1 - Lenny Vuocolo, Problem Set 1 PDF

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Lenny Vuocolo, Problem Set 1...

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Name _________________________________________ Number______ 09-105 Fall 2016 PROBLEM SET 1 (20 points) DUE MONDAY 9/12 IN LECTURE Recitation (CIRCLE BELOW ONE TA and ONE TIME): Yookie (A,B)

Sikandar (C,D)

Kyle (E,F)

Julia (G,H)

Stephanie (I,J)

6:30

7:30

As in completing ALL assignments in the course, you should refer to only our textbook, class notes, and additional materials posted on our Blackboard site. You may refer to valid academic (not Wikipedia) websites to assist you in further understanding applicable concepts or to view additional, different problem examples that apply those concepts. The use of and copying from external web resources that I do not provide or that do not fit the aforementioned criterion-including posted solutions to related or past posted questions/problems-is a violation of Academic Integrity. Additionally refer to pages 8-10 of the syllabus for additional information regarding Academic Integrity.

I. Complete the problems on the Sapling site labeled as “Problems for Problem Set 1”. (4 points) (PLEASE DO NOT FORGET TO COMPLETE THESE BEFORE THE DUE DATE)

II. In order to receive full credit, please clearly show all work used to answer the following. 1. Complete the following calculation by providing the correct number of significant figures and correct units. 25. 5 mL + 37.4 mL  1 min  73.55 s    60 s 

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Name ______________________________ ___________ Number______ 09-105 Fall 2016 PROBLEM SET 1 (20 points) DUE MONDAY 9/12 IN LECTURE Recitation (CIRCLE BELOW ONE TA and ONE TIME): Yookie (A,B)

Sikandar (C,D)

Kyle (E,F)

Julia (G,H)

Stephanie (I,J)

6:30

7:30

2. Gay-Lussac measured the gas volumes of several gas-phase reactions, resulting in his conclusion of the Law of Combining Volumes:

Gaseous N2 and gaseous H 2 are reacted at given, constant pressure and temperature conditions to form gaseous ammonia, NH3. Assuming a complete reaction between N2 and H2, determine the that forms from the reaction of 15.0 L of H2 with a sufficient amount of N2 under the same conditions. ( (

: 2 +N3 H 2  2 NH3) )

(DO NOT USE THE CONCEPT OF MOLES IN YOUR EXPLANATION).

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3. Determine the (1) symbol and (2) number of protons for the only possible isotope (E) for which the following conditions are met: -The mass number of E is 2.50 times its atomic number. -The atomic number of E is equal to the mass number of another isotope (Y). In turn, isotope Y has a number of neutrons that is 1.33 times the atomic number of Y and equal to the number of neutrons of selenium-82. : (a) What is the symbol of selenium, what does the number 82 represent, and what pertinent information from the periodic table allows us to find the number of neutrons of this isotope and hence those of isotope Y? Se ; mass number of the isotope ; atomic number (Z) [Mass number – Z = number of neutrons] (b) How is the mass number of Y determined? [Number of neutrons + atomic number] (c) What quantities are needed to determine the symbol and number of protons of isotope “E”? Its atomic number, which gives the element symbol and number of protons, and its mass number to write the complete isotope name as “element name – mass number”

4. Germanium has three major naturally occurring isotopes: 70Ge (69.92425 amu; 20.85%), 72 Ge (71.92208 amu; 27.54%), and 74Ge (73.92118 amu; 36.29%). There are also two minor isotopes: 73 Ge (72.92346 amu) and 76Ge (75.92140 amu). Calculate the percent natural abundances of the two minor isotopes. How many peaks would appear in a mass spectrum for Ge? : (a) What information about Ge do you need in order to determine these percentage abundance values? Atomic mass from the periodic table (b) What is the relationship between isotopic masses, percentage abundance of isotopes, and your answer to (a) above? Atomic mass of an element is the sum of the products of each isotope’s fractional abundance times its mass (i.e. a weighted average of the masses of all of its isotopes) (c) What do the number of peaks in an element’s mass spectrum equal? Number of isotopes

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Name ______________________________ ___________ Number______ 09-105 Fall 2016 PROBLEM SET 1 (20 points) DUE MONDAY 9/12 IN LECTURE Recitation (CIRCLE BELOW ONE TA and ONE TIME): Yookie (A,B)

Sikandar (C,D)

Kyle (E,F)

Julia (G,H)

Stephanie (I,J)

6:30

7:30

5. To the right is the mass spectrum of 1 H2Te in which only 1+ ions are formed. There are 8 peaks present. (a) How many isotopes of Te are there? Briefly explain your answer.

