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Anjeli M.
Molecular and Cell Biology Major at UC Berkeley
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Writing
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Question:

My teacher told me to simplify and reword the following sentences, could you give me some help? Lady Macbeth wishes she and Macbeth “unsexed,” as she wants the advantages associated with both genders, though she wants no label. She opposes gender labels of any kind and she wishes almost to be androgynous. Lady Macbeth shows that although she strives for androgyny, she nonetheless wants to keep the benefits of being a woman. When Lady Macbeth says, shortly after reading of Macbeth’s fortune, “Come you spirits, That tend on mortal thoughts, unsex me here, And fill me from the crown to the toe top-full Of direst cruelty,” she is showing not only that she wished to have no sex or gender whatsoever, but also that she believes that if she has a specific gender, then she cannot be filled with direst cruelty and she cannot act immorally as she wishes to do.

Anjeli M.

Chemistry
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Question:

How do I use the following kinetic data to determine the order of reaction with respect to NO and H2 in the reaction 2NO + 2H2 = N2 + 2H2O? Experimental run: P(NO)/atm: P(H2)/atm: Initial rate/ atm s^-1: 1 .11 .1 1.07 x 10^-3 2 .11 .2 2.13 x 10^-3 3 .33 .1 9.64 x 10^-3

Anjeli M.

We will start by finding the order of reaction with respect to NO. You want to look at two experimental runs where the concentration of NO is changed, while the concentration of H2 is constant. That way, you can see how changing the concentration of NO affects the overall rate of reaction. You should notice that in experimental runs 1 and 3, the concentration of H2 is constant and the concentration of NO is tripled. You can also see that the rate of reaction is multiplied by 9 between trials 1 and 3. I like to set up the following rate law expressions to determine the order of reaction with respect to NO: 1.07 x 10^-3 = [NO]^x 9.64 x 10^/3 = [3NO]^x Make sure to note that in the second equation, NO is multiplied by 3 because .33 is 3 x .11. Also note that the entire expression 3NO is raised to the power of x. You are trying to solve for x (the order of reaction with respect to NO). When you go from 1.07 x 10^-3 to 9.64 x 10^-3 you multiply by 9. This means that [NO] should also be multiplied by 9 between the two expressions. That leads you to the equation 9 = 3^x. We know that 3^2 is equal to 9, which means that x = 2. This means that the reaction is second order with respect to NO. You should use the same process to find the order of reaction with respect to H2. This time, however, you should use experimental runs 2 and 3.

Calculus
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Question:

How can I use the ratio test to determine if a series is convergent? And does this test tell me that the series is absolutely or conditionally convergent?

Anjeli M.

First of all, remember that "absolutely convergent" means that the absolute value of the series is convergent. Conditionally convergent means that the absolute value of the series does not converge, but the series converges (usually by the alternating series test). When you apply the ratio test to a series, you take the limit as n--> infinity of the absolute value of (a sub (n+1))/(a sub n). "a sub (n+1)" is just the series with "(n+1)" substituted in everywhere you have an "n." "a sub n" is just the original series. Once you have written out the limit expression, it's just a matter of simplifying the expression and then taking the limit. If your answer is less than 1, your series is absolutely convergent. If your answer is greater than 1, your series is divergent. If your answer is equal to 1, the ratio test is inconclusive and you need to use a different test to determine whether your series is convergent or divergent. If there's a specific problem you're having trouble with, let me know and I can guide you :)

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