Click here for a PDF copy of the User Guide

 

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Brief Theory of Operation

·        The thermodynamic properties for all the substances in the ChemReaX database are based on standard state conditions. Gas species are ideal gases at the standard pressure of 1 bar. Solute standard states are based on molality, and solutions are at 1 molal concentration at the standard pressure of 1 bar.

·         Since all gas species are ideal gases at the standard pressure, the corresponding fugacity coefficients are the low-pressure value of 1. Therefore, the equilibrium constant on a partial-pressure basis, Kp, is nearly equal to the thermodynamic equilibrium constant K.

·        All aqueous solutions are assumed to be dilute, therefore the thermodynamic equilibrium constant Km written in terms of molality (moles/kg) is assumed to be nearly equal to the equilibrium constant Kc written in terms of molarity (moles/L).

·        All aqueous solutions are assumed to be dilute, therefore the thermodynamic equilibrium constant Km written in terms of molality (moles/kg) is assumed to be nearly equal to the equilibrium constant Kc written in terms of molarity (moles/L).

·        All chemical reactions considered here are assumed to take place at constant temperature and pressure under typical laboratory conditions.

·        The standard free-energy change of a reaction at temperature T is: rGo(T) =  rHo(T) - T * ∆So(T), where rHo(T) is the net change in the enthalpies of formation and ∆So(T) is the change in entropy of the sytem.  rGo(T) is an ideal theoretical property of a reaction at a specified temperature and quantifies the free-energy change corresponding to the transformation from reactants at standard states to products at standard states at that temperature.

·        The reaction free-energy change at temperature T is: rG(T) = rGo(T) + R * T * ln Q, where R is the gas constant, T is the temperature and Q is the reaction quotient. For a generic reaction aA + bB <--> cC + dD, rGo(T) = cfGco(T) + dfGdo(T) - afGao(T) - bfGbo(T), where the subscript f implies free-energy of formation.

·        The reaction free-energy change ∆rG(T) = ∆rH(T) - T * ∆S(T) relates the idealized standard free-energy change rGo(T) (which corresponds to standard conditions for all reactants and products) to the actual conditions consisting of specific non-standard concentrations or partial pressures for the reactants and products. While rGo(T) is a static property of the reaction and a snapshot of the reaction in time, rG(T) is a dynamic state function of the reaction system that varies over time as the reaction proceeds in either direction, and is the slope of the free energy G(T) plotted against the extent of the reaction. Chemical reactions are spontaneous in the direction of decreasing free energy (by way of increasing the system entropy and/or decreasing the system enthalpy), which essentially maximizes the entropy of the universe (system + surroundings).

o   If rG(T) is negative, the reaction proceeds spontaneously to the right and increases product concentrations or partial pressures at the expense of reactants, increasing Q and bringing rG(T) closer to zero; if positive, the reaction proceeds spontaneously to the left and increases reactant quantities, decreasing Q and again bringing rG(T) closer to zero. In both cases, the free energy, G(T), decreases spontaneously. ∆rG(T) is zero if and when the reaction reaches equilibrium and G(T) is at a minimum -- then neither the forward nor the reverse reaction has a tendency to occur.

o   If the system entropy decreases in a reaction, then for the change to be spontaneous, some of the system energy must escape as heat and increase the entropy of the surroundings in order to compensate for the reduction in the system entropy. rG(T) is the portion of the enthalpy change of the system that is available for doing non-expansion work after increasing the entropy of the surroundings. If the system entropy increases in a reaction, then the free energy available for doing non-expansion work is more than the enthalpy change since some additional energy from the surroundings (upto T * ∆S(T)) can be drawn into the system.

o   Note that endothermic reactions (with positive enthalpy change for the system, resulting in an entropy reduction of the surroundings) can still be spontaneous if the system entropy increases enough to make rG(T) negative.