(b) What specific quantity (that we mentioned in the notes, unlike the reference to the unit in our text) is graphed on the x-axis?

(c) Using the above spectrum, what is the mass number of the

isotope of Te.

: What feature of a mass spectrum designates the relative abundance of a species in a mass spectrum?

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(d) In the above spectrum, the compounds of H2Te containing only the H isotope of hydrogen are 2 contain the H isotope, how present. For the possible compounds of H 2Te that could

many additional peaks would be present in the spectrum? (again still assume only 1+ ions form) Te compounds if the 2H isotope : What is/are the possible formulas of the 2H

is included among the mixture of H-atom contributions to the compound?

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6. A compound used to make many common plastics contains only C, H, and O. Combustion of 19.81 mg of this compound produces 41.98 mg of CO 2 and 6.45 mg of H 2O. If 0.250 mol of this compound has a mass of 41.5 g, determine the molecular formula of this compound. : (a) What values for C, H, and O do you ultimately need to determine the of this compound? What is the relationship between these values that will yield this formula? The number of moles; the smallest integer ratio (b) How can you use the masses of CO 2 and H2O to determine the values in your answer to (a)? After finding the number of moles of each compound, you find the number of moles of C and H in each respective compound (1 mole of C for every mole of CO2; 2 moles H for every mole of H2O) (c) What is the relationship between the you initially find and the being requested? The molecular formula has a molar mass that is some integer multiple of the empirical formula’s molar mass

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A mixture of NaCl and NaNO3 is 31.7% sodium by mass. What is the percent of NaCl in this mixture? : (a)

Is the mass of the mixture known? No Do you need to know the exact mass of the mixture? Why or why not? No, because only mass percentages are both given and being requested ; however, we have to define an arbitrary one to establish relationships between the compounds and their properties (ex. Can assume a mass of 100 g)

(b) What are the unknowns that can be defined? Mass of NaCl, mass of NaNO3 (c) What equation relates the unknowns defined in (b) above? Mass of NaCl + mass of NaNO3 = 100 g (or whatever mass you choose) Call “x” Call “y” Thus x + y = 100 (d) How can you determine the mass of Na in unknowns defined in (b) above?

of the two salts, in terms of each of the

Mass of Na in NaCl = [(atomic mass Na)/(molar mass NaCl)] x (unknown mass NaCl) Mass of Na in NaNO3 = [(atomic mass Na)/(molar mass Na NO 3)] x (unknown mass Na NO 3) [ ] (e) What second equation, involving the relationships from (d) above, represents the of Na in the mixture of both salts? Add 2 expressions in (d) together. With applicable molar masses and above defined unknowns:

31.7 = (23/58.5)x + [(23/85)(100-x)]

SEE NEXT PAGE

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Suppose you did an experiment in the lab where you exposed 2 different metals to electromagnetic radiation and you wanted to confirm graphically that the metals underwent the photoelectric effect. (a) Sketch the graph, on the same set of labeled axes, that you would anticipate. (b) What specific types of values could you obtain from this graph? : (i) How does the equation for the photoelectric effect yield a straight line plot? Graph of kinetic energy of electrons on y-axis and frequency of incoming photon on x-axis (ii) Between the graphs for each metal, which value(s) would be similar and which would be different? The slopes of h, Planck’s constant, would be equal, and the x-intercept (minimum frequency required) and y-intercept (work function) would be different

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1 . Photons of 315 nm or less are needed to eject electrons from cadmium. What is the maximum velocity of electrons ejected from cadmium by photons of 200 nm?

(a) What equation applies here, and to what wavelengths in that equation does each of the wavelengths given in the problem correspond? EK = hc/λ − hc/λ0 (λ = 200 ;λ0 = 315)

(b) What values must be calculated before determining this velocity? hc/λ (energy of incoming photon), hc/λ0 (work function – minimum energy required), and kinetic energy (the difference shown in (a) above)

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Name ______________________________ ___________ Number______ 09-105 Fall 2016 PROBLEM SET 1 (20 points) DUE MONDAY 9/12 IN LECTURE Recitation (CIRCLE BELOW ONE TA and ONE TIME): Yookie (A,B)

Sikandar (C,D)

Kyle (E,F)

Julia (G,H)

Stephanie (I,J)

6:30

7:30

Problems 10-13 explore the challenges associated with widespread use of solar energy. We start by considering how big a solar cell would need to be to power the US. We then explore two factors that need to be considered in designing a solar cell. The first is the need to absorb many different wavelengths of light. The second is that the solar cell must last for a long time in direct sunlight.

