Molar concentration, expressions

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

Enzymes are excellent catalysts for two reasons great specificity and high turnover rates. With but few exceptions, all reac tions in biological systems are catalyzed by enzymes, and each enzyme usually catalyzes only one reaction. For most of the important enzymes and other proteins, the amino-acid sequences and three-dimensional structures have been determined. When the molecular struc ture of an enzyme is known, a precise molecular weight could be used to state concentration in molar units. However, the amount is usually expressed in terms of catalytic activity because some of the enzyme may be denatured or otherwise inactive. An international unit (lU) of an enzyme is defined as the amount capable of producing one micromole of its reaction product in one minute under its optimal (or some defined) reaction conditions. Specific activity, the activity per unit mass, is an index of enzyme purity. 

The symbol used is dependent upon the method of expressing the concentration of the solution. The recommendations of the IUPAC Commision on Symbols, Terminology and Units (1969) are as follows concentration in moles per litre (molarity), activity coefficient represented by y, concentration in mols per kilogram (molality), activity coefficient represented by y, concentration expressed as mole fraction, activity coefficient represented by f... 

As a result standard solutions are now commonly expressed in terms of molar concentrations or molarity (AT). Such standard solutions are specified in terms of the number of moles of solute dissolved in 1 litre of solution for any solution,... 

Remember that although equilibrium calculations require concentrations in molarities for solutes, the equilibrium constant expression is dimensionless. The solubility product has a... 

The use of two different polymer concentrations, C2 and v, in preceding equations results from deference to custom in expressing electrolyte concentrations in molarities (or in molalities). Confusion might have been minimized in Eq. (45) by substituting C2m = V2m/yu-... 

We determine the amounts of H30+ and OH" and then the amount of the one that is in excess. We express molar concentration in millimoles/milliliter, equivalent to mol/L. 

In complex systems, fA is not a unique parameter for following the course of a reaction, unlike in simple systems. For both kinetics and reactor considerations (Chapter 18), this means that rate laws and design equations cannot be uniquely expressed in terms of /A, and are usually written in terms of molar concentrations, or molar flow rates or extents of reaction. Nevertheless, fA may still be used to characterize the overall reaction extent with respect to reactant A. 

It should be stressed that the pH value of an actual buffer solution prepared by mixing quantities of the weak acid or base and its conjugate base or acid based on the calculated ratio will likely be different from what was calculated. The reason for this is the use of approximations in the calculations. For example, the molar concentration expressions found in Equations (5.23) to (5.30), e.g., [H+], are approximations. To be thermodynamically correct, the activity of the chemical should be used rather than the concentration. Activity is directly proportional to concentration, the activity coefficient being the proportionality constant ... 

As with other absorption spectroscopies, NMR SIN is directly dependent on sample concentration expressed as Ns, the number of spins per unit volume, in Equation 7.6. Because spectral SIN can be increased through signal averaging, in making comparisons between probes it is instructive to calculate the concentration sensitivity, Sc, by dividing SIN by the square root of the acquisition time and the molar concentration... 

A = latm. The units of are (mL gas)/(LSWatm), giving [A(aq)] units of (mL gas)/G. SW). In this concentration unit, the gas abundance is expressed as the volume it would occupy if extracted from the seawater and subjected to STE Under these conditions, the gas s molar volume is 22,414 mL (assuming ideal gas behavior). Thus, gas concentrations expressed in units of can be converted to molarity and molinity (mol/kg) using the following ... 

It is usually difficult to express the enzyme concentration in molar unit because of difficulties in determining enzyme purity. Thus, the concentration is sometimes expressed as a unit, which is proportional to the catalytic activity of an enzyme. The definition of an enzyme unit is arbitrary, but one unit is generally defined as the amount of enzyme that produces 1 pmol of the product in 1 min at the optimal temperature, pH and substrate concentration. 

Assuming that the mixture only contains these two components, and if CA and CB are the concentration expressed in mass % of A and B with molar masses of MA and MB, then ... 

Molality (in) is concentration expressed as moles of substance per kilogram of solvent (not total solution). Molality is independent of temperature. Molarity changes with temperature because the volume of a solution usually increases when it is heated. 

SI base units include the meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), and mole (mol). Derived quantities such as force (newton, N), pressure (pascal. Pa), and energy (joule, J) can be expressed in terms of base units. In calculations, units should be carried along with the numbers. Prefixes such as kilo- and milli- are used to denote multiples of units. Common expressions of concentration are molarity (moles of solute per liter of solution), molality (moles of solute per kilogram of solvent), formal concentration... 

A common unit of concentration used by chemists is molarity, which is the solution s concentration expressed in moles of solute per liter of solution ... 

