Chemistry Questions and Answers April 21, 2020

1. Which one of the following pairs is paramagnetic 1) Cl,0, SO, 3) CIO,, NO, 4) SO,, N,O 2) P,O, N,O, 2. CO, NO,,BO The correct increasing order of extent of pbonding in above molecules are II II 1)I II III 2) III II I 3) III P As Bi 2) BP As B 3) B

1. Which one of the following pairs is paramagnetic 1) Cl,0, SO, 3) CIO,, NO, 4) SO,, N,O 2) P,O, N,O, 2. CO, NO,,BO The correct increasing order of extent of pbonding in above molecules are II II 1)I II III 2) III II I 3) III P As Bi 2) BP As B 3) B

1. Which one of the following pairs is paramagnetic 1) Cl,0, SO, 3) CIO,, NO, 4) SO,, N,O 2) P,O, N,O, 2. CO, NO,,BO The correct increasing order of extent of pbonding in above molecules are II II 1)I II III 2) III II I 3) III P As Bi 2) BP As B 3) B

1. Which one of the following pairs is paramagnetic 1) Cl,0, SO, 3) CIO,, NO, 4) SO,, N,O 2) P,O, N,O, 2. CO, NO,,BO The correct increasing order of extent of pbonding in above molecules are II II 1)I II III 2) III II I 3) III P As Bi 2) BP As B 3) B

TH, has two electrons in 3) o Accodng ery, a moleule 4) o Hydrogen bondd is 2) A weak electrostatic force 4) It is not a bond 1)A weak covaient bund 3) A weak metallic force 11. Bydrogen bond may 1) Two bydrogen am 2) Hydrogen atce and clectropositive atom med between 3) Hae and eiectonegative atm with small size 4) Htom and electronegative atom

Numerical Value Type Questions 24. Maximum number of electrons that can be present in any molecular orbital is 25. Number of bonding electrons in N, molecule are 26. Calculate the average bond order of IO bond in IO, (upto 3 decimal places) 27. How many of the following molecule(s) isare known to exist KHF, KHCI,, KHBT,, KHI, KHA., 28. What is

Numerical Value Type Questions 24. Maximum number of electrons that can be present in any molecular orbital is 25. Number of bonding electrons in N, molecule are 26. Calculate the average bond order of IO bond in IO, (upto 3 decimal places) 27. How many of the following molecule(s) isare known to exist KHF, KHCI,, KHBT,, KHI, KHA., 28. What is

Numerical Value Type Questions 24. Maximum number of electrons that can be present in any molecular orbital is 25. Number of bonding electrons in N, molecule are 26. Calculate the average bond order of IO bond in IO, (upto 3 decimal places) 27. How many of the following molecule(s) isare known to exist KHF, KHCI,, KHBT,, KHI, KHA., 28. What is

Numerical Value fype Questions 24 Maximum aumber of elecouns that san be gesent in aey mohocular orhisal is Number of bonding electnus i N. molecule are JA Calculane the average bond anter of O nd in 10cugno1 decimal places) How many of the following moleeuleis are known o exiat KHF KIICI, KI KHI, KIHA. What is the otal member of aati bonding

Water has a higher boiling point than the corresponding hydrides H,S, H,Se and H,le. This i hecause water has d)Vander Waals forces ) lonic bonds ) Hydrogen bonds c) Covalent bonds Which one smong the following does not have the hydrogen bond b) liquid NH, d) Phenol c) Water ) iquid HC 14. Among the following which has the highest boiling point

Water has a higher boiling point than the corresponding hydrides H,S, H,Se and H,le. This i hecause water has d)Vander Waals forces ) lonic bonds ) Hydrogen bonds c) Covalent bonds Which one smong the following does not have the hydrogen bond b) liquid NH, d) Phenol c) Water ) iquid HC 14. Among the following which has the highest boiling point

Wale ling pt a he ooing ydrides . 1,5e and diVander Wals fo Cavalent bondi ly idi wing do l de lyd fenic bnde 4) Phenol Wer 14 ng e ng wich h ighst di CH, Aall, g fonding is pt in Naliyl id hydugin ebloride di benzophenone a pleol 16 whk e b he ling d) C,H,OH A Pahydrory bealdyde i m solute in water han irthohydruxy henzaldehyde Parhyony healdeyde

