Calculating with Molarity

The answer is correctly given to one significant digit. The units cancel correctly to give the desired unit, mol. There should be less than 0.5 mol HCl, because less than 1 L of solution was used. 

Sample Problem C To produce 40.0g of silver chromate, you will need at least 23.4 g of potassium chromate in solution as a reactant. All you have on hand Is 5 L of a 6.0 M KjCrO solution. What volume of the solution is needed to give you the 23.4 g K CrO needed for the reaction  

The molarity indicates the moles of solute that are in 1 L of solution. Given the mass of solute needed, the amount in moles of solute can then be found. Use the molarity and the amount, in moles, of K2Cr04 to determine the volume of K2Cr04 that will provide 23.4 g. 

To get the moles of solute, you ll need to calculate the molar mass of K2Cr04. 1 mol K2Cr04 = 194.2 g K2Cr04 1 mol K.,CrO. 

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Vapor-pressure lowering is calculated with mole fraction freezing-point depression and boiling-point elevation are calculated with molality and osmotic pressure is calculated with molarity. 

By making calculations with molar masses, you can find the number of molecules of methanol in your 500 g the number of molecules of carbon dioxide and hydrogen that reacted and the masses of carbon dioxide, hydrogen, methanol, and water in grams. Figure 12.6 shows the molar masses of some compounds. 

Calculate the molar concentration of NaCl, to the correct number of significant figures, if 1.917 g of NaCl is placed in a beaker and dissolved in 50 mF of water measured with a graduated cylinder. This solution is quantitatively transferred to a 250-mF volumetric flask and diluted to volume. Calculate the concentration of this second solution to the correct number of significant figures. 

The molar refraction, / m, is a measure of the size of a molecule. It is calculated with Eq. (8.5), the Lorenz-Lorentz equation, where , d, and M are the refractive index, the density, and the molecular weight, respectively. 

In an effusion experiment, argon gas is allowed to expand through a tiny opening into an evacuated flask of volume 120 mL for 32.0 s, at which point the pressure in the flask is found to be 12.5 mm Hg. This experiment is repeated with a gas X of unknown molar mass at the same T and P. It is found that the pressure in the flask builds up to 12.5 mm Hg after 48.0 s. Calculate the molar mass of X. 

In this chapter the ideal gas law has been used in all calculations, with the assumption that it applies exactly. Under ordinary conditions, this assumption is a good one however all real gases deviate at least slightly from the ideal gas law. Table 5.2 shows the extent to which two gases, 02 and CO2, deviate from ideality at different temperatures and pressures. The data compare the experimentally observed molar volume, Vm... 

The escape velocity required for gas molecules to overcome the earths gravity and go off to outer space is 1.12 X 103m/s at 15°C Calculate die molar mass of a species with that velocity. Would you expect to find He and H2 molecules in the earth s atmosphere How about argon atoms ... 

As an example we may calculate the e.m.f. of the Daniell cell with molar concentrations of zinc ions and copper(II) ions ... 

Prepare 250 mL of 0.02 M potassium dichromate solution and an equal volume of ca 0.1 M ammonium iron(II) sulphate solution the latter must contain sufficient dilute sulphuric acid to produce a clear solution, and the exact weight of ammonium iron(II) sulphate employed should be noted. Place 25 mL of the ammonium iron(II) sulphate solution in the beaker, add 25 mL of ca 2.5M sulphuric acid and 50 mL of water. Charge the burette with the 0.02 M potassium dichromate solution, and add a capillary extension tube. Use a bright platinum electrode as indicator electrode and an S.C.E. reference electrode. Set the stirrer in motion. Proceed with the titration as directed in Experiment 1. After each addition of the dichromate solution measure the e.m.f. of the cell. Determine the end point (1) from the potential-volume curve and (2) by the derivative method. Calculate the molarity of the ammonium iron(II) sulphate solution, and compare this with the value calculated from the actual weight of solid employed in preparing the solution. 

