If f is a complex function and f* is its complex conjugate, then the function g

Question

If f is a complex function and f* is its complex conjugate, then the function g = f f* is a) Complex b) Imaginary c) Real with positive and, of negative values d) Real with only positive values Refer to the figure below for the reaction 5A---- rightarrow products (time is in minutes) Estimate the initial rate of reaction in M/min. (show work) (a) 2.375 M/min (b) 2.5 M/min (c) 0.813 M/min (d) 0.475 M/min The rate of decomposition of a certain compound: A(g)---- rightarrow Products initially at a Pressure (Po) of Po = 363 torr was 1.07 torr/s when 5% had reacted and 0.76 torr/s when 20% had reacted. The order of reaction is: (a) n = log(1.07/0.76)/log(363/0.20 times 363) (b) n = log(1.07/0.76)/log(0.05 times 363/0.20 times 363) (c) n = log(1.07/0.76)/log(363 times 0.95/0.80 times 363) (d) n = log(1.07/0.76)/log(363 times 0.20/0.95 times 363) The decomposition of nitrogen dioxide, NO_2 is second order with a rate constant, k = 12.5/(M*s). If the initial concentration of NO_2 is 0.00500M, what is the [NO_2] after 55.0 s (show work) (a) 2.64 times 10^-3 M (b) 3.64 times 10^-3 M (c) 1.31 times 10^-3 M (d) 1.57 times 10^-3 M (e) 1.13 times 10^-3 M

Explanation / Answer

I will answer your last 2 questions. The first two post them in another question thread:

8C. The general expression for rate law is: R = k[A]n

So solving for n, we can write an expression for both rates:

Rate1 = k[A1]n
1.07 = k(363 * 0.05)n

Rate 2:
0.76 = k(363*0.2)n

Doing a ratio rate1/rate2:
1.07/0.76 = (363*0.05/363*0.2)n ---> to solve for n, we use log:
log(1.07/0.76) = nlog(363*0.05/363*0.2)
n = log(1.07/0.76) / log(363*0.05/363*0.2)

Therefore Option B is the correct option.

8D) as is a second order reaction, the expression to use is:
1/A = 1/Ao + kt

then, for the given values, A:
1/A = 1/0.005 + 12.5*55
1/A = 887.5
A = 0.00113 M or 1.13x10-3 M

Here the correct option is e) instead of b).

Hope this helps

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