10. Solar panels need to have fairly large surface area Given the following: - On an average day, the peak electrical energy needs of the United States are ~1000 GW (G is the metric prefix for 109, so a GW = 109 Watts = 109 Joules/second) 3 - In the Arizona desert, the total amount of solar energy reaching the ground is about 10 W/m2 .

(a) Consider building a solar plant in the Arizona desert to meet the peak power needs of the United States. The plant will be a square patch of solar panels, each of which is 100% efficient at converting energy from the sun into useable energy. What is the length, in km, of a side of the patch (e.g. is it 1 km by 1km, or 10,000 km by 10,000 km)?

(b) Unfortunately, only about 15% of the energy reaching a typical solar panel is converted to usable energy. (i) By what factor does your estimate for the area of the solar plant change? (ii) Calculate the new, changed area and the length of a side of the patch.

(c) The current market price for a 15% efficient polycrystalline silicon solar panels is $300/m2. (i) How much would it cost to build the panels for this plant?

The Gross National Product (GNP) is about 17 trillion dollars. (ii) Calculate the ratio of your estimated cost to the $1.2 trillion dollars spent on energy from the GNP each year.

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Name ______________________________ ___________ Number______ 09-105 Fall 2016 PROBLEM SET 1 (20 points) DUE MONDAY 9/12 IN LECTURE Recitation (CIRCLE BELOW ONE TA and ONE TIME): Yookie (A,B)

Sikandar (C,D)

Kyle (E,F)

Julia (G,H)

Stephanie (I,J)

6:30

7:30

11. Solar panels need to absorb broad-band radiation.

The above graph shows the solar power coming from the sun, as a function of the wavelength of radiation. The total area under this curve is about 1000 W/m2, which represents the total amount of solar energy reaching the earth. Suppose you had a solar panel that only absorbed, and converted to energy, light in the range of 500 to 510 nm. Suppose it is 100% effective at converting light with these wavelengths to useable energy. (Estimate, to an accuracy of about ±10%, the efficiency of the solar cell. Here, efficiency is defined as the total amount of solar energy hitting the earth that is converted to useable energy. (For this calculation, you will need to estimate the area under the above curve between 500 and 510 nm. One way to do this estimate is to replace the area under the curve with a rectangle that has approximately the same area.)

You should find that, even if we assume the molecule is 100% efficient, the overall efficiency of the solar cell is low. This is because the solar cell is absorbing only a small fraction of the total spectrum. By broadband absorption, we mean a solar cell that can absorb light with many different wavelengths. One way to achieve broadband absorption is to use a mixture of molecules, where each component of the mixture absorbs a different range of wavelengths.

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Name ______________________________ ___________ Number______ 09-105 Fall 2016 PROBLEM SET 1 (20 points) DUE MONDAY 9/12 IN LECTURE Recitation (CIRCLE BELOW ONE TA and ONE TIME): Yookie (A,B)

Sikandar (C,D)

Kyle (E,F)

Julia (G,H)

Stephanie (I,J)

6:30

7:30

12. Solar panels need to last a long time in direct sunlight Another important issue in solar cell technology is the durability of the materials. The current material used in solar cells is silicon, which is readily available, but expensive to process. Organic dye molecules also have potential uses in solar cells, but lifetime is an issue. Consider putting a red T-shirt in the desert sun. How red do you think it will it be one year later? Every time a molecule absorbs a photon, there is a chance it will degrade. Here, we consider the lifetime of a solar cell, if it is based on molecule that can, on average, absorb about a billion photons before decaying. We will assume the following: -

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The solar cell has a single layer of molecules. Each molecule occupies a square patch that -10 is 20 Å x 20 Å. (1 Å = 1 Angstrom = 10 m) The molecule absorbs every photon that hits the molecule and that has a wavelength between 500 and 510 nm. (You may use the average wavelength of 505 nm to calculate the energy of each of these photons.) 9 The average number of photons the molecule can absorb before decomposing is 10 .

With the above assumptions, how long would the solar cell last? Hints: Consider the following: -

The amount of solar energy per second 500 nm and 510 nm you estimated in Problem 11 The amount of solar energy per second, between 500 nm and 510 nm, hitting each molecule (given that the molecule has an area of 20Å x 20Å) The number of photons per second, between 500 nm and 510 nm, hitting each molecule (using the energy of a photon with a wavelength of 505 nm)

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