1l (Species) ColumnII (Bond angle) A) Bond order of NO, P) 2 B) Bond order of SO.2 4 Q) Equal to bond order of benzene C) Bond order of C He 8, R) 1.33 10 D) Bond order of CO, S) 1.5 Integer Type Questions 36. The total no of ions in the unit cell of CsCl is 37. The maximum covalency that iodine can exhibit is 38. The no of sigma bonds in

Integer Type Questions 36. The total no of ions in the unit cell of CSCI is 37. The maximum covalency that iodine can exhibit is 38. The no of sigma bonds in tetracyano ethlylene is 39. Number of hydrogen bonds in H,O, species is 40. The ratio of lone pairs between ACI and CO, is 41. Out of. I, , ICI,, BeCl,, XeF,, XeF, BrF3, HC CH. How many will

Integer Type Questions 36. The total no of ions in the unit cell of CSCI is 37. The maximum covalency that iodine can exhibit is 38. The no of sigma bonds in tetracyano ethlylene is 39. Number of hydrogen bonds in H,O, species is 40. The ratio of lone pairs between AICI, and CO, is 41. Out of. I , ICI,, BeCl,, XeF,, XeF, BrF5, HC CH. How many

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1. Find the three stiffness matrices A, B, and D for a 090 glassepoxy laminate. Use the properties of glassepoxy unidirectional lamina from Table 2.2 and assume the lamina thickness to be 0.1 mm. Also, find the mass of the laminate if the top surface area of the laminate is 6 cm x 7 cm. Use densities of glass and epoxy from Table 3.3 and Table

(a)A steel railroad track has a length of 30.0 m when the temperature is 0F. What is its length on a hot day when the temperature is 40.0F (b) Suppose the track is nailed down so that it cant expand. What stress results in the track due to the temperature change a) 0.018 m b) 2.20 x 108 Pa a) 0.018 m b) 3.20 x 108 Pa a) 0.026 m b) 1.20 x 108 Pa a)

(a)A steel railroad track has a length of 30.0 m when the temperature is 0F. What is its length on a hot day when the temperature is 40.0F (b) Suppose the track is nailed down so that it cant expand. What stress results in the track due to the temperature change a) 0.018 m b) 2.20 x 108 Pa a) 0.018 m b) 3.20 x 108 Pa a) 0.026 m b) 1.20 x 108 Pa a)

(a)A steel railroad track has a length of 30.0 m when the temperature is 0F. What is its length on a hot day when the temperature is 40.0F (b) Suppose the track is nailed down so that it cant expand. What stress results in the track due to the temperature change a) 0.018 m b) 2.20 x 108 Pa O a) 0.018 m b) 3.20 x 108 Pa a) 0.026 m b) 1.20 x 108 Pa

For the first picture which would be the correct product? For the second picture what possible reagent could make the reaction true?

HBr Br Br Br JII IV I xd OH OH

Suppose we have an economy with two consumers, i = 1, 2, who have identical Cobb- Douglas preferences over their private goods consumption, xi, and a public good, g, that can be represented by the utility function ui(xi,g)=3lnxi +2lng,leading to marginal utilities of MUx,i = 3 and MUg,i = 2. xi g The resources the economy has are the incomes of

Find the population mean or sample mean as indicated Sample 18 18, 10 10, 1 1, 11 11, 20 20 Compute the sample mean for this data set Select the correct choice below and fill in the answer box to complete your choice

O A. u O B. x

Tom Regan argues that the basic similarity between human beings, and the basic similarity between humans and the animals they eat and trap is that Group of answer choices

Which of the following statements is true? A. Primordial nucleosynthesis did not take place during the first three minutes of the universe because the temperature of the universe was sufficiently high to immediately dissociate any deuterium formed. B. Once the temperature of the universe dropped below 9 108 K, protons and neutrons fused, forming

Using the single-step global mechanism for combustion of a hydrocarbon with air,compare the mass rates of fuel carbon conversion to CO, for 0 =1, P 1 atm, and T=1600 K for the following fuels:%3DA. CH4 methaneB. C;Hg-propaneC. C;H18 - octaneSingle-step global mechanism:kGC,H, +(x+ y/4)0,XCO, +(y/2)H,0Cu,rord[C,H,]-E-AexpRTdt[=lgmol/cm-Make sure

The reaction 2NOBr 2NOBr2 exhibits the rate law NOB ANOBr At Rate where k 1.0 x 105 Ms at 25C. This reaction is run where the initial concentration of NOBR (NOBIJ,) is 0.30 M. What is one halflife for this experiment O 3.0 s O 1.5 x 105s O 6.9 x 104s 3.3 x 10 s none of these

Calculate the volume (in mL) of 1.5M Tris-HCl solution that would need to be added to 10mL of UTC7 so that the Tris-HCl concentration is 50mM.

