Answers to the following problems are found in the folder "Ch. 09 (Simultaneous Equations)" in the "Problems & Solutions" folder on the CD.
1. Solve the following system of four simultaneous equations:
2. Current flow in a circuit is described by Kirchhoffs laws. A particular circuit network yielded the following three simultaneous linear equations:
Find the currents I\I2 and /3 in the circuit network.
3. Solve the following system of four simultaneous equations:
2.829*, - 2.253*2 + 6.777*3 + 3.970*4 = 6.235 1.212*, + 1.995*2 + 2.265*3 + 8.008*4 = 7.319 4.553*1 + 5.681*2 + 8.850*3 + 1.302*4 = 5.730 5.808*i - 5.030*2 + 0.098*3 + 7.832*4 = 9.574
4. The UV-visible spectra of aqueous solutions of C0CI2, NiCl2 and CuCl2 are shown in Figure 9-16.
350 450 550 650 750
Wavelength, nm
Figure 9-16. UV-visible spectra of cobalt, nickel and copper solutions.
350 450 550 650 750
Wavelength, nm
Figure 9-16. UV-visible spectra of cobalt, nickel and copper solutions.
Three wavelengths were chosen at which the absorbance of the three species, Co2+, Ni2+ and Cu2+, differed significantly. The molar absorptivities of the three species at the three wavelengths are shown in Table 9-1.
A,/nm |
Co2+ |
Ni2+ |
Cu2+ |
394 |
0.995 |
6.868 |
0.188 |
510 |
6.450 |
0.215 |
0.198 |
808 |
0.469 |
1.179 |
15.052 |
A mixture of the three metal ions gave the following absorbance readings at the three wavelengths: 394 nm, 0.845; 510 nm, 0.388; 808 nm, 1.696, when measured using a cell with a 1.00-cm path length. Calculate the concentration of the three metal ions in the mixture, using Beer's Law: A = sbc (A = absorbance, e = molar absorptivity, b = cell path length in cm, c = concentration in mol/L).
5. The following sets of simultaneous equations may or may not be solvable by the Gaussian Elimination method. For each case, explain why. If solvable, solve.
2 |
-1 l" |
"4" | ||||||||||||||||||||||||||||||||||||||||||||||||||
(b) |
1 |
3 2 |
12 | |||||||||||||||||||||||||||||||||||||||||||||||||
3 |
2 3_ |
6. Solve the following system of six simultaneous equations:
7. Solve the following system of nonlinear equations: 8. Solve the following system of nonlinear equations: |
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