CHEM-51 Midterm: CHEM 51 Dartmouth 122Exam 3SolutionsSpring 09

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turquoisegnu128

31 Jan 2019

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Find bases of the following vector spaces and state their. A basis of col(a) is formed by the pivot columns of a, namely. So dim(col(a)) (cid:3) 2. (b) the row space of a. Nonzero rows of rref(a) form a basis of row space, namely (1, 3, 0, 2, 5) and (0, 0, 1, 2, 1). So dim(row(a)) (cid:3) 2. (c) the null space of a. Free variables: x2 (cid:3) t1, x4 (cid:3) t2, x5 (cid:3) t3. Ax (cid:3) 0: x1 (cid:3) 3t1 2t2 5t3, x2 (cid:3) t1, x3 (cid:3) 2t2 + t3, x4 (cid:3) t2, x5 (cid:3) t3. General solution in vector form is x (cid:3) t1v1 + t2v2 + t3v3, where v1 (cid:3) These three vectors form a basis of nul(a). So dim(nul(a)) (cid:3) 3. (d) the orthogonal complement of the column space of a. A vector y in r3 is perpendicular to the columns of a if and only if aty (cid:3) 0.

Related Questions

3. Write the product formed in the following reactions in the space provided. If the reaction does not take place write NO RXN. Indicate physical states by (s), (l), (g), (aq). Make sure the reaction is balanced! Please write the net ionic equation below.

a. Pb(CH₃CO₂)_2(aq) + Na₂SO₄_(aq) Ã

b. AgNO_3(aq) + NH₄Br_(aq) Ã

4. Balance the following reactions and answer the questions below.

a. Al_(s) + HCl _(aq) Ã AlCl₃ + H₂

What is the element that is oxidized _______________________

What is the element that is reduced _______________________

Which compound is the oxidizing agent ____________________

Which compound is the reducing agent ____________________

b. Na_(s) + FeCl₂ Ã NaCl + Fe

What is the element that is oxidized _______________________

What is the element that is reduced _______________________

Which compound is the oxidizing agent ____________________

Which compound is the reducing agent ____________________

8. Using the unbalanced equation how many grams of lithium nitrate will be needed to make 250g of lithium sulfate, assuming that you have an adequate amount of lead (IV) sulfate to do the reaction.

Pb(SO₄)_2(aq) + LiNO_3(aq) Ã Pb(NO₃)_4(s) + Li₂SO_4(aq)

9. Using the following equation determine how many grams of sodium fluoride can react with 184.4 grams of magnesium.

Mg + NaF₂ Ã MgF₂ + Na

10. Determine how many Oxygen atoms are present in 46.7g of Zr(SO₄)₂

10. Given the following unbalanced equation:

Al₂O_3(aq) + Fe_(s) Ã Fe₂O_3(aq) + Al_(s)

Determine how many grams of Iron (III) Oxide can be formed if 224 grams of aluminum oxide is reacted with iron.

Multiple choice:

10b. Which of the following statement is true about 1 mole of Ca(NO₃)₂?

a. It contains the 6.02 x 10²³ NO₃^- ions.

b. It weighs 146 grams

c. It will most likely dissolve in a bucket of water.

d. It will produce equal number of Ca⁺² and NO₃^- ion in a solution.

10. How many molecules are present in 48.0 grams of oxygen gas? (O₂)

a. 6.02 x10²³ b. 1.81 x10²⁴ c. 9.03 x10²³ d. 1.03x10²⁴

12. If there are 12 moles of carbon in 1 mole of sucrose, C₁₂H₂₂O_11.How many atoms of carbon are there in 1 mole of sucrose?

a. 1 x6.03 x 10²³ b. 12x 6.03 x 10²³ c. 22 x 6.03 x 10²³

13. Determine the oxidation state of oxygen in the compound Cr₂O₃ in the following equation:

Cr₂O_3(s) + 2Al_(s) Ã Cr_(s) + Al₂O_3(s)

-2 b. -6 c. 6 d. 2

16. Determine the oxidation state of Al in the following equation:

Al_(s) + HCl Ã AlCl_3(aq) + H₂

+2 b. 0 c. +3 d. -5

Observations In columns 3 and 4, record the color and intensity seen. In columns 5 and 6, determine if the substance is an acid or a base, and if the substance is ionic. For the last column, determine which chemical species is acting as an acid or base.