A compound containing only carbon and hydrogen produces 113.49 g CO2 and 54.36 g H2O when combusted. What is the empirical formula of this compound? If it has a molar mass of 86.20 g/mol, what is its molecular formula?

What is the molar mass of a gas whose density is 168 gL at STP.

Which value indicates a stronger correlation coefficient r0.918 or r0.932 OA Neither OB. 0.932 OC. r0.918 D. Both

Distinguish between the following interest rates for bonds payable (a) Yield rate. (b) Nominal rate. (c) Stated rate. (d) Market rate. (e) Effective rate.

10 ml of a 1 M acetic acid (pK, 4.75) are titrated with 0.5 M NaOH. a. Calculate the pH value of the solution after the addition of 0, 5, 10, 15, 19.5, 20, 25 ml of the base solution. Briefly show how you do the calculations. b. Roughly sketch the titration curve.

1. Using your titration results, determine the remaining concentration of HCl in your 25 ml aliquot 2. Determine the number of miles of HCl that were neutralized by the TUMS tablet.

75 mL Osmg your weighing bottle, accurately weigh by difference your TUMS antacid tablet and place it in an appropriately labeled 250 mL Erlenmever flask. Accurately (i.e, use a volumetric pipet) add 190 ml of the standardized HCI (0.15 M) to the flask Swirl the mixture to dissolve some of the tablet. (Record the EXPERIMENTAL concentration of the

1. Develop a general pollutant model for the amount of biphenyl bpresent in the river and a general oxygen model for the amount of oxygen xin the river, both measured in ppm, and both as functions of time r(measured in hours after release). 2. Develop two specific pollutant models using two possible ratesR(t)at which the farm releases biphenyl

Bond Strength Homework Unanswered Arrange the following molecules from least stable (highest or least negative potential energy at the top) to most stable (lowest or most negative potential energy at the bottom) based on bond strength Drag and drop options into correct order and submit. For keyboard navigation. Show More HS H, Se HF H0

The net current flowing at the equilibrium potential is zero. Yet this is a dynamic situation with equal opposing cathodic and anodic current components whose absolute value is i 0. Suggest an experimental route for estimating the value of i 0.

CH,CH3 HCH, Dye A (a) Draw the conjugated structures for each dye (b) Figure out the number of z electrons, estimate the length of the conjugated units (assume all of the bond angle of 120, bond length of CC 1.407A, and CN, 1.395 A) (c) Calculate energy difference for the electron transition in each case (d) Calculate the wavelength for the

No. 1, January 1971, and draw a flow chart of interdomain conversion on the following instrument pH meter NMR UV Vis Spectrometer

QUESTION 6 For an uncharged isotope with 54 protons and 75 neutrons, write the symbol in the form GE, where A is the mass number, Z is the atomic number, and E is the elemental abbreviation on the periodic table of elements.

Problem 2. An aqueous solution of ferrous sulfate (FeSO4) is prepared by adding 100 mg to 500 mL of 3, water. The solution pH 4 (H10 M, OH 101 M). (a) Assuming that the salt dissociates completely, express the concentration of each of the dissociation products in micromolar, millimolar, molar, and normal concentrations. (b) Determine the

the ratio of alkenes formed by the E2 elimination of 2 Bromo 2 methyl butane need not be the same as the ratio formed when the bromide undergoes E1 elimination during solvolysis Explain this phenomenon and provide a diagram if it is helpful.

