thermodynamics of redox reactions can be determined using their standard reduction potentials and the Nernst equation.
- In order to calculate thermodynamic quantities like change in Gibbs free energy $\Delta G$ for a general redox reaction, an equation called the Nernst equation must be used.
- Walther Nernst was a German chemist and physicist who developed an equation in the early 20th century to relate reduction potential, temperature, concentration, and moles of electrons transferred.
- The Nernst equation allows the reduction potential to be calculated at any temperature and concentration of reactants and products; the standard reaction potential must be measured at 298K and with each solution at 1M.
- If T is held constant at 298K, the Nernst equation can be condensed using the values for the constants R and F:
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- In electrochemistry, the Nernst equation can be used to determine the reduction potential of an electrochemical cell.
- In electrochemistry, the Nernst equation can be used, in conjunction with other information, to determine the reduction potential of a half-cell in an electrochemical cell.
- It is named after the German physical chemist who first formulated it, Walther Nernst.
- The Nernst equation gives a formula that relates the electromotive force of a nonstandard cell to the concentrations of species in solution:
- The number of moles of electrons transferred is 2 and Q is $\frac{[Ni^{2+}][Pb]}{[Pb^{2+}][Ni]}$, where Pb and Ni are pure solids whose concentrations remain constant, so they are dropped from the equation.
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- Finally, Nernst divided by the amount of charge transferred to arrive at a new equation that now bears his name.
- The Nernst equation is:
- The Nernst equation can be used to calculate the output voltage changes in a pair of half-cells under non-standard conditions.
- It is calculated via the Nernst equation.
- Discuss the implications of the Nernst equation on the electrochemical potential of a cell
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- The equilibrium constant K can be calculated using the Nernst equation.
- In electrochemistry, the Nernst equation can be used, in conjunction with other information, to determine the equilibrium reduction potential of a half-cell.
- The Nernst equation gives a formula that relates the numerical values of the concentration gradient to the electrical gradient that balances it.
- The cell equilibrium constant, K, can be derived from the Nernst equation:
- Calculate the equilibrium constant, K, for a galvanic cell using the Nernst equation
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- The third law was developed by the chemist Walther Nernst during the years 1906-1912.
- It is often referred to as Nernst's theorem or Nernst's postulate.
- Nernst proposed that the entropy of a system at absolute zero would be a well-defined constant.
- Provided that the ground state is unique (or W=1), the entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because log(1) = 0.
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- 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.
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- 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.
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- 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.
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- 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:
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- 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.