For most substances a rough value of the heat of vaporization can be predicted from Trouton s rule, which states that the quotient of the molal heat of vaporization by the absolute boiling point has a constant value, about 21. For example, this rule predicts that the molal heat of vaporization of carbon disulfide, b.p. 319.3 A, be 21 X 319.8 6700 cal the experimental value is 6391 cal. The heats ol vaporization of water and alcohol are larger than expected from Trouton s rule, apparently because of the strong intermolecular forces in the liquids, due to the action of hydrogen bonds. [Pg.641]

The corresponding rule for the quotient of two functions f(x) and g(x) obtains from Rule 2 as [Pg.113]

Based on the rules for writing the reaction quotient, we have [Pg.548]

The familiar rules for combining derivatives with sums, products and quotients apply to complex-valued functions. [Pg.22]

However, as a rule the thermodynamic data for the calculation of the quotient k/oc are not readily available. In this case, the average value of the / P// X ratio of Table 15.8 can be used. [Pg.544]

To differentiate AG/T, apply the rule for differentiating a quotient to give [Pg.128]

Because two different rules are used for the subtraction and division, note that the numerator of part (b) has only two significant digits, as shown in part (a). Therefore the quotient has only two significant digits. [Pg.72]

Let us now differentiate AG/T, with respect to temperature. From the usual rule for differentiating a quotient, we find that [Pg.153]

The partial derivative with respect to V is somewhat trickier. For the first term we use the rule for differentiating a quotient (Chapter 35) while for the second we write l/V as The partial derivative is thus [Pg.141]

Le Chatelier s principle is a handy rule for predicting changes in the composition of an equilibrium mixture, but it doesn t explain why those changes occur. To see why Le Chatelier s principle works, let s look again at the reaction quotient Qc. For the initial equilibrium mixture of 0.50 M N2,3.00 M H2, and 1.98 MNH3 at 700 K, Qc equals the equilibrium constant Kc (0.291) because the system is at equilibrium [Pg.550]

The condition in this theorem is clearly the appropriate functorial definition for quotient group schemes the naive idea of requiring all F(R)-+ G(R) surjective would rule out many cases of interest. The functorial statement can be understood as a sheaf epimorphism condition, as the next section will briefly explain. [Pg.149]

We can apply this procedure to calculate the quotient of two exponential numbers even when the denominator has a larger magnitude than the numerator. For example, let s divide 8.0 x 10 by 4.0 x 10. The rule for dividing exponential numbers gives the following resnlt [Pg.49]

Multiplication or division. The product or quotient should be rounded off to the same number of significant figures as the least accurate number involved in the calculation. Thus, 0.00296 x 5845 = 17.3, but 0.002960 x 5845 = 17.30. However, this rule should be applied with some discretion. For example, consider the following multiplication [Pg.47]

To divide one number by another, put them both in standard scientific notation. Divide the first lefthand factor by the second, according to the rules of ordinary division. Divide the first righthand factor by the second, according to the division law for exponents—that is, by subtracting the exponent of the divisor from the exponent of the dividend to obtain the exponent of the quotient. [Pg.9]

Problems in chemistry sometimes require the differentiation of functions which are more complicated than those discussed so far. In the previous chapter it was seen how to differentiate a function multiplied by a constant, and sums and differences of simple functions. For completeness, these rules are formalised here, before products and quotients of functions are considered. [Pg.126]

By minimizing the error between b ) and the b simultaneously, which are respectively the intercept and the slope of the graph, one can find the best fit for the calculated data points. In (18.3), w, is the weight of the point on the line determined from the error bars in each isothermal-isobaric simulation. For the propagation of error, and in particular, by using the uncertainty in sums and differences and the uncertainty in products and quotients rules, the intersection of the lines, x, can be shown to be [Pg.362]

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