·        At equilibrium, rGo(T) = -R * T * ln Qeq = -R * T * ln K. The equilibrium constant K is independent of the initial compositions of the reactants and products, and depends only on thermodynamic quantities that are constant in the reaction at the given temperature. K represents the equilibrium reaction quotient Qeq expressed in terms of partial pressures or concentrations depending on whether the reaction involves gases or occurs in solution. A relatively large K indicates that the reaction will move spontaneously to the right. For a generic reaction aA + bB <--> cC + dD, K can be written as the proper quotient of partial pressures or molar concentrations (under assumptions of ideal gases and dilute aqueous solutions):

o   K = Kp = Qeq = (pc(C) * pd(D))/(pa(A) * pb(B))

o   K = Kc = Qeq = ([C]c * [D]d)/([A]a * [B]b)

·        The concentrations (more formally, the activities) of pure solids and liquids (including solvents) are excluded from the reaction quotient because they are constant at constant temperature and usually very large compared to the concentrations of gases and solutions. There are exceptions, such as when a pure solid is used as a solute in a solution and a pure liquid is a product of a reaction in small quantities.

o   The reaction quotient Q = exp((∆rG(T) - ∆rGo(T)/(R * T)). The reaction free-energy change includes the free-energy change of each reactant/product. As an example of a pure solid, consider a system in which there is ice at -10C. The vapor pressure (p) of ice remains constant at this temperature, so that G(T) - Go(T) = R * T* ln(p/p0) = 0 for the ice; therefore the ice has no impact on how the reaction moves towards equilibrium and can be excluded from the reaction quotient Q. Similarly, the concentration of liquid water is constant at constant temperature and has no impact on the progress of the reaction and can be excluded from Q.

o   Rewriting the reaction free-energy change as ∆rG(T) = R * T * ln Q/Qeq = R * T * ln Q/K, it is easy to see that any reactant or product which is at constant partial pressure or concentration throughout a reaction (at the given temperature) will have no impact on the reaction free-energy change. The partial pressure or concentration of that reactant/product will simply cancel out in the ratio Q/Qeq and can therefore be omitted from Q and K.

o   Based on the above, two assumptions are needed to simulate reactions: (1) Pure solids and liquids that are excluded from the reaction quotient are not limiting reactants and have no impact on the reaction progress. (2) The reaction has at least one gas or solution species (including solids, liquids or gases acting as solutes and not excluded from the reaction quotient), which drive(s) the reaction towards equilibrium.

·        Per Le Chatelier's principle, changes in temperature, concentration or pressure will shift the reaction equilibrium such that the changes can be absorbed.

o   An increase in reactant concentrations will move the equilibrium to the right such that the increase can be consumed, and an increase in product concentrations will move the equilibrium to the left.

o   An increase in temperature will move the equilibrium to the right for endothermic reactions and to the left for exothermic reactions in order to absorb the additional heat being supplied. A decrease in temperature will have the opposite effect. (See next bullet below for more insight into the thermodynamics behind this behavior.)

o   If the pressure within a reaction vessel is increased or decreased by confining the gas species to a smaller or larger volume (when a reaction is at equilibrium otherwise), then the equilibrium composition of the gases will change such that the total number of gas molecules are decreased or increased. Equilibrium will shift towards the reactants or products depending on which direction counteracts the pressure change. rGo(T) and K are independent of the pressure. As an example (from Atkins and De Paula), consider the reaction: N2 + 3H2 <---> 2NH3. Using partial pressures, the equilibrium constant K = p2NH3/(pN2 * p3H2) = x2NH3/(xN2 * x3H2 * p2) = Kx/p2 , where the x's are mole fractions and p is the sum of all the reactant/product partial pressures. Kx is the part of the equilibrium constant that is based on mole fractions. If pressure doubles in this example, then Kx should increase by a factor of 4 in order to maintain a constant value of K, thus changing the equilibrium composition of the gases. The new mole fractions based on the increased Kx value can be converted back to equilibrium partial pressures via multiplying each of them by 2p in this case. Note that injecting an inert gas into the reaction vessel will not shift the equilibrium since the partial pressures of  all reactants/products will be unchanged (for ideal gases).

