Molar solutions, molarity

The units of molarity are mole/liter (of solution), but they are commonly replaced with a capital M, which symbolizes molarity. Yet, there will be times when you will need to replace M with mole/liter when analyzing units and solving problems. If a sodium hydroxide solution is labeled 2 M (read as two-molar), it means that 2 moles of NaOH are dissolved in 1 L of solution, 2 moles/liter. If you need to brush up on mass-mole conversions, review the pertinent material in Chapter 5. In all the problems dealing with molar solutions, molarity will be written as a conversion factor to emphasize the canceling and retention of units, just as was done with the percent concentrations. The molarity term for a solution that is 0.55 M in NaOH could be written in four ways to make the required conversion factor ... 

Vegard s law In phases in which there is a range of composition of solid solution then the cell dimensions vary linearly with the molar proportions of the constituents. The (aw is rarely followed exactly. 

Still another situation is that of a supersaturated or supercooled solution, and straightforward modifications can be made in the preceding equations. Thus in Eq. IX-2, x now denotes the ratio of the actual solute activity to that of the saturated solution. In the case of a nonelectrolyte, x - S/Sq, where S denotes the concentration. Equation IX-13 now contains AH, the molar heat of solution. 

An equation algebraically equivalent to Eq. XI-4 results if instead of site adsorption the surface region is regarded as an interfacial solution phase, much as in the treatment in Section III-7C. The condition is now that the (constant) volume of the interfacial solution is i = V + JV2V2, where V and Vi are the molar volumes of the solvent and solute, respectively. If the activities of the two components in the interfacial phase are replaced by the volume fractions, the result is... 

One hundred milliliters of an aqueous solution of methylene blue contains 3.0 mg dye per liter and has an optical density (or molar absorbancy) of 0.60 at a certain wavelength. After the solution is equilibrated with 25 mg of a charcoal the supernatant has an optical density of 0.20. Estimate the specific surface area of the charcoal assuming that the molecular area of methylene blue is 197 A. ... 

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. 

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

Figure Bl.22.8. Sum-frequency generation (SFG) spectra in the C N stretching region from the air/aqueous acetonitrile interfaces of two solutions with different concentrations. The solid curve is the IR transmission spectrum of neat bulk CH CN, provided here for reference. The polar acetonitrile molecules adopt a specific orientation in the air/water interface with a tilt angle that changes with changing concentration, from 40° from the surface nonnal in dilute solutions (molar fractions less than 0.07) to 70° at higher concentrations. This change is manifested here by the shift in the C N stretching frequency seen by SFG [ ]. SFG is one of the very few teclnhques capable of probing liquid/gas, liquid/liquid, and even liquid/solid interfaces.

Place 0 5 ml. of acetone, 20 ml. of 10% aqueous potassium iodide solution and 8 ml. of 10% aqueous sodium hydroxide solution in a 50 ml. conical flask, and then add 20 ml. of a freshly prepared molar solution of sodium hypochlorite. Well mix the contents of the flask, when the yellow iodoform will begin to separate almost immediately allow the mixture to stand at room temperature for 10 minutes, and then filter at the pump, wash with cold w ater, and drain thoroughly. Yield of Crude material, 1 4 g. Recrystallise the crude iodoform from methylated spirit. For this purpose, place the crude material in a 50 ml. round-bottomed flask fitted with a reflux water-condenser, add a small quantity of methylated spirit, and heat to boiling on a water-bath then add more methylated spirit cautiously down the condenser until all the iodoform has dissolved. Filter the hot solution through a fluted filter-paper directly into a small beaker or conical flask, and then cool in ice-water. The iodoform rapidly crystallises. Filter at the pump, drain thoroughly and dry. 

The way out of this dilemma is to make measurements at several (nonideal) molarities m and extrapolate the results to a hypothetieal value of at m = 0. In so doing we have extrapolated out the nonideality because at m = 0 all solutions are ideal. Rather than ponder the philosophical meaning of a solution in which the solute is not there, it is better to concentrate on the error due to interionic interactions, which becomes smaller and smaller as the ions become more widely separated. At the extrapolated value of m = 0, ions have been moved to an infinite distance where they cannot interact. 

Find the partial molal volume of ZnCl2 in these solutions at 0.5, 1.0, 1.5 and 2.0 molar concentrations. 