Calculate the molarity of the HCl solution used in the titration in Procedure 8. You should calculate the molarity for each of your three measurements, and then calculate the mean molarity (M) and the standard error. You should present you molarity in this form: XXX XXX M ( SEM) Show your work . Be sure to consider significant figures in your

FIT Jx B F G H K L M N P R Table 8. Results of a titration of HCI using NaOH 1 2 Initial Burette Final Burette Burette mLs NaOH 3 Reading (mL) Reading (mL) dispensed 0.01M 4 0.09 5.30 5.21 1.00mlHCI 5 5.30 10.61 5.31 6 10.61 15.32 4.71 7 8 9 5.077ml NaOH 0.01M NaOH. 10 1.00ml HCI 0.05 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

vanonenge If 10.5 g of dry ice (solid carbon dioxide) at 80.00C is placed into a 2.3L chamber with water Yow man temperature of 115C and a pressure of 1.00 atm, at what temperature will the system equilibrater Youmauha

CHM 227001 Fall 2020 Organic Chemistry I Problem Set 1 (available Thursday 3 September, due Tuesday 8 September) 1.(15 points) Fill in the data table with regard to the lineangle drawings given. Be sure to show all your important work for full or partial credit on this problem. Structure OH OH H H,C CH CH H,C Data CH, H,C CH N By Inspection

What is its molecular formula of the compound below OA C8HgO OB. C7H90 Oc CSH9O OD C7H140 C7HgO

Question 9 5 pts Consider the reaction I2 (g) Cl2 (9) 2ICI (g) at 25 C, K, 20.2 Calculate AGen at 25 C. rxn Put your answer in units of kJ. Do not include the units in your answer. Include one decimal place. Be sure to include a negative sign if your answer is negative.

In Chapter 3, the consumption and creation of several types of energy were described solar, kinetic, tidal, volcanic, earthquake, thermal, combustion, electrical, potential, wind. Describe two examples of energy processes, creation or consumption, that you have observed around you this week. Try to identify more subtle, modest energy processes

Exercise 4. The inside radius of a small test tube can be determine using the following method. Fill the test tube nearly to the top with water (refer to Figure 1). The height, h, of the water level above the bottom of the frosted label on the tube is measured along with the total mass of the system. Water is then removed from the test tube using

1) Identify Ar and He is a 2) Identify N2 is a More than one answer may be correct. Select one or more pure compound pure element homogeneous mixture atomic

5. (3 pts) Compare the melting and boiling points of trimethylamine and trimethylammonium chloride. On the basis of this information, which compound will have a more unpleasant odor. Explain your reasoning. 6. (3 pts) Look at the labels of some of the householdwork items you use and see if there are any chemical names that remind you of something

TABLE OF ELECTRONEGATIVITY FORMAT FAMILY ATOMIC 7 ELEMENT ELECTRONEGATIVITY 3.0 1 2 3 4 5 6 7 (8) 1 H 2.1 3 4 6. 7 8 9 Li Be C N F 1.0 1.5 2.0 2.5 3.0 3.5 4.0 11 12 13 14 15 16 17 Na Mg Al Si P S Cl 0.9 1.2 1.5 1.8 2.1 2.5 3.0 20 L Ca l 19 31 32 33 34 35 K Ga Ge As Se Br 0.8 1.0 1.6 1.8 2.0 2.4 2.8 The table above gives a relative value

The formal charges of oxygen labeled 3,2,1 in ozone respectively are (A) 1, 1,0 (B) 0,0, 1 (C) 1, 0, 1 (D) 0, 1, 1

The bond angle between two hybrid orbitals is 105. The percentage of scharacter of hybrid orbital is between (A) 5055 (B) 912 (C) 2223 (D) 1112

The correct increasing bond order of the following species 0, (A), 0 (B), CO (C), NO (D)will be (A) (A) (B) (D) (C) (B) (A) (B) (C) (D) (C) (D) (C) (B) (A) (D) (B) (A) (D) (C)

Correct order regarding bond energies is (A) NO NO NO (B) NO NO NO (C) NO N0 NO (D) NO NO NO OA B

Which of the following resonating structures is not correct for CO2 (A) c (B) c (C) 0c0 (D) 0co

Correct order of polarizing power is (A) Cs K Mg Al3 (B) K Cs Mg Al (C) Cst K A Mg (D) K Cs Al3 Mg OA OB D

Ozmolecule is paramagnetic because it contains (A) two unpaired electrons in r2p molecular orbital (B) two unpaired electrons in 72p, molecular orbital (C) two unpaired electrons in 72p, and 2p,molecular orbital (D) two unpaired electrons in 72p, orbitals

hich of the following order of energies of olecular orbitals of Nais correct (A) (m2p) (02p.) (2p.) (2 (iap.) (12 (B) (r2p,) (o2p.) (2p.) (72p. (C) (2p,) (02p.) (2p.) (2 (i2p.) (i2 (D) (72py) (02p) (2p.) (2

