Applications to Non-Homogeneous Systems

Excerpts

• Applications to Non-Homogeneous Systems

  This means that the internal energy of lead and sulphur, when separate, is $18,400$ calories greater than that of their combination at the same temperature.

• Applications to Non-Homogeneous Systems

  It, therefore, depends on the initial and final states only, and not on the intermediate steps of the process.

• Applications to Non-Homogeneous Systems

  The pressure has, however, very little influence on the internal energy; in fact, none at all in the case of perfect gases [equation % [eqn:(35)](35)%].

• Applications to Non-Homogeneous Systems

  In our equations we shall therefore use $Q$ (the heat absorbed) with the negative sign, in processes with positive heat effect (*e.g.* combustion); with the positive sign, in those with negative heat effect (*e.g.* evaporation, fusion, dissociation).

• Applications to Non-Homogeneous Systems

  For this reason we classify substances according to their physical and not according to their chemical homogeneity.

• Applications to Non-Homogeneous Systems

  Furthermore, most chemical processes are accompanied by a rise in temperature, or, if the initial temperature be re-established, by an external yield of heat (exothermal processes).

• Applications to Non-Homogeneous Systems

  He denoted by the formulæ for the atomic or molecular weight of the substances enclosed in brackets, the internal energy of a corresponding weight referred to an arbitrary zero of energy.

• Applications to Non-Homogeneous Systems

  These symbols may be treated like algebraic quantities, whereby considerations, which would otherwise present considerable complications, may be materially shortened.

• Applications to Non-Homogeneous Systems

  But since its change of energy $U_{2} - U_{1}$ depends on the initial and final states only, a greater amount of work done against the external forces necessitates a smaller heat effect for the process, and *vice versâ*.

• Applications to Non-Homogeneous Systems

  The heat effect, however, is not equal to the difference of the internal energies $U$, but to the difference of the values of the quantity $(U + p_{0} V)$ at the beginning and end of the process.

• Applications to Non-Homogeneous Systems

  Frequently, of two ways of transition, one is better adapted for calorimetric measurements than the other. Thus, the heat effect of the decomposition of hydrogen peroxide into water and oxygen cannot readily be measured directly.

• Applications to Non-Homogeneous Systems

  The difference between these values is $-7.71$, and, therefore, the heat of combustion of a gram molecule of hydrogen decreases with rising temperature by $7.7~\Unit{cal.}$ per degree Centigrade.

Equations

• Applications to Non-Homogeneous Systems

  Q + W = U_{2} - U_{1}

  The external effects (heat Q and external work W) together equal the change of internal energy from state 1 to state 2.

• Applications to Non-Homogeneous Systems

  \ce{[Pb] + [S] - [PbS]} = 18,400~\Unit{cal.}

  Forming one molecule of lead sulphide from separate lead and sulphur atoms at the same temperature releases 18,400 calories, so the internal energy of the separate atoms exceeds that of the compound by this amount.

• Applications to Non-Homogeneous Systems

  \ce{[PbS]} = -18,400~\Unit{cal.}

  With the uncombined elements taken as the zero of energy, the energy of a molecule of lead sulphide is -18,400 calories.

• Applications to Non-Homogeneous Systems

  \ce{(H2O) - [H2O]} = 80 × 18 = 1440~\Unit{cal.}

  The fusion of ice at 0 degrees C absorbs 1440 calories per gram molecule of water (80 calories per gram times 18 grams).

• Applications to Non-Homogeneous Systems

  \ce{(H2SO4) + 5(H2O) - (H2SO4 . 5H2O)} = 13,100~\Unit{cal.}

  Dissolving one molecule of sulphuric acid in five molecules of water gives out 13,100 calories of heat.

• Applications to Non-Homogeneous Systems

  \ce{(H2SO4) + 10(H2O) - (H2SO4 . 10H2O)} = 15,100~\Unit{cal.}

  Dissolving one molecule of sulphuric acid in ten molecules of water gives out 15,100 calories of heat.

