Given the following information: Rate = [BrO_3] [Br][H]^2 Give the order for eac

Question

Given the following information: Rate = [BrO_3] [Br][H]^2 Give the order for each substance in the reaction. Give the overall order for the reaction. By what factor does the rate change for each of the following: [BrO_3] is doubled [Br] is halved [H^+] is quadrupled Give the units of the rate constant if a reaction has each of the following overall orders and the reaction is measured in minutes. 5/2 3^rd Give the overall reaction order that corresponds to a rate constant with each of the following units. M^3/2 min^-1 yr^-1 An intravenous pyelogram (IVP), is an X-ray test that provides pictures of the kidneys, the Madder, the ureters and the urethra. During the test an iodine contrast material is injected into a vein in the patients arm and X ray pictures are taken at timed intervals. IVP is often done to identify urinary tract diseases, such as kidney stones or tumors. The dye used is a radioisotope of iodine with a half-life of 2.2 hours. If 5.6 mM dye is injected into the patient, how much of the dye is still in the patient when the test is complete 3.5 hours later? The growth of Pseudomonas bacteria is modeled as a first order process with k = 0.035 min^-1 at 37 degree C. The initial Pseudomonas population density is 1.0 times 10^3 cells/L. What is the population density after 2 hours? What is the time required for the population to go from 1.0 times 10^3 to 2.0 times 10^3 cells/L.

Explanation / Answer

Rate = [BrO3-]1 [Br-]1 [H+]2

(i) The order of BrO3- is 1.

The order of Br- is 1.

The order of H+ is 2.

The overall reaction is (1+1+2) = 4.

(ii) a) if [BrO3-] is doubled, rate changes by a factor 2.

Rate = 2[BrO3-]1 [Br-]1 [H+]2

b) if [Br-] is halved, rate changes by a factor 1/2.

c) if [H+] is quadrupled, rate changes by a factor 16.

Rate = [BrO3-]1 [Br-]1 (4[H+])2 = 16[BrO3-]1 [Br-]1 [H+]2

(b) Formula: units of rate constant = mol1-n Ln-1 min-1

n is order of reacion.

(i) if order of reaction is 5/2, units for rate constant = mol-3/2 L3/2 min-1

(ii) if order of reaction is 3, units for rate constant = mol-2 L2 min-1

(c)

(i) units of rate constant is M3/2 min-1 = mol3/2 L-3/2 min-1

1-n = 3/2, So, n = 1-3/2 = -1/2

The order of reaction is -1/2.

(ii) Units of rate constant is yr-1 = mol0 L0 yr-1

1-n = 0. So, n= 1

The order of reaction is 1.

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