The fluoride ISE is used routinely for measuring fluoridated water and fluoride ion in dental products such as mouthwash. A 50 mL aliquot of water containing sodium fluoride is analyzed using a fluoride ion electrode and the MSAs. The pH and ionic strength are adjusted so that all fluoride ion is present as free F- ion. The potential of the ISE/reference electrode combination in a 50 mL aliquot of the water was -0.1805 V. Addition of 0.5 mL of a 100 mg/L F- ion standard solution to the beaker changed the potential to -0.3490 V. Calculate the concentration of (1) fluoride ion and (2) sodium fluoride in the water sample.

NASA is sending a remote-sensing spacecraft to Mars.

Given:

Earth parking orbit altitude= 1000 km

Mars Parking orbit altitude=  500 km

μ_Earth =  3.99x10⁵ km³/s²

μ_Mars =  4.280x10⁴ km³/s²

μ_Sun =  1.33x10¹¹ km³/s²

^{Earth's orbital radius =   1.50 x108 km (assume Earth has a circular orbit for this problem)}

Mars' orbital radius =  2.28  x10⁸ km (assume Mars has a circular orbit for this problem)

Find the semi major axis of the transfer orbit, v∞Earth , v∞Mars, ΔVboost,ΔVretro ,ΔVmission (enter your answer as a number which will be assumed to be in km)

During isobaric process m=64 kg of wet water stream at temperature t=262.7?C and pressure p=49 bar changed its specific volume from v1 =0.0018 m3/kg to v2=0.035 m3/kg. Find initial and final quality of steam, change of internal energy of steam, work done by steam, amount of heat exchanged with surroundings. Draw the process at the enthalpy-entropy diagram. From tables for p=49 bar: v’=0.0013 m3/kg, v”=0.0403 m3/kg, h’= 1148.4 KJ/kg, h”= 2794.7 KJ/kg

A galvanic (voltaic) cell consists of an electrode composed of nickel in a 1.0 M nickel(II) ion solution and another electrode composed of gold in a 1.0 M gold(III) ion solution, connected by a salt bridge. Calculate the standard potential for this cell at 25 °C.

____V

2)Consider these two entries from a fictional table of standard reduction potentials.

X2+ + 2e- => X(s) E=2.26 V
Y2+ + 2e- => Y(s) E=0.14 V

Which pair of species would react under standard conditions?

_X2+ and Y
_X2+ and Y2+
_X and Y
_X and Y2+

(a) Let λ be a real number. Compute A − λI.

(b) Find the eigenvalues of A, that is, find the values of λ for which the matrix A − λI is not invertible. (Hint: There should be exactly 2. Label the larger one λ1 and the smaller λ2.)

(c) Compute the matrices A − λ1I and A − λ2I.

(d) Find the eigenspace associated with λ1, that is the set of all solutions v = v1 v2 to (A − λ1I)v = 0.

(e) Find the eigenspace associated with λ2 similarly.

Repeat the process to find the eigenvalues and corresponding eigenspaces for

A = [ 0 2 0

2 0 0

1 1 4 ]

(Note that this matrix has three eigenvalues, not 2.)

The plates of an air-filled parallel-plate capacitor with a plate area of 15.0 cm² and a separation of 8.95 mm are charged to a 170-V potential difference. After the plates are disconnected from the source, a porcelain dielectric with

κ = 6.5

is inserted between the plates of the capacitor.

(a) What is the charge on the capacitor before and after the dielectric is inserted?

(b) What is the capacitance of the capacitor after the dielectric is inserted?
F

(c) What is the potential difference between the plates of the capacitor after the dielectric is inserted?
V

(d) What is the magnitude of the change in the energy stored in the capacitor after the dielectric is inserted?
J

A robot moves in rectilinear motion along the ? axis to the positive ? direction. The motion starts
from rest at x = 0 at time t = 0. During the time interval 0 … 6 s the acceleration of the robot is (in
units of m/s2, when t is in seconds)

a(t)=2t, when t=0...2s
a(t)=-t+6, when t=2...6s

Give the corresponding expressions for a) the velocity v(t) and b) the position x(t) of the robot as functions of time in the interval 0 … 6 s. What are c) the final velocity v(6 s), and d) the final position x(6 s) of the robot?

A satellite of mass mS orbits the Earth (with mass m_E and radius R_E) with a velocity v and an altitude h. The gravitational force F_G and the centripetal force F_C are given by:

F_G = G(m_S · m_E)/(R_E + h)^2 ,

F_C =(m_S · v^2)/(R_E + h) ,

G = const.

(a) Find an equation for the kinetic energy E_kin(h) of a satellite with an altitude h.

(b) Based on the kinetic energy, how much liquid hydrogen (energy density: 10^6J/Litre) is at least needed to bring a small 1 kg satellite in an orbit of 400 km. (Use literature to find m_E, R_E, G.)

A battery is constructed from these two half reactions:

            i.   VO²⁺   +   2 H⁺ + e-   → V³⁺   + H₂O        E^o = 0.337 V vs SHE

            ii.   TiF₆^{2 ̶}   +   4 e-   →   Ti(s) + 6 F ^̶                           E^o = ̶ 1.191 V

(a) (0.2 pt) Which half reaction is in the anode compartment?   Circle one:     vanadium rxn      titanium rxn

(b) Which half reaction is in the cathode compartment? Circle one:    vanadium rxn      titanium rxn

(c) Write the balanced chemical equation for the overall battery reaction.

(d) Show the shorthand notation for representing this particular battery:

(e) Calculate the E^o of the battery.