Page 208 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 8 ROOTS OF EQUATIONS 185

Problems

Answers to the following problems are found in the folder "Ch. 08 (Roots of
Equations)" in the "Problems & Solutions" folder on the CD.

1. A circuit consisting of a source, a resistor and a load, has a current i that
oscillates as a function of time t according to the following:

7T 7T
i = 2.5 sin(-)e-2.5' + 2.5 sin(2.5t - -)
4 4
Find the first time after t = 0 when the current reaches zero.)

2. In pipe flow problems the relationship
aD3 + bD + c = 0
is encountered. Solve for D, if a = 700, b = -2.9, c = -300.

3. When the sparingly soluble salt BaC03 is dissolved in water, the following
simultaneous equilibria apply:
BaC03 e Ba2++ C03'- Ksp = [Ba2'][C032-] = 5.1 x lo-'

C0:- + H20 + HCO< + OH- Kb = [OH-][ HCO<]/[ C032-] = 2.1 x lo4
Employing mass- and charge-balance equations, the following relationship
can be obtained for a saturated solution of BaC03 in water:
[Ba2+I2 - JKbKsp [Ba2+]1'2 - Ksp = 0

Find the concentration of free Ba2' in the saturated solution.

4. A solution of 0.10 M nitric acid (HNO3) is saturated with silver acetate
(AgAc), a sparingly soluble salt. The system of mass- and charge-balance
equations describing the system is
NO^-] = 0.1 o (mass balance)

[Ag'] = S (mass balance)
[Ac-] + [HAc] = S (mass balance)
[Ag'] + [W] = [Ac-] + [NOS-] (charge balance)
[Ag'][Ac-] = 4.0 x KSp
[H'][Ac-]/[HAc] =1.8 x KO