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chemistry
organic chemistry
Questions and Answers of
Organic Chemistry
Report the melting point of your aspirin product, both the approximate and more accurate observations. Find out the melting point of pure aspirin. How can we use the actual melting point to get an
How else could you check the purity of your aspirin product? Explain.
Observe the end of the glass tube and note what happens.
Complete combustion of a hydrocarbon causes the carbon atoms in the hydrocarbon molecule to be oxidised to their highest oxidation state, +4. See the experiment which shows the complete combustion of
What does the word 'decant' mean? In which steps of the experiment, could we have decanted a liquid?
Draw out the line drawings of benzoic acid and naphthalene.
Write out a balanced chemical equation for the reaction that occurs in step 5 of the procedure.
Write out a balanced chemical equation for the reaction that occurs in step 15 of the procedure.
Butter contains esters of glycerol with several different carboxylic acids. We refer below to butyric (butanoic) acid (R = C3) for simplicity, but many of the acids have R= C15-C17.
Name some other household products that contain fats that could be used in this experiment instead of butter.
Why is the soap layer the upper layer and the aqueous layer the lower layer?
What is the colour of the universal indicator paper? What is the pH? Explain your observations.
What did you observe when you added the soap to the hard water and soft water ? Explain your observations.
Note what you observe when you add salt to the soap solution, and explain it.
What is the cause of the cleansing properties of soap? (Hint: look up "micelles" in an organic chemistry textbook).
Predict the product of the following reaction:
In the context of Example 4.6, use dynamic programming to compute the optimal portfolio for the general power utility, U(x) = x γ/γ .
Find the optimal portfolio for the exponential utility from terminal wealth in continuous time by solving the HJB PDE.
Using the martingale approach in the single-period binomial model, find the optimal portfolio strategy for maximizing E[log(X(1)] and E[Xγ|(1)= γ], for γ < 1.
You have a choice between two investment opportunities. One pays $20,000 with certainty, while the other pays $30,000 with probability 0.2, $6,000 with probability 0.4, and $1,000 with probability
Using the martingale approach in the two-period binomial model, find the optimal portfolio strategy for maximizing E[1−expf−X(1)g].
In the context of Example 4.10, find the optimal portfolio for the exponential utility using the duality approach.
Find the optimal portfolio and consumption strategies for the log utility in continuous-time, by solving the HJB PDE (4.43). try to find a solution of the HJB PDE of the form V (t, x) = f(t) + g(t)
Given a random variable C whose value is known by time T, and such that E[|C|] is finite, show that the process M(t) := Et[C] is a martingale on the time interval [0, T].
Let A(x) denote the absolute risk aversion of utility function U(x). What is the absolute risk aversion of utility function V (x) = a + bU(x)?
Suppose your utility function is U(x) = log(x). You are considering leasing a machine that would produce an annual profit of $10; 000 with probability p = 0:4 or a profit of $8; 000 with probability
Consider a single-period binomial model: The price of the stock at time 0 is S(0) = 100. At time 1 it can move up to 110 with probability 1/3, and down to 90 with probability 2/3. There is also a
You can invest in asset 1 with μ1 = 0.1, σ1 = 0.3 and asset 2 with μ2 = 0.2, σ2 = 0.5, with correlation p = 0.2. You can also invest in the risk-free asset with return R = 0.05. Find the optimal
Suppose that the risk-free rate is 5%. There are three risky portfolios A, B and C with expected returns 15%, 20%, and 25%, respectively, and standard deviations 5%, 10%, and 14%. You can invest in
Compute the historical daily 90% VaR of a portfolio whose daily losses in the last 10 days were, in millions of dollars (minus sign indicates a profit). 1,−0.5,−0.1, 0.7, 0.2,
Compute the daily 99% and 95% VaR of a portfolio whose daily return is normally distributed with a mean of 1% and a standard deviation of 0.5%. The current value of the portfolio is $1 million.
Small investor Taf has 70% of his portfolio invested in a major market-index fund, and 30% in a small-stocks fund. The mean monthly return rate of the market-index fund is 1.5%, with standard
Consider a mutual fund F that invests 50% in the risk-free security and 50% in stock A, which has expected return and standard deviation of 10% and 12%, respectively. The risk-free rate is 5%. You
Consider two European call options on the same underlying and with the same maturity, but with different strike prices, K1 and K2 respectively. Suppose that K1 > K2. Prove that the option prices
Provide no-arbitrage arguments for equation (6.9).
Argue equation (6.13) for forward contracts.
Provide detailed no-arbitrage arguments for expression (6.5).
Consider a single-period binomial model of Example 6.3. Suppose you have written an option that pays the value of the squared difference between the stock price at maturity and $100.00; that is, it
Given a random variable C whose value is known by time T, and such that E[|C|] is infinite, show that the process M(t) : = Et[C] is a martingale on the time interval [0, T].