·        Rewriting the free-energy change as -∆rG(T)/T =  -rH(T)/T + ∆S(T) provides further insight into the thermodynamics of temperature changes. -∆rH(T) is the enthalpy increase of the surroundings, -∆rH(T)/T is the change of entropy of the surroundings, and ∆S(T) is the change of entropy of the reaction system. A reaction proceeds in the direction that maximizes the increase in the total entropy of the universe, which is the sum of the entropy increases of the surroundings and of the system. When a reaction is exothermic, the entropy of the surroundings increases since -rH(T)/T is positive for the surroundings (heat flows from system to surroundings); however, as T increases, the entropy of the surroundings does not increase as much, and the equilibrium falls less to the right. For en endothermic reaction, -∆rH(T)/T is negative for the surroundings (heat flows from surroundings to system) and the entropy of the surroundings decreases; however, as T increases, the entropy of the surroundings does not decrease as much and the equilibrium falls more to the right. Since ∆S(T) changes only minimally as T varies (within some range), nearly the entire response of the reaction equilibrium to temperature changes is dependent on the entropy of the surroundings.

·        Using a similar insight, when a liquid turns into vapor at room temperature, the ∆S(T) of the system is large enough to allow sufficient rH(T) to be drawn from the environment (thus decreasing the entropy of the surroundings by ∆rH(T)/T ) and still increase the total entropy of the universe. For liquids that need a higher temperature to evaporate, ∆S(T) is not large enough and rH(T) must be drawn from the environment at a higher temperature in order for the entropy drop of the surroundings to be less than the entropy increase of the system.

·        Patterns of entropy changes in solutions:

o   When a solid solute is added to a solvent, the entropy of the solvent and the solute each increases in the solution since the motional energy of individual solute/solvent molecules is more dispersed.

o   When a gas solute is dissolved in a solvent, entropy decreases since a solvated gas has lower entropy than in the pure gas phase.

o   When a solute is ionized in an aqueous solution, the ions tend to orient the water molecules and cause the entropy to decrease, especially for small or highly charged ions.

·        For the dissociation of acids and bases, the ionization or dissociation constants Ka and Kb (determined by experiment) are related to the thermodynamic standard free-energy change by: rGo(T) = -R * T * ln Ka/b. Given the standard enthalpy change based on thermodynamic properties, the entropy change for acid/base dissociation can be calculated as: ∆So(T) =  rHo(T)/T + R * ln Ka/b

·        The law of mass action states that the rate of a reaction at a constant temperature depends only on the concentrations of the substances (usually one or more reactants) that influence the rate. The rate also depends on catalysts which do not appear in the balanced equation.  In practice, the reaction rates -- including the overall order -- can only be determined by experiment under specific conditions. A generalized integrated reaction rate model used in ChemReaX is: Rate = k * [R1]X * [R2]Y * [R3]Z, where R1, R2 and R3 are the reactants. The constants k, X, Y and Z must be experimentally determined for a given reaction at a given temperature. The overall order of a reaction is X+Y+Z. Only the reactants are included in this rate model since the product concentrations do not vary independently and are dependent on the reactant concentrations at every point in time. When ChemReaX simulates a reaction, it is essentially integrating the differential equations numerically.

·        An acid-base titration can be used to determine the concentration of an acid or base (the titrand) by exactly neutralizing it with a strong acid or base (the titrant) of known concentration. Incremental amounts of the titrant are added to a given amount of the titrand, and pH is measured at each increment after the solution reaches equilibrium. The result is plotted as the pH of the solution as a function of the titrant added. The end point or equivalence point of a titration is the region of steepest rise/fall in pH, where the titrant has exactly neutralized the titrand. Either the titrand or the titrant will be a limiting reagent in these reactions. Titration involves an acid-base equilibrium at each increment of the titrant volume, where two competing simultaneous equilibria must be accounted for: the ionization of the titrand (which could be a strong/weak acid or base) and the water autoionization. The final H(+) and OH(-) concentrations -- and the pH -- at each titrant increment are an outcome of resolving these simultaneous equilibria.

