Reaction quotient units

You may wonder why the equilibrium constant, 11, has no units. The reason is that each term in the reaction quotient represents the ratio of the measured pressure of the gas to the thermodynamic standard state of one atmosphere. Thus the quotient (f3No2)2/f>N2o4 in Experiment 1 becomes... 

Equilibrium constants are dimensionless numbers, yet the concentrations used in an equilibrium constant expression have units. To understand this, we need to explore the reaction quotient Q, introduced in Chapter 14. In Section 16-1 we explore in detail the link between Q and Keq. Here we use Q to address the issue of concentration units and the equilibrium constant. 

We can write a reactant quotient at any point during the reaction, but the most meaningful point is when the reaction has reached equilibrium. At equilibrium, the reaction quotient becomes the equilibrium constant, Kc (or Kp if gas pressures are being used). We usually express this equilibrium constant simply as a number without units since it is a ratio of concentrations or pressures. In addition,... 

Where Q is the reaction quotient (discussed in Chapter 14), n is the number of electrons transferred in the redox reaction, R is the universal gas constant 8.31 J/(mol K), T is the temperature in kelvins, and Fis the Faraday constant 9.65x10 coulombs/mol, where coulomb is a unit of electric charge. With this information, you can assign quantitative values to the EMFs of batteries. The equation also reveals that the EMF of a battery depends on temperature, which is why batteries are less likely to function well in the cold. 

At any radius r, the rate of reaction per unit area can be calculated from the quotient, (dn/dt)r/Sr. Consequently, the specific rate of reaction and calculated carbon dioxide concentration (both taken at the same value of r) can be plotted to determine the true order of reaction, independent of diffusion control. Figure 19 presents such data for the carbon rod reacted at 1200°, assuming the relative concentrations for Case 3 in Table VI to be applicable. From an auxiliary plot similar to Fig. 19, a finite reaction rate at zero carbon dioxide concentration is found. Since the concentrations of carbon dioxide were calculated assuming Co to be zero, it is clear that this reaction rate is due to a finite Co concentration at the center of the rod. The actual values of concentration at values of r were estimated by extrapolat-... 

Equations such as those for the equilibrium constant, the reaction quotient and the Nemst equation are written mostly in terms of concentrations and partial pressures. This is correct only for very dilute solutions or ideal gases. In general, the amount of active material present appears to be less than the nominal amount measured in the customary units (in moles per litre, or in atmospheres). In order to retain the form of the equations used here and yet increase precision, thermodynamics replaces the concentration terms by the activity, which is an effective concentration, and the pressure by the fugacity, which is an effective pressure. Thus, the equilibrium constant for the reaction... 

The term that appears in the natural logarithm of Equation 2.16, which is a ratio of product and reactant activities raised to their appropriate stochiometric coefficients, has a special name. It is known as the reaction quotient Q. As we discussed in the section on dynamic equilibrium, it is important to think of all processes, including chemical reactions, as dynamic processes that can occur in both the forward and backward directions. Thus, you should think of a chemical reaction as being like a balance between the reactant and product species—and the reaction quotient is essentially a quantitative indicator of that balance. The reaction quotient indicates whether the current balance of a reaction under any arbitrary set of conditions has been skewed more toward the reactant or product side as compared to the standard-state conditions. At the standard-state condition, all of the reactants and product species are at unit activity, and thus the reaction quotient is 1. In this case, AG = AG°, which makes sense, since AG is the free energy under standard-state conditions. 

The for a half-reaction is the potential of that reaction versus the standard hydrogen electrode, with all species at unit activity. Most reduction potentials are not determined under such conditions, so it is expedient to define a formal reduction potential. This is a reduction potential measured under conditions where the reaction quotient in the Nernst equation is one and other nonstandard conditions are described solvent, electrolyte, pN, and so on. Formal reduction potentials are represented by °. Reduction potentials determined by cyclic voltammetry are usually formal potentials. The difference between standard and formal potentials is not expected to be great. Other definitions of the formal potential are offered. ... 

Because for dilute aqueous concentrations the molality is approximately equal to the molarity, it is not uncommon to write equilibrium concentrations in units of molarity. (In fact, this is how it is usually done in introductory courses.) However, this adds an additional approximation in our expression of reaction quotients and equilibrium constants. 