Data Table 1: Acids and Bases Acting in Water
Well	Substance	1drop BTB	Plus 1 drop of substance	Acid or base (Q1)	Ionic? Y/N (Q2)	Species acting as acid or base (Q3)
1	NaHCO3
2	CH3COOH
3	HCL
4	Na2CO3
5	H2SO4
6	CH3COONa
7	NaOH
8	HNO3
9	NaHSO4
10	NH3
11	H3PO4
12	NaH2PO4
13	Na2HPO4
14	Na3PO4
15	NaHSO3

Data Table 2: Following Acid/Base neutralization reactions
Well #	1 Drop of Each	Observation	+2 Drops Acid	Observation	+2 Drops Base	Observation
1	BPB + NaOH		HCl		NaOH
2	BPB + NaOH		H2SO4		NaOH
3	BPB + NaOH		CH3COOH		NaOH
4	BPB + NaOH		H3PO4		NaOH
5	BPB + Ca(OH)2		HCl		Ca(OH)2
6	BPB + Ca(OH)2		H2SO4		Ca(OH)2
7	BPB + Ca(OH)2		CH3COOH		Ca(OH)2
8	BPB + Ca(OH)2		H3PO4		Ca(OH)2
9	BPB + NH3		HCl		NH3
10	BPB + NH3		H2SO4		NH3
11	BPB + NH3		CH3COOH		NH3
12	BPB + NH3		H3PO4		NH3

Please note here if any of the other starting materials is other than a clear, colorless solution.

Data Table 3: Investigating Odor as a Means of Indicating Neutralization.
Substance(s)	Odor
2 Drops of HCl in Well #1
1 Drop of Ammonia on Swab
Swab with Ammonia & HCl

Data Table 4: Investigating Evaporation as a Means of Indicating a Neutralization Reaction.
Reaction Mixture	Observation (When Wet)	Observation (When Dry)
HCl + NaOH
CH3COOH + NH3
HNO3 + NaOH

PART 5: Mini-Experiments

1. Use BTB to classify four household products as acidic or basic. Possible substances to test include home cleaning products, glass cleaner, liquid detergent, bleach, soft drinks, liquid from food items, etc. Remember to:

a. Hypothesis (What you think will happen and why) or purpose:

b. Method used to test your hypothesis:

c. Data and Observations Put your data and observations in the space below. You can include pictures that you âdraw.â

d. Conclusions

2. Find one common, highly colored substance that can be used as an acid-base indicator.

Possible substances include fruit/vegetable juice or products, inks, food coloring, flower

petals, etc. If using fresh fruit, veggies, or flowers, crush the substance with a little water or

rubbing alcohol to extract the colored pigments. If red cabbage is available, it makes a superb

acid-base indicator. Then use a few drops of the colored extract as the indicator. Test four

more household products using the freshly made acid-base indicator. Remember to:

a. State a hypothesis or purpose.

b. State the testing method.

c. Use the prepared indicator to test four substances known to be acids or bases from either the LabPaq or home materials and record results.

d. State conclusions in terms of the hypothesis or purpose.

Questions

A. Review the substances used in Part 1. Determine whether each substance contains an acid or a base based on the BTB results. Place answers to this question in column 6 of Data Table 1.

B. Review the responses to Question 3. The anion that is produced in the dissociation of the compound goes on to react with the water. Identify the anion product in each reaction. Place the formulas for these species into column 7 of Data Table 1. If the substance is not ionic and thus does not dissociate, then list the substance in column 7, just as it appears in column 1.

C. For each ionic species in Data Table 1, write the equation showing the dissociation of the compound in water. Hint: thereâs one for each line provided below.

a. NaHCO3 Ã Na

+ HCO3

Review the responses to Question 3. The anion that is produced in the dissociation of the compound goes on to react with the water. Identify the anion product in each reaction. Place the formulas for these species into column 7 of Data Table 1. If the substance is not ionic and thus does not dissociate, then list the substance in column 7, just as it appears in column 1.

D. Write the reaction of each acid or base the substance listed in column 7 with water.

Acids: Bases:

a) HCO - + H-OH Ã H CO

+ OH-

3 2 3

1. What is produced in each and every reaction of an acid with water?

2. What is produced in each and every reaction of a base with water?

E. Review the results in Data Table 2. For each reaction mixture, write the reaction equation describing the acid/base neutralization reaction:

2) 2NaOH + H2SO4 Ã 2H2O + Na2SO4

F. Define the term âneutralizationâ and provide an example of a neutralization equation. List the three ways used in this lab to detected neutralization.

G. Define the term âsalt,â and provide an example.

H. Review Data Table 3. What happened when the two chemicals were mixed? What indicates that conclusion? What reaction took place?

I. Review Data Table 4. What happened when the solution mixtures on the glass slide were heated? Describe the process that took place.

J. In Part 4, for HCl + NaOH, what is left on the slide after heating? Provide the formula. What is the common name of this substance?