• Applications to Non-Homogeneous Systems

  \ce{(H2SO4 . 5H2O) + 5(H2O) - (H2SO4 . 10H2O)} = 2000~\Unit{cal.}

  Diluting the five-molecule solution of sulphuric acid by five more molecules of water gives out 2000 calories.

• Applications to Non-Homogeneous Systems

  \ce{(H2SO4) + ($\aq$) - (H2SO4 $\aq$)} = 17,900~\Unit{cal.}

  The heat effect of infinite dilution of one molecule of sulphuric acid is 17,900 calories, with the solvent taken as any amount sufficient for an infinitely dilute solution.

• Applications to Non-Homogeneous Systems

  U_{2} - U_{1} = Q

  When volume changes are negligible (solids and liquids only), the heat effect alone is the change of energy, depending only on initial and final states.

• Applications to Non-Homogeneous Systems

  W = -\int_{1}^{2} p_{0}\, dV = p_{0} (V_{1} - V_{2})

  At constant pressure the external work equals the pressure times the decrease of volume.

• Applications to Non-Homogeneous Systems

  U_{2} - U_{1} = Q + p_{0} (V_{1} - V_{2})

  At constant pressure the change of internal energy equals the heat effect plus the pressure times the decrease of volume.

• Applications to Non-Homogeneous Systems

  V_{1} - V_{2} = R \frac{\theta}{p_{0}} (n_{1} - n_{2})

  The decrease of gaseous volume in a reaction is proportional to the change in the number of gas molecules, at fixed temperature and pressure.

• Applications to Non-Homogeneous Systems

  \frac{W}{J} = \frac{p_{0} (V_{1} - V_{2})}{J}

  The heat equivalent of the external work at constant pressure is the external work divided by the mechanical equivalent of heat.

• Applications to Non-Homogeneous Systems

  \frac{R}{J} \theta (n_{1} - n_{2}) = 1.97 \theta (n_{1} - n_{2})~\Unit{cal.}

  The heat equivalent of the external work at constant pressure equals 1.97 calories per degree times the temperature times the change in number of gas molecules.

• Applications to Non-Homogeneous Systems

  -Q = U_{1} - U_{2} + 1.97 \theta (n_{1} - n_{2})~\Unit{cal.}

  The heat effect of a process at constant pressure equals the decrease of internal energy plus the heat equivalent of the external work.

• Applications to Non-Homogeneous Systems

  -Q = \ce{\{H2\} + $\tfrac{1}{2}$ \{O2\}} - \ce{(H2O)} + 860~\Unit{cal.}

  The heat of combustion of one gram molecule of hydrogen with half a gram molecule of oxygen at 18 degrees C and constant pressure is 860 calories more than the decrease of internal energy.

• Applications to Non-Homogeneous Systems

  (U + p_{0} V)_{2} - (U + p_{0} V)_{1} = Q

  At constant pressure the heat effect equals the difference of the heat function U + p0 V between the final and initial states.

• Applications to Non-Homogeneous Systems

  (U_{2} + p_{0} V_{2})_{\theta} - (U_{1} + p_{0} V_{1})_{\theta} = Q_{\theta}

  At temperature theta, the heat effect at constant pressure equals the difference of the heat function between final and initial states.

• Applications to Non-Homogeneous Systems

  \ce{(NaHCO3 $\aq$) + (NaHO $\aq$) - (Na2CO3 $\aq$)} = 9200~\Unit{cal.}

  The heat of neutralization of a solution of sodium bicarbonate with caustic soda is 9200 calories (Thomsen).

• Applications to Non-Homogeneous Systems

  \ce{(CO2 $\aq$) + 2(NaHO $\aq$) - (Na2CO3 $\aq$)} = 20,200~\Unit{cal.}

  The heat of neutralization of carbon dioxide by caustic soda to sodium carbonate is 20,200 calories (Thomsen).