The application of thermodynamics to electrochemical systems also helps us understand potentials at nonstandard conditions and gives us a relationship with the equilibrium constant and reaction quotient. However, we understand now that concentration is not necessarily the best unit to relate to the properties of a solution. Rather, activity of ions is a better unit to use. Using Debye-Hiickel theory, we have ways of calculating the activities of ions, so we can more precisely model the behavior of nonideal solutions. 

No, equilibrium is a dynamic process. Both the forward and reverse reactions are occurring at equilibrium, just at equal rates. Thus the forward and reverse reactions will distribute C atoms between CO and CO2. 11. 4 molecules HjO, 2 molecules CO, 4 molecules H2, and 4 molecules CO2 are present at equilibrium. 13. K and are equilibrium constants as determined by the law of mass action. For K, the units used for concentrations are mol/L, for partial pressures in units of atm are used (generally). Q is called the reaction quotient. Q has the exact same form as K or K, but instead of equilibrium concentrations, initial concentrations are used to calculate the Q value. Q is of use when it is compared to the K value. When Q = K (ov when 2p = p)> the... 

The question arises as to whether comparisons with protein enzymes are justified. In other words, what can ribozymes really do An important parameter for measuring the efficiency of enzymes is the value of kc-JK. This quotient is derived from the values of two important kinetic parameters kc-Al is a rate constant, also called turnover number, and measures the number of substrate molecules which are converted by one enzyme molecule per unit time (at substrate saturation of the enzyme). Km is the Michaelis-Menten constant it corresponds to the substrate concentration at which the rate of reaction is half its maximum. 

The quotient of rate constants obtained in steady-state treatments of enzyme behavior to define a substrate s interaction with an enzyme. While the Michaelis constant (with overall units of molarity) is a rate parameter, it is not itself a rate constant. Likewise, the Michaelis constant often is only a rough gauge of an enzyme s affinity for a substrate. 2. Historically, the term Michaelis constant referred to the true dissociation constant for the enzyme-substrate binary complex, and this parameter was obtained in the Michaelis-Menten rapid-equilibrium treatment of a one-substrate enzyme-catalyzed reaction. In this case, the Michaelis constant is usually symbolized by Ks. 3. The value equal to the concentration of substrate at which the initial rate, v, is one-half the maximum velocity (Lmax) of the enzyme-catalyzed reaction under steady state conditions. 

Here A is the pre-exponential factor, E is an effective activation energy or temperature coefficient for the overall reaction, R = 8.314 JK moP is the Gas Constant and T is the local absolute temperature. The quotient E/R has units of temperature and is sometimes known as the Arrhenius temperature It is a characteristic feature of combustion processes that if Ta is the ambient temperature, then Tatt> so that the group RTJE and, more generally, the scaled or dimensionless temperature RTIE are typically (very) small quantities in the systems of interest. 

Figure 7.2 shows the basic essentials of the reactor. Since it is used largely for liquid phase reactions with little change of volume, it will be appropriate to use Cj, the number of moles of per unit volume, as the concentration variable with the corresponding extent variable The total volume flow rate of the feed (including both reactants and any inert gases or diluents) into the reactor is denoted by and the volume of the reacting mixture in the reactor by K. In normal operation, V will be constant, and so the volume flow rate out of the reactor rib will also be q. The quotient Vjq = 6... 

This is the general reaction isotherm, also known as the van t Hoff isotherm it is of prime importance. The logarithmic ratio is sometimes known as the activity quotient, and is written Q. As before, AG is a measure of the affinity of the process actually occurring, where the logarithmic term makes adjustment for non-unit activities. This equation would apply for example when it was required to determine the feasibility of a reaction for which all starting activities are known. 

Equation 22-13 reveals that the constant is equal to the half-cell potential when the logarithmic term is zero. This condition occurs whenever the activity quotient is equal to unity, such as. for example, when the activities of all reactants and products are unity. Thus, the standard potential is often defined as the electrode potential of a half-cell reaction (versus SHE) when all reactants and products have unit activity. 

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