Which of the following statements isare correct about oand 7molecular orbitals 1) Tbonding orbitals are ungerade. II) Tantibonding orbitals are ungerade. I) oantibonding orbitals are gerade. Choose the correct option (A) Only I (B) Il and III I and (C) Only II (D) Only I

Electron pair occupy localized orbitals. Their orbitals are oriented in such a way that the repulsion between electron clouds becomes (A) zero (B) minimum (C) maximum (D) infinite

The correct sequence of increasing covalent character is represented by (A) LiCl NaCI BeCl, (B) BeClz LiCl NaCl (C) NaCl LiCl BeCl2 (D) BeClz NaCl LiCI

The correct order of increasing scharacter (in percentage) in the hybrid orbitals of following moleculesion is 1) CO II)XeF, IV) NCl V)BeCl2 III)I, (A) II III IV

Which of the following pair is isoelectronic as well as isostructural (A) COzand SO2 (B) SOzand NO, (C) NO, and CO (D) SOzand CO

The correct order in which the O Obond length increase in the following is (A) O2 H202 O3 (B) O3 H2O2 O2 (C) H2O2 O2 O3 (D) 02 O3 H2O2

N2 and Ozare converted into monocations, N, and 0, respectively. Which of the following is wrong (A) In N. , N Nbond weakens (B) In O, the O Obond order increases (C) In O, paramagnetism decreases (D) N becomes diamagnetic

According to molecular orbital theory which of the following statement about the magnetic character and bond order is correct regarding 0, (A) paramagnetic and bond order O2 (B) paramagnetic and bond order O2 (C) diamagnetic and bond order 02 (D) diamagnetic and bond order 02

Amongst LiCI, RBCI, BeClzand MgCl2, the compounds with the greatest and the least ionic character, respectively are (A) LiCland RBCI (B) RbCland MgCl2 (C) RbCland BeCl2 (D) MgCly and BeCl2

The bond dissociation energy for different bonds are given below EHH 1042kcal mol 1 Ectci 58k. EHCI 432kcal mol Electronegativity of hydrogen 2.05 The elctronegativity of chlorine is Backspace

The number of antibonding electron pairs in O, molecular ion on the basis of molecular orbital theory is (atomic number of O is 8) Backspace 7 8 9 4 5 6 1 2 3 0.

Dipole moment of X is 1.6D. What is the dipole moment of the following compound

How many of the following compounds violate octet rule BCI3, PCI5, SF6, H,SO4, SCI2, IF, Xe Backspace 7 8 9 4 5 6 1 2 3

What is the number of lone pairs of electrons in OF,molecule is Backspace 7 8 9 4 5 6 1 2 3

O Attempt 2 Question 7 of 18 To assist in completing this question, you may reference the Animated Technique Video Gel Electrophoresis (SDS PAGE). A protein sample complex consists of two proteins, a smaller protein, X, and a larger protein, Y. Protein X is composed of two polypeptide chains linked by disulfide bonds. Protein Y is composed of

Standard potential of S(s)S system depends on pH of solution. Using the following information S(s) 2e S (main system) E 0.476 V HS pKai 7.02, pK 13.0 Derive conditional standard potential equations, E f (pH), for pH ranges pH 13.0 (main system), 7.02 pH 13.0, and pH 7.02 Draw a diagram of E f (pH) and show the forms of each system on

Computation of Specific Heat for Unknown Metal. Please help by showing forumlas used. I'm not sure where to even start with the math portion for this.

Trial 1 Trial 2 Mass of calorimeter and water (g) 46.68 46.58 Temperature of boiling water bath (C) 99.54 100.04 Initial temperature of calorimeter water (C) 22.03 22.33 Final temperature of water and metal (C) 29.13 29.47 Determining Calories per Mass of Food Food being analyzed Doritos Mass of can (g) 12.68 Mass of can and water (g) 123.61

AIral centers, as they are each bonded to four different groups. 15.110 Page 693 Compound A is branched and optically active and contains C, H, and O. (a) A 0.500g sample burns in excess O2 to yield 1.25 g of CO2 and 0.613 g of H2O. Determine the empirical formula. (b) When 0.255 g of compound A vaporizes at 755 torr and 97C, the vapor occupies

