Water molar heat capacity

A/H the molar heat (enthalpy increase) of fusion of ice to pure water, molar heat capacity of liquid water (constant pressure) at P, molar heat capacity of ice (constant pressure) at P, the molar mass of water, molality of solution. 

E5.4 The apparent molar heat capacity of sucrose (2) in water (1) is given as a function of the molality, m by the expression... 

Heat capacity is an extensive property the larger the sample, the more heat is required to raise its temperature by a given amount and so the greater is its heat capacity (Fig. 6.10). It is therefore common to report either the specific heat capacity (often called just specific heat ), Cs, which is the heat capacity divided by the mass of the sample (Cs = dm), or the molar heat capacity, Cm, the heat capacity divided by the amount (in moles) of the sample (Cm = C/n). For example, the specific heat capacity of liquid water at room temperature is 4.18 J-(°C) -g, or 4.18 J-K 1-g and its molar heat capacity is 75 J-K -mol1. 

These expressions may be rearranged to calculate the specific or molar heat capacity from the measured temperature rise caused by a known quantity of heat. The specific heat capacity of a dilute solution is normally taken to be the same as that of the pure solvent (which is commonly water). Table 6.2 lists the specific and molar heat capacities of sume common substances. 

Hydrochloric acid oxidizes zinc metal in a reaction that produces hydrogen gas and chloride ions. A piece of zinc metal of mass 8.5 g is dropped into an apparatus containing 800.0 mL of 0.500 M HCl(aq). If the initial temperature of the hydrochloric acid solution is 25°C, what is the final temperature of this solution Assume that the density and molar heat capacity of the hydrochloric acid solution are the same as those of water and that all the heat is used to raise the temperature of the solution. 

Calculate the standard entropy of vaporization of water at 85°C, given that its standard entropy of vaporization at 100.°C is 109.0 J-K -mol 1 and the molar heat capacities at constant pressure of liquid water and water vapor are 75.3 J-K -mol 1 and 33.6 J-K -mol, respectively, in this range. 

A Z depends on the identity of the material. For instance, 50 J of heat increases the temperature of 1 mol of gold more than it increases the temperature of 1 mol of water. The dependence of AT on the identity of the material is expressed by the molar heat capacity (C, units J moP ° C ). The molar heat capacity is the amount of heat needed to raise the temperature of 1 mol of substance by 1 °C. Eveiy substance has a different value for C. The molar heat capacities of several chemical substances are listed in Table 6-1. 

EXAMPLE 18.10. What is the final temperature of 2.25 mol of water initially at 17.l°C from which 1910J of heat is removed The molar heat capacity of water is 75.38 J/mol deg. 

We note several things about this example. First, the number of moles of water and the molar heat capacity were used. Second, since the heat was removed, the value used in the equation was negative. The final temperature is obviously lower than the initial temperature, since heat was removed. 

For liquid water and for aqueous solutions we wiU assume Cp = 1 cal/g K, and, since the density p of water is -1 g/cm, we have pCp = 1 cal/cm K or pCp =1000 cal/Uter K. To estimate the heat capacity of gases, we will usually assume that the molar heat capacity Cp is j R cal/mole K. There are thus three types of heat capacity, the heat capacity per unit mass Cp, the heat capacity per unit volume pCp, and the heat capacity per mole Cp. However, we will use heat capacity per unit volume for much of the next two chapters, and we use the symbol pCp for most of the equations. 

Table 6.1 Comparison of the mean molar heat capacities for carbon dioxide and hydrogen, and carbon monoxide and water...

For very many liquids, the entropy of vaporization at the normal boiling point is approximately 21 cal/mole °C water is not typical. The units for changes in entropy are the same as those for molar heat capacity, and care must be used to avoid confusion. When referring to an entropy change, a cal/mole °C is often called an entropy unit, abbreviated e.u. In order to avoid later misunderstanding, note now that this method of calculating AS from A HIT is valid only under equilibrium conditions. For transitions, for example, this method can be used only at temperatures where the two phases in question can coexist in equilibrium with each other. 

Continued addition of heat to liquid water raises the temperature until it reaches 100°C. We can calculate from the molar heat capacity of liquid water [75.4 J/(mol °C)] that 7.54 kj/mol is required ... 

Draw a molar heating curve for sodium similar to that shown for water in Figure 10.10. Begin with solid sodium at its melting point, and raise the temperature to 1000°C. The necessary data are mp = 97.8°C, bp = 883°C, AHvap = 89.6 kj/mol, and AHfusion = 2.64kJ/mol. Assume that the molar heat capacity is 28.2 J/(K mol) for both liquid and vapor phases and does not change with temperature. 

Mixtures of these surfactants with water result in solutions with unique properties that we want to consider. We will use the alkylpyridinium chlorides as examples. Figure 18.11 compares the osmotic coefficient 0, apparent relative molar enthalpy 4>L, apparent molar heat capacity Cp, and apparent molar volumes V as a function of molality for two alkylpyridinium chlorides in water.w19... 

The heat capacity of a body is the amount of heat required to raise the temperature of that body 1K (1°C). For pure substances, it is most convenient to refer to quantities of molar heat capacity (heat capacity per mole) and, as discussed above, the specific heat capacity or, more commonly, the specific heat (heat capacity per unit of mass). As an example, the average specific heat of water is... 

Using these data for water, the molar heat capacity is 18.02 cal/mol K (approximately 75.40 J/mol K). Note that the deviations from this average are all less than 1 percent between the freezing and boiling points. The point being made is that the heat capacity may depend (slightly) on temperature, but is a reasonably stable value making it possible to consider heat capacity as a constant, as it is in this book. 

There are several advantages, particularly in the context of aqueous solutions, in representing water using eqn (16). Thus, to a first approximation, a solute which increases (H20)b at the expense of (H20)d is a structure former a structure breaker has the opposite effect. The large heat capacity for water can be attributed to the need to melt part of (H20)b. In these terms, the partial molar heat capacity of solutes in water often indicates their effect on water structure. 

Figure 46. Solvent dependence of the partial molar heat capacity of sodium tetraphenyl-borate in t-butyl alcohol + water mixtures at 298 K as a function of alcohol mole fraction, xj (Arnett and McKelvey, 1966b).

Thus the partial molar enthalpy of Bu4N+Br increases sharply when t-butyl alcohol is added to aqueous solutions until x2 - 0 1 and then decreases slowly (Mohanty et al., 1971). Similar complex patterns emerge in the enthalpies of these salts when amide cosolvents are added, e.g. formamide (de Visser and Somsen, 1974a,b). Striking changes are observed in the partial molar heat capacities of salts in TA mixtures when x2 is varied (Avedikian et al., 1975). Thus for Am4N+Br in t-butyl alcohol + water mixtures (Mohanty et al., 1972), the partial molar heat capacity increases as x2 increases to a maximum near x2 — 0-04, drops sharply to a minimum and then... 

The molar heat capacity (molar thermal capacity), which is the energy required to increase the temperature of 1 mol by 1°C, is 75.4 J mol-1 °C-1 for water. The energy to heat water from 0°C to 25°C therefore is... 

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