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Material Type: Assignment; Class: Chemical Energetics & Kinetics; Subject: Chemistry; University: Albion College; Term: Fall 2008;
Typology: Assignments
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Chem 301 Problem Day # Fall 2008 Answers
a. f(x)=x^3 +3x^2 +
3 6 2 6 6
2 (^2) x dx
d f x x dx
df
b. f(θ)=sin^2 θ
2 2 2
2 2 sin sin 2 sin cos 2 sin sin cos cos 2 sin cos dx
d f d
d dx
df
c. f(x)=ln(1+x) (first derivative only)
dx x
df 1
a. dx x^2
x
b. dx x
(^33) ln( x ) x
c.
2
1
( x^3 3 x^21 ) dx
3
(^24)
1
3
4 x x x
d. e^4 xdx 2
(^3) x x e^4 e^4 8
y
f x x y
y y
x x
y
2 x
f y^2
ln( 2 ) y
x x
Other problems (pay attention to units!):
T = 40+273 = 313 K PV = nRT V = 2.46 dm^3 n = PV/RT = 1.40(2.40) / (.083145)(313) P = 140 kPa = 1.40 bar n = 0.132 moles
PBr2 = 628 torr x 133.322 Pa/torr x bar / 100000 Pa = 0.837 bar PCH4 = 1.43 atm x 1.01325 bar/1atm = 1.45 bar Ptotal = 0.837 + 1.45 = 2.29 bar P 1 /T 1 = nR/V = P 2 /T 2 T 1 = 70 + 273 = 343 K 2.29/343 = P 2 / T 2 = 14 + 273 = 287 K P 2 = 1.91 bar
T 1 = 23 + 273 = 296 V 1 = n 1 RT 1 /P 1 = (414)(.083145)(296)/(103.4) P 1 = 102 atm = 103.4 bar = 98.7 L n 1 = 11600 g x 1 mole/28.06 g = 414 mole
T 2 = 296 n 2 = P 2 V 2 /RT 2 = (75.8)(98.7)/(.083145)(296) P 2 = 74.8 atm = 75.8 bar = 304 mole V 2 = 98.7 L mass = 304 mole x 28.06 g /mole = 8.51 kg n 2 = ??
b. Energy will be a focus of much of our work this semester. The SI units for energy are Joules (J). Express the Joule unit in terms of seconds, kg, and meters. Energy is the work done by a force along a fixed distance: N·m. This is equivalent to kg·m^2 ·sec-