Question 10 Determine the Langmuir constants a for the adsorption of benzene on activated carbon, given the following isotherm data. PC6H6 kPa W, kg C6H6kg carbon 0.027 0.129 0.067 0.170 0.133 0.204 0.266 0.240

Can someone help me determine the molecular structure of this from the given IR, NMR, and Mass Spec data

Melting point measurements Table 1. Melting point of pure compounds Start melting temperature (C) Complete melted temperature (C) Pure benzoic acid 122 125 Pure mandelic acid 117 123 Table 2. Melting point for mixtures of benzoic and mandelic acid Start melting temperature (C) Complete melted temperature (C) 8020 mixture (benzoic acidmandelic

these stOCKS prepare mM EDT 4. You are asked to prepare a 200ml stock of 20 (wv) Sodium Dodecyl Sulfate (SDS, 288.37 gmol). This is provided to you as a white powder. How would you prepare this 5. Calculate the GC of the following primer sequence. Provide the complementary sequence to which this primer will bind. 5AGAGCAGCATGTGCTAGAGAGTT 3

In molecules, C, H, O, and N atoms usually make andbonds respectively. O 3, 2, 1, 4 O 4,1, 3, 2 O3, 2, 4, 2 2, 1, 3, 4 4, 1, 2, 3 Previous Answers Correct Correct By knowing this, youll make your study of chemistry much easier. Conaratulations P Pearson

Find the number of 90 angles in XeF, molecules. Backspace 7 8 9 4 5 6 1 2 3

You need to make 200mL of a 15% NaOH, 1M Tris-HCl working solution. Luckily you have lab stock solutions available including 40% NaOH solution and a 4M Tris-HCl solution. Write out your math for making the working solution and don't forget to tell us how much water to add to bring up the solution to 200mL.

Show how you would accomplish the following conversions. (a) cishex3ene to mesohexane3,4diol (b) cishex3ene to (d1)hexane3,4diol (c) transhex3ene (d) transhex3ene to mesohexane3,4diol to (41)hexane3,4diol

Percent Error At 25 C, the density of water is 0.997044 gmL. Use this value to determine the percent error for the two density measurements. Calculate the percent error for density using graduated cylinder. Calculate the percent error for density using the burette readings.

Translate the given theoretical conformer from the H wedgeanddash drawing into its Newman projection. Cl I Cl F Br OH F Br

Complete the calculations for the given experiment.

Experiment 6 Data and Calculations Determination of Iron by Reaction with PermanganateA Redox Titration Mass of sample tube plus contents L0868 Mass after removing Sample 1 l.023 Mass after removing Sample II Mass after removing Sample II 0.01467 m Molarity of standard KMNO, solution II III Sample 0,00 ml. 26.95 mit. 0.00 0.00 mL mL Initial buret

Given the 2dimensional surface below, use the library of functional groups provided to design a complementary surface to maximize the interaction between the two surfaces. Draw one continuous 2D surface (below) to complement the shown 2D surface. You do not need to use each functional group in the library, and you may use an individual functional

1. Benzene is a planar molecule with bond angles of 120. All six CtoC bonds have identical lengths of 0.139 nm. Is benzene the same as 1,3,5 cyclohexatriene Explain. 2. Write the chemical equations for the substitution reactions of benzene. 3. What are the properties of benzene that gives it its aromatic character 4. Draw the hybrid structure of

13. Watch your units carefully in the following problem and give units in all of your answers. (There are 3 parts to this question with a total of 12 points.) Total enzyme The following data was obtained for 0.005 mM hexokinase using ATP as a substrate S, mM Vo, (micromoleliterYsec to maari 0.003 0.004 28 40 Change 0.010 0.020 70 95 112 0.040

Question 5 a) A semibatch reactor is charged with a fixed volume of substrate which is then reacted with a continuous feed of propylene oxide. The reaction rate is controlled by the feed rate of propylene oxide. Should the propylene oxide feed controller fail dangerously, leading to an excess flow of propylene oxide, then this could in turn lead

(a) For a particle in the Sphere case, write the Laplacian operator both in Cartesian as well as in spherical coordinates. (b) Write the mathematical expression of the energy of a particle in a Sphere. When the particle can be considered as in rest and why?