o   An additional adjustment to the pH must be made for the hydrolysis of water by the salts produced by the neutralization of weak acids/bases. The conjugate acid or base produced by the neutralization can extract an OH- or H+ from water to form the original weak base/acid and release additional H+ or OH- into the solution. As a result, aqueous solutions of salts of weak acids are basic, and aqueous solutions of salts of weak bases are acidic. ChemReaX graphs the pH (as a function of titrant volume) with and without hydrolysis in order to demonstrate the difference -- hydrolysis basically accelerates the pH change as the titration approaches the equivalence point.

o   In the case of polyprotic acids (strong or weak acids with more than one H+ to lose), there are multiple equivalence points corresponding to multiple ionizations. ChemReaX simulates only the first two ionizations of such acids, and ignores any additional ionizations. Hydrolysis is simulated for both ionizations, but omitted for clarity in any ionization where the equilibrium constant is less than 1e-9. The second ionization is assumed to start once the first H+ from the acid has been completely neutralized, which is a reasonable assumption if the equilibrium constant of the first ionization is much greater than that of the second ionization (such that as each individual proton in the aqueous solution is neutralized by the base, the first ionization will preferentially supply the next proton). Note that a relatively strong second ionization can depress the pH at the end of the first ionization to well below the neutral value of 7.

 

 

How to Use ChemReaX to Model/Simulate General Reactions

Click on the "General Reactions" tab, and then:

1. With "Select Ionization Reaction" unchecked:

·        Select reactants and products using the drop-down lists.

o   Up to three reactants and three products can be selected.

o   For solutes in aqueous solutions, choose gas or solid (crystal) species from the drop-down lists.

·       Balance the reaction by entering the correct stoichiometric coefficient for each reactant or product.

·        Use the checkbox to exclude pure solids and liquids from the reaction quotient calculations.

o   This is provided as an option if certain pure liquids (usually as products of  reactions and in small quantities) do need to be included in the reaction quotients. Solids need to be included when they are used as solutes in solutions.

·        Alternately, click “Reaction Selector” to choose from a pre-defined list of reactions. This automatically fills in the reactants and products, balances the equation, and indicates whether certain pure solids or liquids must be excluded from the reaction quotient. (This list of pre-defined reactions will be extended over time.)

·        Enter the initial composition for reactants and products using the following units:

o   Aqueous ions or liquids: moles/L

o   Gases: bars

o   Gases used as solutes in an aqueous solution: moles/L

o   Solids (crystals) used as solutes in an aqueous solution: moles/L

o   Pure solids (crystals) that are not used as solutes do not have a composition unit.

·        Specify a temperature in the range 200K to 5000K (298.15K is the default temperature).

·        Optionally specify a pressure factor of greater than or less than 1 to indicate increasing/decreasing pressure after the reaction reaches equilibrium at some constant pressure (the default is a pressure factor of 1, indicating no change to the pressure). Set the "Pressure Factor" to a value between 0.1 and 10. This option is effective only when all reactants and products are gas species (or excluded liquids/solids), with unequal numbers of reactant and product molecules.

·        Click “Run the Reaction” to perform the equilibrium thermodynamic calculations and simulate the reaction until a final steady state is reached. Results are provided in tabular and graphical forms.

·        Click “Get Thermodynamic Properties Only” in order to quickly get only the thermodynamic properties (the standard enthalpy of formation and entropy at the specified temperature) of reactants/products for hand calculation or other applications.

·        See examples 1-15 below. In addition, examples 23-28 include scenarios where the pressure factor is set greater than or less than 1 (to increase or decrease the pressure,  relative to the baseline pressure, after reaching equilibrium under a constant baseline pressure) for selected gas-phase reactions.

·        The results panel at the bottom of the page shows the final compositions with and without pressure adjustment. The chart shows the reaction progress and kinetics without the pressure adjustment (since the pressure adjustment is applied only after reaching equilibrium).

2. With "Select Ionization Reaction" checked (for the aqueous ionization/dissociation reactions of buffers and other compounds):

·        Select a buffer/compound (including 1st, 2nd or 3rd ionization) from the single dropdown list below the checkbox. This will populate the reactant and products automatically.