Dissolve 20 g of tetra-n-butylammonium iodide in 100 mL of dry methanol and pass this solution through the column at a rate of about 5 mL min - L the effluent must be collected in a vessel fitted with a Carbosorb guard tube to protect it from atmospheric carbon dioxide. Then pass 200 mL of dry methanol through the column. Standardise the methanolic solution by carrying out a potentiometric titration of an accurately weighed portion (about 0.3 g) of benzoic acid. Calculate the molarity of the solution and add sufficient dry methanol to make it approximately 0.1M. 

By adopting mixing rules similar to those given in Section II, Chueh showed that Eq. (55) can be used for calculating partial molar volumes in saturated liquid mixtures containing any number of components. Some results for binary systems are given in Figs. 7 and 8, which compare calculated partial molar volumes with those obtained from experimental data. 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

Self-Test 12.12A Calculate the molar concentration of Y1H in a saturated solution of YF3 by using a cell constructed with two yttrium electrodes. The electrolyte in one compartment is 1.0 M Y(NO ),(aq). In the other compartment you have prepared a saturated solution of YF3. The measured cell potential is +0.34 V at 298 K. 

In all calculations the molar masses given in the top of Table I were used. First of all, the effects of variations in the concentration of trifunctional monomers were determined, as exemplified by the nine formulations of Table I and the resulting prepolymer characteristics after full conversion given in Table II. Formulations FIO to F40 result in branched prepolymers, which are cured in the third stage by difunctional monomers. On the other hand, formulations FOO to F04 result in the same linear prepolymer, which is subsequently cured with various mixtures of di- and trifunctional monomers. The number average functionalities of PI (and P2) and of the mixtures of E and F monomers are varied systematically between 2.0 and 2.4. Therefore, the only difference between formulations FjO and FOj is the stage in which the branching units are added. 

Another way to calculate this molar mass is by working with the individual components of the formula. Each formula unit of the compound contains one iron(II) cation, two nitrate anions, and six waters of hydration ... 

C03-0092. A chemist places 3.25 g of sodium carbonate in a 250.-mL volumetric flask and fills it to the mark with water, (a) Calculate the molarities of the major ionic species, (b) Draw a molecular picture that shows a portion of this solution, making sure the portion is electrically neutral. 

Calculate the molarities of the ionic species present in 0.150 L of solution containing 27.0 g of sodium chloride, (b) Calculate the new molarities if 50.0 mL of this solution is diluted with water to give 450. mL of a new solution, (c) Draw molecular pictures of portions of the solutions described in (a) and (b), showing how they differ. 

C04-0030. The acidic component of vinegar is acetic acid. When 5.00 mL of vinegar was added to water and the solution titrated with the 0.1250 M NaOH, it took 33.8 mL to reach the stoichiometric point. Calculate the molarity of acetic acid in vinegar. 

X 10 J of energy or by emission of positrons with 1.04 X 10 J of energy, (a) Write the two decay reactions, (b) Calculate the molar masses of the two elemental products using mass-energy equivalence. 

Due to varying solvent systems, varying purities and water contents of purified pigments, different molar extinction coefficients have been reported." - - The most reliable ones commonly applied are 60,000 L/mol cm for betanin, 56,600 L/mol cm for amaranthin, and 48,000 L/mol cm for betaxanthins. ° Pigment contents may be calculated with the following formulae." - ... 

With molarity and volume of solution, numbers of moles can be calculated. The numbers of moles may be used in stoichiometry problems just as moles calculated in any other way are used. Also, the number of moles calculated as in Chap. 8 can be used to calculate molarities or volumes of solution. 

The Flenry s law constant data calculated as the ratio of vapor pressure to solubility in Figure 1.7.13 are quite scattered. There is little systematic variation with molar volume. Most values of log H lie between -0.1 to -0, i.e., H lies between 0.8 and 0.08, and the resulting air-water partition coefficient KAW or H/RT thus lies between 3 x 10-4 and 3 x 10-5. 

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