Assume that the future dividends on a given stock S are known, and denote their discounted value at the present time t by (t). Argue the following:
Why is an American option always worth more than its intrinsic value? (As an example, recall that the intrinsic value at time t for the call option is max(S(t) − K; 0).)
Given stock trades at $95, and the European calls and puts on the stock with strike price 100 and maturity three months are trading at $1.97 and $6 respectively. In one month the stock will pay a
In order to avoid the problem of implied volatilities being different for different strike prices and maturities, a student of the Black-Scholes theory suggests making the stock's volatility σ a
In a two-period CRR model with τ = 1% per period, S(0) = 100, u = 1.02 and d = 0.98, consider an option that expires after two periods, and pays the value of the squared stock price, S2(t), if the
Find the price of a 3-month European call option with K = 100, r = 0.05, S(0) = 100, u = 1.1 and d = 0.9 in the binomial model, if a dividend amount of D = $5 is to be paid at time τ = 1.5 months.
Consider the following two-period setting. the price of a stock is $50. Interest rate per period is 2%. After one period the price of the stock can go up to $55 or drop to $47 and it will pay (in
In a two-period CRR model with r = 1% per period, S(0) = 100, u = 1.02, and d = 0.98, consider an option that expires after two periods, and pays the value of the squared stock price, S2(t), if the
Consider a Merton-Black-Scholes model with r = 0.07, σ = 0.3, T = 0.5 years, S(0) = 100, and a call option with the strike price K = 100. Using the normal distribution table (or an appropriate
In the context of the previous two problems, with no dividends, compute the price of the chooser option, for which the holder can choose at time t1 = 0.25 years whether to hold the call or the put
Let S(0) = $100:00, K1 = $92:00, K2 = $125:00, r = 5%. Find the Black-Scholes formula for the option paying in three months $10:00 if S(T) ≤ K1 or if S(T) ≥ K2, and zero otherwise, in the
Show that, if S is modeled by the Merton-Black-Scholes model, then S and its futures price have the same volatility.
Compute the price of a European call on the yen. The current exchange rate is 108, the strike price is 110, maturity is three months and t he price of a three-month T-bill is $98.45. We estimate
Consider a single-period binomial model with two periods where the stock has an initial price of $100 and can go up 15% or down 5% in each period. The price of the European call option on this stock
Suppose that the stock price today is S(t) = 2:00, the interest rate is r = 0%, and the time to maturity is 3 months. Consider an option whose Black-Scholes price is given by the function V (t, s) =
Show that the interest rate r(t) in the Vasicek model has a normal distribution.
In the previous problem, show that
Let Ï(t) be a deterministic function such thatConsider the process Use Ito's rule to show that this process satisfies dZ = ÏZdW. Deduce that this process is a martingale
Do you think that the put-call parity holds in the presence of default risk? Why?
The price of three-month and nine-month T-bills are $98.788 and $96.270, respectively. In our model of the term structure, three months from today the six-month interest rate will be either 5.5% or
You are a party to a swap deal with a notional principal of $100 that has 4 months left to maturity. The payments take place every three months. As a part of the swap deal you have to pay the
Show that the value of the swaption S+(T) is equal to the value of the cash flow of call options ΔT[R(T)− ]+ paid at times t = T1,. . . , Tn, where R(T) is the swap rate at time T, for the swap
Consider a floating-rate coupon bond which pays a coupon ci at time Ti, i = 1, . . , n, where the coupons are given by ci = (Ti − Ti−1)L(Ti−1, Ti) and Ti - Ti-1 = ΔT is constant. Show that the
In Example 8.3 find the price of the at-the-money call option on the three-year bond, with option maturity equal to two years.
Consider a binomial model with a stock with starting price of $100. Each period the stock can go up 5% or drop 3%. An investment bank sells for $0.80 a European call option on the stock that matures
In the previous problem suppose that another option with the same maturity is available with the Black-Scholes price given by the function c(t; s) = s3e6(T−t) . If you still hold 10 units of the
Show that the payoff given by equation (9.6) is, indeed, equal to the payoff of the butterfly spread. Also show that the butterfly spread can be created by buying a put option with a low strike
The Black-Scholes price of a three-month European call with strike price 100 on a stock that trades at 95 is 1.33, and its delta is 0.3. The price of a three-month pure discount risk-free bond
The stock of the pharmaceutical company "Pills Galore" is trading at $103. The European calls and puts with strike price $100 and maturity in one month trade at $5.60 and $2.20, respectively. In the
Consider a two-period binomial model with a stock that trades at $100. Each period the stock can go up 25% or down 20%. The interest rate is 10%. Your portfolio consists of one share of the stock.
