Page 55 - Physical Chemistry

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1.56 Give a molecular explanation for each of the following sum (1.58) for x 0.1, 0.01, and 0.001; take the x values at
i
facts. (a) For solids and liquids, k usually decreases with in- the left end of each subinterval. Compare your results with the
creasing pressure. (b) For solids and liquids, ( k/ T) is usually exact value. (b) Use (1.58) with x 0.01 to obtain an ap-
P
1 x
positive. proximate value of 0 e 2 dx.
1.57 Estimate the pressure increase needed to decrease 1.67 (a) Find log (4.2 10 1750 ). (b) Find ln (6.0 10 200 ).
10
isothermally by 1% the 1-atm volume of (a) a typical solid (c) If log y 138.265, find y. (d) If ln z 260.433, find z.
10
1
with k 5 10 6 atm ; (b) a typical liquid with k 1
1
10 4 atm . 1.68 Find (a) log 32; (b) log 1.
2
43
Section 1.8 General
1.58 (a) Evaluate 4 (2J 1). (b) Write the expression
J 0
x V x V x V using summation notation. (c) Write 1.69 Classify each property as intensive or extensive; (a) tem-
1 1 2 2 s s
out the individual terms of the double sum 2 6 b . perature; (b) mass; (c) density; (d) electric field strength; (e) a;
i 1 j 4 ij
( f) mole fraction of a component.
1.59 Prove the sum identities in (1.50) and (1.51). (Hint:
Write out the individual terms of the sums.) 1.70 For O gas in thermal equilibrium with boiling sulfur,
2
the following values of PV versus P are found:
m
2
4
1.60 Evaluate: (a) 3 2 (2V 5V ) dV; (b) V 1 dV;
2
2
3
(c) V 3 dV; (d) p/2 x cos x dx.
q
1 0 P/torr 1000 500 250
p
1.61 Find (a) sin ax dx;(b) sin ax dx;
0 1
2
p
(c)(d/da) sin ax dx;(d) (a/T ) dT. PV /(L atm mol ) 59.03 58.97 58.93
m
0
1
1.62 For H O(l) at 50°C and 1 atm, a 4.576 10 4 K ,
2 (Since P has units of pressure, P/torr is dimensionless.) From a
1
3
k 44.17 10 6 bar , and V 18.2334 cm /mol. (a) Esti-
m plot of these data, find the boiling point of sulfur.
at 52°C and 1 atm and compare the result with the
mate V m,H 2 O
3
experimental value 18.2504 cm /mol. Neglect the temperature 1.71 True or false? (a)Every isolated system is closed.
at 50°C and 200 bar and (b)Every closed system is isolated. (c)For a fixed amount of
dependence of a. (b) Estimate V m,H 2 O
3
compare with the experimental value 18.078 cm /mol. an ideal gas, the product PV remains constant during any
process. (d) The pressure of a nonideal gas mixture is equal
1.63 State whether each of the following is a number or is a to the sum of the partial pressures defined by P x P.
2
2
203
x
x
x
function of x: (a) e dx; (b) 1 2 e dx; (c) x 1 e . 2 i i
(e) dy/dx is equal to y/ x for all functions y. ( f ) dy/dx is
1.64 In which of the following is t a dummy variable? equal to y/ x only for functions that vary linearly with x
2
2
t
t
100
5
(a) e dt; (b) 0 3 e dt; (c) t 1 t . according to y mx b. (g)ln(b/a) ln (a/b). (h)Ifln x
is negative, then x lies between 0 and 1. (i) Ideal-gas
3
5x
1.65 (a) If df(x)/dx 2x 3e , find f(x). (b) If f(x) dx
8
3x C, where C is a constant, find f(x). isotherms farther away from the axes of a P-versus-V plot
correspond to higher temperatures. ( j) The partial derivative
1.66 (a) Use a programmable calculator or a computer to ( P/ T) is an infinitesimally small quantity. (k)If G is a
V
3
2
obtain approximations to the integral x dx by evaluating the function of T and P, then dG ( G/ T) ( G/ P) .
2 P T