Question 1 a) The UV-visible spectrum of a complex ion shows an absorption in th

Question

Question 1 a) The UV-visible spectrum of a complex ion shows an absorption in the visible region with a wavelength Amax 518 nm. Convert this wavelength into "wavenumbers", b) Comparing the binding energies (BE) of 2p electrons in Ti-metal and TiO2 it is found that their BE are 453.8 eV and 458.5 eV, respectively. Calculate the energy difference between the two BE expressed in J. c) To eject an electron of a certain metal from its surface it takes 4.32E-19 J of energy. Calculate the longest possible wavelength, in nanometers, that is required to ionize the metal. Question 2 a) What mass of AgNO3 (169.9 g/mol) is needed to convert 2.33 g of Na2CO3 (106.0 g/mol) to Ag2 CO3? b) What mass of Ag2Co3(s) (257.7 E/mol) will be formed? a) The unit of power is Watt (W) after the Scottish inventor James Watt. Show that the S uunit of Watt is J/s if power (P) is defined: P (Force x Distance) /time b) What is the energy consumption of an electrical circuit that has power consumption of 40 Watts for a time duration of 3 minutes. Note that your answer should be given in the unit kJ

Explanation / Answer

Q1)

a)Wavenumber is defined as the number of waves in a unit distance.

In order to calculate wavenumber, we need to find the inverse of the given wavelength as wavenumber is represented by the inverse of wavelength .

Hence, wavenumber = 1 / wavelength,

wavenumber = 1 / 518 nm-1 = 1.931 * 10-3 nm-1

As 1 nm = 10-7cm , 1.931 * 10-3 nm-1 = 1.931 * 10-10 cm-1

b) Difference in their binding energies :- 458.5 - 453.8 = 4.7 eV

As 1 eV = 1.6 * 10-19 J,

4.7 eV = (1.6 * 10-19 J / 1 eV)* 4.7eV = 7.52 * 10-19 J

c) We first need to find out the corresponding frequency for electron emission. This is the least value of incident frequenct which must be applied for emission of electron. After that, we find out the corresponding wavelength, which is the longest value of wavelength which can emit electrons from the metal surface:

As per the relation , E = h? ,

We calculate frequency ? = E / h

=> ? = 4.32 * 10-19 J / 6.626 * 10-34 Js = 6.519 * 1014 s-1

We can now calculate required wavelength by the relation : c = v? or ? = c / v

hence, wavelength ? = 3 * 108 ms-1/  6.519 * 1014 s-1 = 4.602 * 10-7 m

As 1 m = 109 nm, 4.602 * 10-7 m = (109 nm / 1 m) * 4.602 * 10-7 m = 460.2 nm

Q2

a) For given reaction , Na2CO3(aq)+2AgNO3 (aq) --> 2NaNO3(aq)+Ag2CO3 (s) , we use mole concept to solve the problem:

2 moles AgNO3 is required to convert 1 mole of Na2CO3 to Ag2CO3

This implies, 2 * 169.9 g AgNO3 is required to convert 106 g of Na2CO3

Hence, 2.33 g of Na2CO3 needs : 2 * 169.9 / 106 * 2.33 g of AgNO3 = 7.47 g of AgNO3

Again, as per reaction , 1 mole Na2CO3 reacts with 2 mole AgNO3 to give 1 mole Ag2CO3

This implies , 106 g Na2CO3 gives 257.7 g Ag2CO3

Hence, 2.33 g  Na2CO3 gives : (257.7 / 106) * 2.33 g Ag2CO3 = 5.66 g  Ag2CO3

Last bit:

a) As P = (Force * distance) / time , we put the SI units of respective quantities in the equation

P = (N * m) / s

= J / s ( As J = Nm)

Hence proved.

b) The energy consumption of a circuit can be found out from the following formula:

E = P * t

P = 40 W, t = 3 minutes = 3 * 60 s = 180s

Hence, Energy E = 40 * 180 J = 7200 J

As 1 kJ = 103J ,  7200 J = 7.2 kJ

If you have any doubt, please let me know in the comments. I'll reach you at the earliest :)

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