Suppose that the annual interest rate is 4%. You have a liability with a nominal value of $300, and the payment will take place in two years. Construct the durationimmunizing portfolio that trades in
Consider a zero-coupon bond with nominal $100 and annual yield of 5%, with one year to maturity. You believe that after one week the yield will change from 5% to 5:5%. Find the expected change in the
Explain why expression (11.14) is the continuous-time version of expression (11.13), and find the Black-Scholes formula for the call option on the continuous geometric mean (11.14).
Use the retrieval of volatility method to find the initial value of the optimal portfolio for maximizing the expected log-utility of terminal wealth E[log(Xx,π(T))], in the Black-Scholes model, with
The one-year spot rate is 6%: According to your model of the term structure you simulate the values of the one-year spot interest rate that could prevail in the market one year from now. You do only
Why do you think it is not easy to apply the Monte Carlo method to compute prices of American options?
Recompute all the examples in section 12.1 with the log utility replaced by the exponential utility U(x) = 1 − e−ax.
The risk-free rate, average return of portfolio P and average return of the market portfolio are, respectively, 4%, 8%, and 8%. The estimated standard deviation of the market portfolio is 12%, and
In a CAPM market, the expected return of the market portfolio is 20%, and the risk-free rate is 7%. The market standard deviation is 40%. If you wish to have an expected return of 30%, what
Suppose that we estimate the standard deviation of a portfolio P to be 10%, the covariance between P and the market portfolio to be 0.00576, and the standard deviation of the market portfolio to be
The expected return and standard deviation of the market portfolio are 8% and 12%, respectively. The expected return of security A is 6%. The standard deviation of security B is 18%, and its
Using electronegativity values from Table 1-2 (in Section 1-3), identify polar covalent bonds in several of the structures in Problem 25 and label the atoms δ+ and δ- , as appropriate.
Draw a Lewis structure for each of the following species. Again, assign charges where appropriate. (a) H- (b) CH3- (c) CH3+ (d) CH3 (e) CH3NH3+ (f) CH3O- (g) CH2 (h) HC2-(HCC) (i) H2O2 (HOOH)
For each of the following species, add charges wherever required to give a complete, correct Lewis structure. All bonds and nonbonded valence electrons are shown.(a)(b)(c)(d)(e)(f)
(a) The structure of the bicarbonate (hydrogen carbonate) ion, HCO3-. is best described as a hybrid of several contributing resonance forms, two of which are shown here.(i) Draw at least one
Several of the compounds in Problems 25 and 28 can have resonance forms. Identify these molecles and write an additional resonance Lewis structure for each. Use electron-pushing arrows to illustrate
Draw two or three resonance forms for each of the following species. Indicate the major contributor or contributors to the hybrid in each case. (a) OCN- (b) CH2CHNH- (c) HCONH2 (HCNH2) (d) O3
Compare and contrast the Lewis structures of nitromethane, CH3NO2, and methyl nitrite, CH3ONO. Write at least two resonance forms for each molecule. Based on your examination of the resonance forms,
Write a Lewis structure for each substance. Within each group, compare(i) Number of electrons,(ii) Charges on atoms, if any,(iii) Nature of all bonds, and(iv) Geometry.(a) Chlorine atom, CI, and
Use a molecular-orbital analysis to predict which species in each of the following pairs has the stronger bonding between atoms.(a) H2 or H2+(b) He2 or He2+(c) O2 or O2+(d) N2 or N2+
For each molecule below, predict the approximate geometry about each indicated atom. Give the hybridization that explains each geometry.(a)(b) (c) (d) (e) (f)
For each molecule in Problem 35, describe the orbitals that are used to form every bond to each of the indicated atoms (atomic s, p, hybrid sp, sp2, or sp3).
Draw and show the overlap of the orbitals involved in the bonds discussed in Problem 36.
Describe the hybridization of each carbon atom in each of the following structures. Base your answer on the geometry about the carbon atom.(a) CH3CI(b) CH3OH(c) CH3CH2CH3(d) CH2 == CH2 (trigonal
Depict the following condensed formulas in Kekule (straight-line) notation. (See also Problem 42.)(a) CH3CN(b)(c) (d) CH2BrCHBr2 (e) (f) HOCH2CH2OCH2CH2OH
Convert the following bond-line formulas into Kekule (straight-line) structures.(a)(b) (c) (d) (e) (f)
Convert the following hashed-wedged line formulas into condensed formulas.(a)(b) (c)
Depict the following Kekule (straight-line) formulas in their condensed forms.(a)(b) (c) (d) (e) (f)
Redraw the structures depicted in Problems 39 and 42 using bond-line formulas.
Convert the following condensed formulas into hashed-wedged line structures.(a)(b) CHCI3 (c) (CH3)2NH (d)
Construct as many constitutional isomers of each molecular formula as you can for (a) C5H12; (b) C3H8O. Draw both condensed and bond-line formulas for each isomer.
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