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1. A radioactive isotope produces 1.00 x 105 disintegrations/minute. After
30 days, the sample produces only 1.00 x 104 disintegrations/minute.
Knowing that radioactive decay is a first-order rate process, what is the
half-life of this isotope?
2. An implantable medical device for cardiac pacing has a sealed metal can
containing electronics (typically called an implanted pulse generator – IPG).
You are testing the seal on the can for water leakage. The maximum
tolerable water level in the can is 25 g/cm3 of internal free volume (space
not occupied by the electronics and battery). The IPG has a free internal
volume of 2 cm3 . You undertake accelerated testing: at 80oC you
measure a rate constant for leakage into the can of 10 pg/s(pg=picogram)
and at 60oC a rate constant of 1 pg/s. The IPG is surgically replaced every
ten years because the internal battery is exhausted. Can you tell your boss
that the seal will last a minimum of twenty (20) years in the body (a safety
factor of two)? You also know the concentration of water outside the IPG is
constant and thus the leakage is independent of the starting water
composition. Support your answer quantitatively.
3. You are asked to prepare a phosphate buffer of pH 7.5. The total
phosphate concentration in the buffer should be 0.1 M.
a. How many grams of 𝑁𝑎𝐻2𝑃𝑂4 (monobasic sodium phosphate, MW=120
g/mol) and 𝑁𝑎2𝐻𝑃𝑂4 (dibasic sodium phosphate, MW=142 g/mol) are
required to make 1 liter of the buffer?
b. What is the pH of 100 ml of buffer from Part a, if 10 ml of 0.05 ml HCl
(hydrochloric acid) are added to the 100 ml aliquot?
4. You have designed a pressure vessel to operate with pure liquid water at
a temperature range from above 100oC to 350oC. Based on the data
provided in Figure 1 – equations and thermodynamic data - what is the
maximum pH of the water that will be encountered in the pressure vessel
over this operating temperature range? (Note that the water remains liquid
over this temperature range due to the pressure inside the vessel).