·        Enter the initial composition for the reactant and products in moles/L

·        Specify a temperature in the range 200K to 5000K (298.15K is the default temperature).

·        (The pressure factor will have no effect since none of the reactants or products is a gas.)

·        Click “Run the Reaction” to perform the equilibrium thermodynamic calculations and simulate the reaction until a final steady state is reached. Results are provided in tabular and graphical forms.

·        See examples 16-17 below.

3. With either of the two reaction modes described above, you can check "Specify Reaction Rate Parameters" and enter parameters to model the reaction kinetics during the simulation:

·        ChemReaX supports this generalized reaction rate model: Rate = k * [R1]X * [R2]Y * [R3]Z, where R1, R2 and R3 are the reactants. The constants k, X, Y and Z are experimentally determined for a given reaction.

·        Enter the constants k, X, Y and Z into the text boxes -- these constants must be in the correct units (which are not checked by ChemReaX). Note that the reactant concentrations are in moles/L or bars and time is assumed to be in seconds.

·        See examples 18-22 below which illustrate a single reaction modeled as zeroth order through third order. The chart shows the reaction progress and kinetics based on the reaction rate model provided by the user. In addition, ChemReaX provides detailed data for the reactant/product compositions over time in tabular form based on the kinetics.

4. Additional options:

·        Click "Get Thermodynamic Properties Only" to get only the standard molar enthalpy of formation and the molar entropy for each of the reactants and products at the specified temperature -- typically for convenient look up of this data for use outside of ChemReaX -- without calculating the thermodynamic equilibrium values or running the simulation.

·        Click "Check Equation Validity Onlyto verify mass conservation and charge balance in the given equation. An error is reported if atoms or charges are out of balance, or if the given reactants cannot produce the required products. This check is also done automatically when "Run the Reaction" is clicked.

 

 

Examples of Setting Up and Simulating General Reactions Using ChemReaX

1.      H2 (g) + I2 (g) <--> 2HI (g)

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2.      2NO2 (g) <--> N2O4 (g)

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3.      C3H8 (g) + 5O2 (g) <--> 3CO2 (g) + 4H2O (l)

·        O2 is a limiting reactant. H2O (liquid) is a product that must be retained in the reaction quotient since it is not a solvent and its concentration is comparable to other reaction components. As the temperature increases from 298.15K to 500K, the equlibrium noticeably shifts to the left towards the reactants in order to absorb some of the heat since rGo(T) is negative.

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4.      H2 (g) + CO2 (g) <--> H2O (g) + CO (g)

·         As the temperature increases from 298.15K to 500K, the equlibrium noticeably shifts to the right towards the products in order to absorb some of the heat since rGo(T) is positive.

·         ss2.PNG

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5.      CO (g) + 2H2 (g) <--> CH3OH (g)

·         rGo(T) is negative at 298.15K and the final state is mostly products. As the temperature increases to 500K, rGo(T) changes sign and becomes positive, and the final state is mostly reactants.

·         ss2.PNG

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6.      H2 (g) + 0.5O2 (g) <--> H2O (l)

·        H2O is  a pure liquid that must be excluded from the reaction quotient.

·         ss2.PNG

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7.      2Hg (l) + O2 (g) <--> 2HgO (c)

·        Hg is a pure liquid and HgO is a pure solid – both must be excluded from the reaction quotient

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8.      H2O (l) <--> H2O (g)

·        H2O is a pure liquid that must be excluded from the reaction quotient for the evaporation of water. No evaporation takes place at 298.15. At 500K, a considerable amount of evaporation takes place.

·         ss2.PNG

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9.      H2O (l) <--> H+ (aq) + OH- (aq)

·        H2O is a pure liquid that must be excluded from the reaction quotient for the dissociation of water.

·         ss2.PNG

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10.   2HCl (g) + F2 (g) <--> 2HF (g) + Cl2 (g)

·        rGo(T) is negative and final state is nearly 100% products.

