Examples of coefficient in the following topics:
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- These orbital coefficients also have a sign (plus or minus) reflecting their phase.
- In the case of 1,3-butadiene, shown in the diagram below, the lowest energy pi-orbital (π1) has smaller orbital coefficients at C-1 and C-4, and larger coefficients at C-2 and C-3.
- The remaining three pi-orbitals have similar coefficients (± 0.37 or 0.60), but the location of the higher coefficient shifts to the end carbons in the HOMO and LUMO orbitals (π2 & π3 respectively).
- Unsymmetrical substitution of a diene or dienophile perturbs the orbital coefficients in an unsymmetrical fashion.
- The dienophile data is reasonably consistent, but the diene LUMO coefficients show variability.
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- In order to balance this, we need to add a stoichiometric coefficient of 2 in front of liquid water:
- To finish balancing the equation, we must add a coefficient of 2 in front of hydrogen gas:
- For reactants, the stoichiometric number is the negative of the stoichiometric coefficient, while for products, the stoichiometric number is simply equal to the stoichiometric coefficient, remaining positive.
- For such species, their stoichiometric coefficients are always zero.
- In our balanced chemical equation, the coefficient for H2(g) is 1, and the coefficient for HCl(g) is 2.
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- The numerical coefficient next to each entity denotes the absolute stoichiometric amount used in the reaction.
- In a balanced chemical equation, the coefficients can be used to determine the relative amount of molecules, formula units, or moles of compounds that participate in the reaction.
- The coefficients in a balanced equation can be used as molar ratios, which can act as conversion factors to relate the reactants to the products.
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- The numerical coefficients next to each chemical entity denote the proportion of that chemical entity before and after the reaction.
- For any balanced chemical reaction, whole numbers (coefficients) are used to show the quantities (generally in moles) of both the reactants and products.
- Reactions are balanced by adding coefficients so that there are the same number of atoms of each element on both sides of the reaction.
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- The coefficients before the reactants and products are their stoichiometric values.
- The ratio of the coefficients of two of the compounds in a reaction (reactant or product) can be viewed as a conversion factor and can be used to facilitate mole-to-mole conversions within the reaction.
- Taking coefficients from the reaction equation (13 O2 and 2 C4H10), the molar ratio of O2 to C4H10 is 13:2.
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- The coefficients next to the reactants and products are the stoichiometric values.
- The next step is to inspect the coefficients of each element of the equation.
- The coefficients can be thought of as the amount of moles used in the reaction.
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- The coefficients next to the symbols of entities indicate the number of moles of a substance produced or used in the chemical reaction.
- The stoichiometric coefficients (the numbers in front of the chemical formulas) result from the law of conservation of mass and the law of conservation of charge (see the "Balancing Chemical Equations" section for more information).
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- The exponents x and y vary for each reaction, and they must be determined experimentally; they are not related to the stoichiometric coefficients of the chemical equation.
- The value of this coefficient k will vary with conditions that affect reaction rate, such as temperature, pressure, surface area, etc.
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- Molecular orbital calculations that give pi-orbital coefficients for dienes and dienophiles are beyond the scope of this text.
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- ln Q is the natural log of $\frac{C^cD^d}{A^aB^b}$, where the uppercase letters are concentrations, and the lowercase letters are stoichiometric coefficients for the reaction: $aA + bB \rightarrow cC + dD$