Conversions, unit solution, 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 ... 

All of the solution concentration units introduced in this chapter are direct proportionalities. Percentage concentration by mass is a direct proportionality between mass of solute and mass of solution molarity, between moles of solute and liters of solution molality, between moles of solute and kilograms of solvent and normality, between equivalents of solute and liters of solution. These proportional relationships allow you to think of solution concentration units as conversion factors between the two units in the fraction. Do you know mass of solution and need mass of solute Use percentage concentration. Do you know volume of solution and need moles of solute Use molarity. Thinking about solution concentration units in this way allows you to become more skilled at solving quantitative problems. 

Molarity (M) A concentration unit defined to be the number of moles of solute per liter of solution, 95q, 259 concentration unit conversion, 261-262 potassium chromate, 263 Mole A collection of6.0122 X 1023 items. The mass in grams of one mole of a substance is numerically equal to its formula mass, 55. See also Amount Mole fraction (X) A concentration unit defined as the number of moles of a component divided by the total number of moles, 116-117,261 Mole-gram conversions, 55-56,68-68q... 

A The molar mass of halothane is given in Example 3-3 in the text as 197.4 g/mol. The rest of the solution uses conversion factors to change units. 

The preceding sections have used standard molar concentration units for RNA and ions, indicated by brackets or the abbreviation M. Thermodynamic definitions of interaction coefficients are made in terms of molal units, abbreviated m, the moles of solute per kilogram of solvent water. Molal units have the convenient properties that the concentration of water is a constant 55.5 m regardless of the amount ofsolute(s) present, and the molality of one solute is unaffected by addition of a second solute. For dilute solutions, M and m units are interchangeable. We use molal units for the thermodynamic derivations in this section, and indicate later (Section 3.1) the salt concentrations where a correction for molar-molal conversion is required. 

Because virtually all stoichiometric calculations involve moles (abbreviated mol) of material, molarity is probably the most common concentration unit in chemistry. If we dissolved 1.0 mol of glucose in enough water to give a total volume of 1.0 L, we would obtain a 1.0 molar solution of glucose. Molarity is abbreviated with a capital M. Notice that, because molarity has units of moles per liter, molar concentrations are conversion factors between moles of material and liters of solution. 

Exercise 7.7.5. A continuous saponification process is carried out in two stirred tanks in series. The reaction is second order. The ester and alkali are added to the system in solutions of the same constant molar concentration and the total volume of the system remains constant. Find the ratio of the volume of the second tank to that of the first so as to give the optimum unit output of soap, when the overall degree of conversion tends to 100%. 

Values of the constant determined via least-squares fits of density data for aqueous solutions of the alkali metal halides are given in table 3.6. Similar fits may be made for other electrolyte solutions so that the conversion of molality to molarity is easily carried out. Once the concentration units are known, values of y are easily calculated from y using equation (3.6.9). These quantities are given in table 3.7 for the NaCl system for concentrations up to 2.4 m. 

Since a large part of the NEA-TDB project deals with the thermodynamics of aqueous solutions, the units describing the amount of dissolved substance are used very frequently. For convenience, this review uses M as an abbreviation of mol-dm for molarity, c, and, in Appendices B and C, m as an abbreviation of mol-kg for molality, m. It is often necessary to convert concentration data from molarity to molality and vice versa. This conversion is used for the correction and extrapolation of equilibrium data to zero ionic strength by the specific ion interaction theory, which works in molality units (c/ Appendix B). This conversion is made in the following way. Molality is defined as moles of substance B dissolved in 1 kilogram of pure water. Molarity is defined as Cg moles of substance B dissolved in (/ - c M) kilogram of pure water, where p is the density of the solution in kg-dm and the molar weight of the solute in kg-mof. ... 

First, determine the mass of NaCl to add to a 1.0-L container. The 0.15M solution must contain 0.15 moles of NaCl per liter of solution. You will need to use the molarity of the solution (0.15 mol NaCl/L solution) as a conversion factor to get from molarity to number of moles of NaCl. You win then use the molar mass of NaCl as a conversion factor to change moles of NaCl to grams of NaCl. To find the molar mass of NaCl (58.5 g/mol), add the atomic masses of Na and Cl, and apply the unit grams/mole to the sum. 

Because the answer we want, molarity, is a ratio of two units (moles of solute—in this case, Na3P04—per liter of solution), we start our unit analysis setup with a ratio of two units. Because we want amount of Na3P04 on the top when we are done, we start with 8.20 g Na3P04 on the top. Because we want volume of solution on the bottom when we are done, we start with 100.0 mL of solution on the bottom. To convert mass of Na3P04 to moles of Na3P04, we use the molar mass of Na3P04. We finish our conversion with a conversion factor that converts milliliters to liters. 

Molarity can be used to convert from volume of solution to moles of solute. (It might be necessary to insert one or more additional conversion factors to convert from the given volume unit to liters or milliliters.)... 

What does 1 ppm represent in terms of moles per liter It depends on the formula weight, but the approximate relationship between concentrations in parts per million (or parts per billion) and in moles per liter can be seen by assuming a formula weight of 100 for an analyte. Then, since 1 ppm = 10 g/L, it is equal to (10 g/L) (10 g/mol) = 10 mol/L. Similarly, 1 ppb = 10 mol/L. Note that this latter concentration is smaller than the hydrogen ion concentration in pure water (10" mol/L) Of course, this relationship is approximate and will vary with the formula weight. One part per million solutions of zinc and copper, for example, will not be the same molarity. Conversely, equal molar solutions of different species will not be equal in terms of ppm unless the formula weights are equal. The former concentration is based on the number of molecules per unit volume, while the latter is based on the weight of the species per unit volume. 

Solution Combining unit conversion steps and solving for molarity from Equation 13.13 ... 

For aqueous-phase chemical reactions the commonly used concentration unit is mol L 1. Aqueous solutions in cloud and raindrops are characterized by concentrations in the range of pmolL. For a dilute aqueous solution molality (mol kg-1) is approximately equal to molarity (mol L-1). The conversion between molar concentration c and molality m is... 

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