As we ve seen, stoichiometry calculations for chemical reactions always require working in moles. Thus, the most generally useful means of expressing a solution s concentration is molarity (M), the number of moles of a substance (the solute) dissolved in each liter of solution. For example, a solution made by dissolving 1.00 mol (58.5 g) of NaCl in enough water to give 1.00 L of solution has a concentration of 1.00 mol/L, or 1.00 M. The molarity of any solution is found by dividing the number of moles of solute by the number of liters of solution. 

Rather than write hydronium ion concentrations in molarity, it s more convenient to express them on a logarithmic scale known as the pH scale. The term pH is derived from the French puissance d hydrogene ("power of hydrogen") and refers to the power of 10 (the exponent) used to express the molar H30+ concentration. The pH of a solution is defined as the negative base-10 logarithm (log) of the molar hydronium ion concentration ... 

Another kinetic parameter in Eq. (2.11) is the maximum reaction rate rmax, which is proportional to the initial enzyme concentration. The main reason for combining two constants k3 and CEq, into one lumped parameter rmax is due to the difficulty of expressing the enzyme concentration in molar unit. To express the enzyme... 

The central term in Equation 2.5 enhances the fact that the adiabatic temperature rise is a function of reactant concentration and molar enthalpy. Therefore, it is dependant on the process conditions, especially on feed and charge concentrations. The right-hand term in Equation 2.5, showing the specific heat of reaction, is especially useful in the interpretation of calorimetric results, which are often expressed in terms of the specific heat of the reaction. Thus, the interpretation of calorimetric results must always be performed in connection with the process conditions, especially concentrations. This must be accounted for when results of calorimetric experiments are used for assessing different process conditions. 

Equations (8.125) and (8.126) are valid for the case in which either mole fractions or molalities are used to express the concentrations. When molarities are used, we must include the temperature derivative of the molarity and of the density or molar volume of the solvent when necessary. Thus, for a solute... 

Concentrations expressed as molality or mole fractions are temperature-independent and are most useful when a physical measurement is related to theory over a range of temperature, e.g., in freezing point depression or boiling point elevation measurements (Chapter 11). Since the density of water is close to 1 g/cm3, molal and molar concentrations are nearly equal numerically for dilute aqueous solutions (<0.1 M). 

Using concentrations expressed in molarity and time in seconds, what are the units of the rate constant, k, for (a) a zero-order reaction (b) a first-order reaction (c) a second-order reaction (d) a third-order reaction (e) a half-order reaction ... 

In the case of solutions (liquid or solid mixtures), besides the molar fraction, we frequently use for expressing the solution composition the molar concentration (or molarity) ct, the number of moles for unit volume of the solution, and the molality mt, the number of moles for unit mass of the solvent (main component substance of the solution) ... 

Commercial vinegar contains 5-6% acetic acid. Acetic acid, CH3COOH, is a monoprotic acid. Therefore, its concentration expressed in molarity or normality is the same. It is a weak acid and when titrated with a strong base such as NaOH, upon completion of the titration, there is a sudden change in the pH in the range from 6.0 to 9.0. The best way to monitor such a change is to use the indicator phenolphthalein, which changes from colorless to a pink hue at pH 8.0-9.0. 

In molar units, the ionic strength is /(M) = 5Z v) (Mlv2, where number densities are concentrations expressed as moles per liter (1 mol/liter = 6.02 x 1023 particles/liter = 6.02 x 1026 particles/m3 = 6.02 x 1020 particles/cm3). 

In this formula K m is the dissociation constant expressed solely by the equilibrium concentrations, according to the classical Guldberg-Waage interpretation of the law of mass action. This value is identical with the true thermodynamical dissociation constant Km in highly diluted solutions only, for which the mean activity coefficient y+w very nearly equals unity. In all other solutions K m is not a true constant, but it depends on the actual concentration and on the presence of additional electrolytes therefore, it is called the apparent dissociation constant, in contradistinction of the true dissociation constant. For concentration expressed in terms of molarity, a similar equation is valid-... 

In such diluted solutions the product of ionic concentrations, expressed in terms of molarities, has practically the same value (K v s cH+ + c0n-) because the density of the solvent is approximately unity. 

Debye-Hiickel equation is valid in unchanged form for concentrations expressed both by molality and molarity. 

In Equation (3) the DBBP concentration is expressed in vol% all other concentrations are molarities. The nitrate ion concentration is the total from all sources. According to Sheppard, Equation (3) holds fairly well for 5M total nitrate ion, but should be considered only approximate at 4 and 6M total nitrate ion. 

This is a way of expressing concentration. One molar (1m) concentration contains the mass one mole in grams dissolved in 11 (1 dm3) of solution. 

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