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11.   N2 (g) + O2 (g) <--> 2NO (g)

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12.    N2 (g) + 3H2 (g) <--> 2NH3 (g)

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13.    H2 (g) + Cl2 (g) <--> 2HCl (g)

·         ss2.PNG

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14.    CH4 (g) + 2O2 (g) <--> CO2 (g) + 2H2O (l)

·         ss2.PNG

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15.    CH4 (g) + 4Cl2 (g) <--> CCl4 (g) + 4HCl (g)

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16.    Ionization: HL (aq) <--> H+ (aq) + L- (aq) ; HL=C2H4O2

·         ss2.PNG

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17.    Ionization: H2CO3 (aq) <--> H+ (aq) + HCO3- (aq)

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18. Reaction Rate Modeling: H2 (g) + I2 (g) <--> 2HI (g)  (zeroth order)

·         ss1.PNG

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19. Reaction Rate Modeling: H2 (g) + I2 (g) <--> 2HI (g)  (first order)

·         ss1.PNG

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20. Reaction Rate Modeling: H2 (g) + I2 (g) <--> 2HI (g)  (second order)

·         ss1.PNG

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21. Reaction Rate Modeling: H2 (g) + I2 (g) <--> 2HI (g)  (second order)

·         ss1.PNG

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22. Reaction Rate Modeling: H2 (g) + I2 (g) <--> 2HI (g)  (third order)

·         ss1.PNG

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23.      Effect of pressure change on equilibrium: 2NO2 (g) <--> N2O4 (g)

·        Example 2 with pressure increased by a factor of 4. Equilibrium shifts to the right.

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·        Example 2 with pressure decreased by a factor of 4. Equilibrium shifts to the left.

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24.      Effect of pressure change on equilibrium: H2 (g) + CO2 (g) <--> H2O (g) + CO (g)

·         Example 4 with pressure increased by a factor of 4. Pressure changes have no effect on the equilibrium since there are equal numbers of gas molecules on both sides of the reaction.

·         ss2.PNG

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25.      Effect of pressure change on equilibrium: CO (g) + 2H2 (g) <--> CH3OH (g)

·        Example 5 with pressure decreased by a factor of 10.

·         ss2.PNG

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26.      Effect of pressure change on equilibrium: H2 (g) + 0.5O2 (g) <--> H2O (l)

·        Example 6 with pressure decreased by a factor of 2.

·         ss2.PNG

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27.      Effect of pressure change on equilibrium: 2Hg (l) + O2 (g) <--> 2HgO (c)

·        Example 7 with pressure increased by a factor of 4.

·         ss2.PNG

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·        Example 7 with pressure decreased by a factor of 4.

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28.      Effect of pressure change on equilibrium: N2 (g) + 3H2 (g) <--> 2NH3 (g)

·        Example 12 with pressure increased by a factor of 10.

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·        Example 12 with pressure decreased by a factor of 10.

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How to Use ChemReaX to Model/Simulate Acid-Base Titrations

Click on the "Acid-Base Titrations" tab, and then:

·        Select a titrand and a titrant using the drop-down lists. Note that one of them must be an acid and the other must be a base in order to simulate a titration.

·        Alternately, click “Reaction Selector” to choose from a pre-defined list of titration reactions. This fills in the titrant and titrand fields. (This list of pre-defined reactions will be extended over time.)

·        Enter the titrand and titrant concentrations, the initial volume of the titrand, and the total amount (volume) of titrant added.

·        Click "Run the Reaction" to simulate the titration until a final steady state is reached at each increment of the titrant volume. Results (pH vs. titrant volume) are provided in tabular and graphical forms. pH values are provided with and without hydrolysis included.

 


Examples of Setting Up and Simulating Acid-Base Titrations Using ChemReaX

1. Titrand: strong acid; Titrant: strong base

 

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2. Titrand: weak acid; Titrant: strong base

 

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3. Titrand: strong base; Titrant: strong acid

 

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4. Titrand: weak base; Titrant: strong acid

 

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5. Titrand: weak polyprotic acid; Titrant: strong base

 

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6. Titrand: strong polyprotic acid; Titrant: strong base

 

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7. Titrand: very weak polyprotic acid; Titrant: strong base

 

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