1. Use Laplace transforms to solve the following differential
equations for ?(?) for ? ≥ 0. Use ?(0) = 0 and ?̇(0) = 1 for each
case.
i. 0 = ?̈(?) + 2?̇(?) + 4?(?)
ii. 0 = ?̈(?) + 3?̇(?) + 2?(?)
iii. 5 = ?̈(?) + 5?̇(?) + 6?(?)
3. For the three differential equations from problem one
determine the steady-state value of the system using:
a. lim?→0 ??(?),
b. lim ?→∞ ?(?) analytically,
c. lim ?→∞ ?(?)...
Solve the following differential equations using Taylor series
centered at 0. It’s enough to find the recurrence relation and the
first 3 terms of the series.
(a) y''− 2y' + y = 0
(b) y'' + xy' + 2y = 0
(c) (2 + x^2 )y'' − xy'+ 4y = 0
Find ∆H and ∆S for the following data.
Calculate percent errors for the enthalpy and entropy of
reaction using the following literature values: ∆H = 110 kJ/mol, ∆S
= 380J/mol*K
Standardized HCl = .5087M
Ksp = [Na^+]^2[Borox^2-]
ln(Ksp) = -∆H/RT + ∆S/R
Temperature of solution;Amount of HCl needed to titrate
borox;Volume aliquot
Trial 1 - 295K;2.50mL;5.8mL
Trial 2 - 316K;5.76mL;5.4mL
Trial 3 - 309K;4.57mL;5.6mL
Trial 4 - 305K;4.34mL;6.5mL
Trial 5 - 311K;7.70mL;5.8mL
Trial 6 - 310K;7.73mL;6.1mL
After I calculated everything...
The following enthalpy and entropy changes are known for the
reactions shown at 298 K.
Reaction
Cu(s) + 2H+(aq) <=> Cu2+(aq) +
H2(g)
Zn(s) + 2H+(aq) <=> Zn2+(aq) +
H2(g)
delta H
65 kJ/mol
-153 kJ/mol
delta S
-2.1 J/mol K
-23.1 J/mol K
Part a
Which of the these two metals, Zn or Cu, should dissolve in 1 M
acid solution? Explain your answer.
Part B -
Calculate Eo for the Zn reaction. Show work to
support your answer....
Differential Equations
22. Solve each of the following systems of equations.
(c) (D-2)x=0; -3x+(D+2)y=0; -2y+(D-3)z=0
I got x=c1e2t, y= 3/4
C1e2t + C2e-2t by using
diffieq method d/dx(ye2t) =
3C1e2t....., but the right answer is
x=4c1e2t, y= 3C1e2t
+ 5C2e-2t , z= -6C1e2t
-2C2e-2t+C3e3t
I want to know where 4 came from, and please do not use matrix
system.
1. Calculate the standard reaction entropy, enthalpy and Gibbs
free energy for the following reactions
a) N2(g) + NO2(g) ---> NO(g) + N2O(g) and
b) 2F2(g) +2H2O(l) ---> 4HF(aq) + O2(g)