• Applications to Non-Homogeneous Systems

  \ce{(CO2 $\aq$) + (NaHO $\aq$) - (NaHCO3 $\aq$)} = 11,000~\Unit{cal.}

  The direct combination of carbon dioxide and caustic soda to sodium bicarbonate releases 11,000 calories, obtained by subtracting the two neutralization results.

• Applications to Non-Homogeneous Systems

  \ce{(SnCl2 . 2HCl $\aq$) + (H2O2 $\aq$) - (SnCl4 $\aq$)} = 88,800~\Unit{cal.}

  Oxidizing stannous chloride in hydrochloric acid by hydrogen peroxide in solution releases 88,800 calories.

• Applications to Non-Homogeneous Systems

  \ce{(SnCl2 . 2HCl $\aq$) + $\tfrac{1}{2}$ \{O2\} - (SnCl4 $\aq$)} = 65,700~\Unit{cal.}

  Oxidizing the same stannous chloride solution by oxygen gas releases 65,700 calories.

• Applications to Non-Homogeneous Systems

  \ce{(H2O2 $\aq$) - $\tfrac{1}{2}$ \{O2\} - ($\aq$)} = 23,100~\Unit{cal.}

  The decomposition of dissolved hydrogen peroxide into oxygen and water releases 23,100 calories, found by subtracting the two oxidation results.

• Applications to Non-Homogeneous Systems

  \ce{[C] + \{O2\} - \{CO2\}} = 97,000~\Unit{cal.}

  The complete combustion of solid carbon to carbon dioxide releases 97,000 calories.

• Applications to Non-Homogeneous Systems

  \ce{\{CO\} + $\tfrac{1}{2}$ \{O2\} - \{CO2\}} = 68,000~\Unit{cal.}

  The combustion of carbon monoxide to carbon dioxide releases 68,000 calories.

• Applications to Non-Homogeneous Systems

  \ce{[C] + $\tfrac{1}{2}$ \{O2\} - \{CO\}} = 29,000~\Unit{cal.}

  The heat of formation of carbon monoxide from solid carbon and oxygen is 29,000 calories, found by subtraction.

• Applications to Non-Homogeneous Systems

  \ce{[S] + \{O2\} - \{SO2\}} = 71,100~\Unit{cal.}

  The combustion of solid sulphur to sulphur dioxide gas releases 71,100 calories.

• Applications to Non-Homogeneous Systems

  \ce{\{CS2\} + 3\{O2\} - \{CO2\} - 2\{SO2\}} = 265,100~\Unit{cal.}

  The combustion of carbon bisulphide vapour to carbon dioxide and sulphur dioxide releases 265,100 calories.

• Applications to Non-Homogeneous Systems

  \ce{\{CS2\} - (CS2)} = 6400~\Unit{cal.}

  The condensation of carbon bisulphide vapour to liquid releases 6400 calories.

• Applications to Non-Homogeneous Systems

  \ce{[C] + 2[S] - (CS2)} = - 19,500~\Unit{cal.}

  The heat of formation of liquid carbon bisulphide from solid carbon and solid sulphur is -19,500 calories, hence negative, obtained by elimination.

• Applications to Non-Homogeneous Systems

  \ce{\{CH4\} + 2\{O2\} - \{CO2\} - 2(H2O)} &= 211,900~\Unit{cal.}

  The complete combustion of methane to carbon dioxide and liquid water releases 211,900 calories.

• Applications to Non-Homogeneous Systems

  \ce{\{H2\} + $\tfrac{1}{2}$ \{O2\} - (H2O)} &= \Z68,400~\Unit{cal.}

  The formation of liquid water from hydrogen and oxygen gas releases 68,400 calories.

• Applications to Non-Homogeneous Systems

  \ce{[C] + 2\{H2\} - \{CH4\}} = 21,900~\Unit{cal.}

  The heat of formation of methane from solid carbon and hydrogen gas is 21,900 calories, obtained by elimination.

Problems

No exercises in this chapter.