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### Question Description

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 β IPG). You are testing the seal on the can for water leakage. The maximum tolerable water level in the can is 25 mg/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 πππ»2ππ4 (monobasic sodium phosphate, MW=120 g/mol) and ππ2π»ππ4 (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 β 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).

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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 β 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 πππ»2ππ4 (monobasic sodium phosphate, MW=120 g/mol) and ππ2π»ππ4 (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 β 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). ...
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