Practice problems for exam 2 ______________

Useful Information:

h=6.626Ã10-34JÂ·s.; c=3.0Ã108 m/sec; E=hï® ; E= hc , ï¬ = h/mv; 1J = 1 kg-m2/s2 ï¬

mass of electron = 9.11 Ã 10-28 g, ïE= q + w ; 1 cal = 4.184 Joules Please Show all Work

1. Which of the following substances have standard heats of formation that are equal to zero by definition (circle your answers): H2(g), H(g), O3(g), H2O(s), H2O(l), Hg(l), Hg(s), Hg(g).

2. Limestone stalactites are formed in the reaction: Ca2+(aq) + HCO3-(aq) ï CaCO3(s) + CO2(g) +

H2O(l)
If one mole of CaCO3 is produced at 298 K under one atmosphere of pressure, the reaction performs 590 calories of expansion work, pushing back the atmosphere as CO2 is formed. At the same time, 9310 calories of heat are absorbed from the environment. What is ïE in Kcal/mole for CaCO3.

3. What is the minimum wavelength of light in AÌ (1 AÌ = 10-8 cm) needed to provide enough energy per quantum to rupture the chemical bond in hydrogen iodide (HI). The bond dissociation energy of HI is 71.4 Kcal/mole.

4. Sketch the shape and orientation of the following types of orbitals: s, px, dxy, dz2, dx2-y2

5. Give the values of (n) , (l) and (ml) for each orbital in the 4p subshell.

6. Write the complete electron configuration for the following: Ti 2+_____________________________________ Cr_______________________________________

N______________________________________

7. Calculate the standard enthalpy of formation ( ï Ho) for diamond from graphite [i.e. C (graphite) ï C (diamond)] given that:

C (graphite) + O2 ï CO2 (g) ( ï Ho = -393.5 KJ/mole) C (diamond)] + O2 ï CO2 (g) ( ï Ho = -395.4 KJ/mole)

If 1.0g of graphite is converted to diamond, what is the energy change? Is this an endothermic or exothermic reaction?

8. An 160 pound astronaut on his way to Mars is buzzing along at 10,000 miles per hour. (a) Express his weight in grams (one pound = 454 grams) so that you can calculate the astronautâs wavelength (1mile/hour = 44.7 cm/sec)

(b) Suppose the astronaut detects outside his spacecraft a proton (m=1.7 x 10-24 g) from a âsolar windâ moving at exactly the spacecraft velocity. What is the proton wavelength is in AÌ (1 AÌ = 10-8 cm.

9. What is the maximum number of electrons that can occupy each of the following subshells? a) 3d_________________ b) 1s____________________ c) 2p ____________________

10. Identify the element represented by the following electronic configuration.

a) [Ne] 3s2____________________

b) What is the electron configuration for the first excited state of this atom.______________

11. Determine the number of valence electrons for each element.
(a) Br___________ (b) Na _________ (c) Sn __________

12. 175 g of Fe at 15.0oC is mixed with 225 g of H2O at 95.0oC. What is the final temperature of the mixture? The specific heats of iron= 0.448 J/g oC and water = 4.184 J/g oC). (keep in mind the following: heat gained + heat lost = 0 and q=mass x heat capacity x ïT)

13. (5 pts) Calculate values of ÎHrxn for the following reactions: CS2(g) + 3O2(g) ï® CO2(g) + 2SO2(g)

The heat of formation for the following substances is given in kJ/mol:

CS2 CO2 SO2 117.4 -393.51 -296.83

14. (6 pts) Use the electron configuration of Li and Be and determine which element has the greatest second ionization energy. Defend your answer.

15. Mark beside each of the following processes either âexoâ or âendoâ according to whether you think the process will release heat or absorb heat.

a. Ca(g) ï Ca(g)+2 + 2e-
b. I(g)+1e-ï I(g)-1
c. Ca(g)+2 + S(g)-2 ï CaS(s) d. I2(g)ï 2I(g)

( ) ( ) ( ) ( )

16. (6 pts) In each of the following pairs, which of the two species is larger?
a) O-2 or Na+ b) Ti+4 or Ti+2 c) B or C d) N or N-3

17. Write down the Lewis dot structure for the following (a) N_______________ (b) Ne________________

18. THE BORN HABER CYCLE: I may have a problem on the Born Haber cycle. Please check my lecture notes to see how to set up the process and then calculate the lattice energy from the various thermodynamic quantities such as in the NaCl example below;

ï H ï¯ f NaCl = -411KJ

Na(s) ï® Na(g) ï H =108KJ
1â2 Cl2 ï® Cl(g) ï H = 122KJ Ionization Energy of Na ï H = 496 KJ Electron affinity of Cl ï H = -349KJ

CHEM-51 Midterm: CHEM 51 Dartmouth 122Exam 3SolutionsSpring 09

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