If the third substance dissolves in both liquids (and the solubility in each of the liquids is of the same order), the mutual solubility of the liquids will be increased and an upper C.S.T. will be lowered, as is the case when succinic acid or sodium oleate is added to the phenol - water system. A 0 083 molar solution of sodium oleate lowers the C.S.T. by 56 -7° this large effect has been applied industrially in the preparation of the disinfectant sold under the name of Lysol. Mixtures of tar acids (phenol cresols) do not mix completely with water at the ordinary temperature, but the addition of a small amount of soap ( = sodium oleate) lowers the miscibility temperature so that Lysol exists as a clear liquid at the ordinary temperature. 

The reagent is conveniently stored as a solution in isopropyl alcohol. The molten (or solid) alkoxide is weighed out after distillation into a glass-stoppered bottle or flask and is dissolved in sufficient dry isopropyl alcohol to give a one molar solution. This solution may be kept without appreciable deterioration provided the glass stopper is sealed with paraffin wax or cellophane tape. Crystals of aluminium isopropoxide separate on standing, but these may be redissolved by warming the mixture to 65-70°. 

For many reductions it is not necessary to distil the reagent. Dilute the dark solution, prepared as above to the point marked with an asterisk, to 1 htre with dry isopropyl alcohol this gives an approximately one molar solution. Alternatively, prepare the quantity necessary for the reduction, using the appropriate proportions of the reagents. 

A more active product is obtained by the following slight modification of the above procedure. Dissolve the succinimide in a slight molar excess of sodium hydroxide solution and add the bromine dissolved in an equal volume of carbon tetrachloride rapidly and with vigorous stirring. A finely crystalline white product is obtained. Filter with suction and dry thoroughly the crude product can be used directly. It may be recrystallised from acetic acid. 

In 1990 Grieco introduced a 5 molar solution of lithium perchlorate as a new medium for the Diels-Alder reaction that is capable of inducing not only an improvement of the rate but also of the endo-... 

Nitration in the presence of strong acids or Lewis acids Solutions of dinitrogen pentoxide in sulphuric acid nitrate 1,3-dimethyl-benzene-4,6-disulphonic acid twice as fast as a solution of the same molar concentration of nitric acid. This is consistent with Raman spectroscopic and cryoscopic data, which establish the following ionisation ... 

Molar ratio of alkylbenzene to benzene No. of equivs. of aromatics in solution in which nitrating agent is consumed Products Relative rate... 

The high reactivity of the 5-position in 1.3-selenazoles toward electrophilic substitution was also observed on azocoupling. By reacting molar quantities of an aqueous solution of a diazonium salt with an ethanolic solution of a 2-arylamino selenazole. for example, the corresponding 2-arylamino-5 azoselenazoles are formed in a smooth reaction (100). They deposit from the deeply colored solution and form intenselv red-colored compounds after their recrystallization from a suitable solvent (Scheme 36l. 

The vibration frequencies of C-H bond are noticeably higher for gaseous thiazole than for its dilute solutions in carbon tetrachloride or tor liquid samples (Table 1-27). The molar extinction coefficient and especially the integrated intensity of the same peaks decrease dramatically with dilution (203). Inversely, the y(C(2jH) and y(C(5(H) frequencies are lower for gaseous thiazole than for its solutions, and still lower than for liquid samples (cf. Table 1-27). 

Given that the p/Ca of imidazolium ion is 7 is a 1 M aqueous solution of imidazolium chloride acidic basic or neutraP What about a 1 M solu tion of imidazole A solution containing equal molar quantities of imidazole and imidazolium chloride ... 

The ionic strength can be estimated from the summation of the product molarity times ionic charge squared for all the ionic species present in the solution, i.e., I = 0.5(ciZi + C2Zi + + qzf). 

A concentrated C.P. reagent usually comes to the laboratory in a bottle having a label which states its molecular weight w, its density (or its specific gravity) d, and its percentage assay p. When such a reagent is used to prepare an aqueous solution of desired molarity M, a convenient formula to employ is... 

Example Sulfuric acid has the molecular weight 98.08. If the concentrated acid assays 95.5% and has the specific gravity 1.84, the volume required for 1 liter of a 0.1 molar solution is... 

V, mL = volume in milliliters needed to prepare 1 liter of 1 molar solution. 

Both molarity and formality express concentration as moles of solute per liter of solution. There is, however, a subtle difference between molarity and formality. Molarity is the concentration of a particular chemical species in solution. Formality, on the other hand, is a substance s total concentration in solution without regard to its specific chemical form. There is no difference between a substance s molarity and formality if it dissolves without dissociating into ions. The molar concentration of a solution of glucose, for example, is the same as its formality. 

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