General Chemistry
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A laboratory student prepared a 0.00155 M KBr solution with a small amount of radioactive 77Br (t1/2 = 57.04 h). She recorded the activity of the solution as 0.127 mCi/mL. She used 25.0 mL of this solution to precipitate an unknown metal Y as YBr. She mixed the KBr solution with 25.0 mL of 0.00234 M YNO3 solution. She removed the precipitate by filtration and the activity of the obtained filtrate after 5 hours was 0.0156 mCi/mL. Calculate the molar concentration of Y+, Br−, and the solubility product of YBr.
Radon is a radioactive noble gas. It is formed when uranium-238 (t1/2 = 4.468×109 y) undergoes a series of nuclear decays. If a 0.450 mg sample of 238U is enclosed in an empty 100 mL sealed flask. Calculate the pressure inside the flask at STP after 50000 years, assuming that all of the pressure inside the flask is due to radon gas.
You have to determine the age of an ancient fabric sample. You burn a small piece of fabric in excess O2, and pass the produced CO2 through slaked lime (Ca(OH)2) to produce a precipitate of CaCO3. The radioactivity of a 0.545 g sample of CaCO3 is 2.15×10−4 Bq. Given that the radioactivity of the sample is due to 14C which has a half-life of 5715 years and the radioactivity of recent samples is 15.3 disintegrations/min per gram carbon, how old is the fabric sample?
Americium is a synthetic radioactive element. An isotopic mixture was made in a laboratory that had equal amounts of 241Am and 243Am in it. After some time, the observed ratio of the two isotopes was 0.158. The half-lives of 241Am and 243Am are 432.2 h and 7370 h, respectively. How old is the mixture after the change?
Radioactive decay is a first-order reaction. Berkelium-250, a radioactive metallic element used in the synthesis of heavier elements, has a half-life of 3.217 hours. Determine the fraction of berkelium-250 that remains after four half-lives.
Calcium is an essential mineral required by the body. One isotope of calcium, 48Ca (abundance = 0.187%), is radioactive with a half-life of 6.4 × 1019 y. Calculate the rate constant for 48Ca and the number of disintegrations per day in 1.50 metric ton CaCl2.
Initially, a sample of 24Na decays at a rate of 450 disintegration/sec. After 200 min, the rate slows down to 385.59 disintegration/sec. Calculate the half-life of 24Na in hours.
Radon-222 has a half-life of 3.82 days and emits α particles. Calculate the number of α particles released from a 1 μg sample of 222Rn in 1 minute.
Plutonium-239 (atomic weight = 239.0522 amu, t1/2 = 24110 y) is produced in a fast breeder reactor. Uranium-238 absorbs a neutron and then undergoes two consecutive beta decays to yield 239Pu. What is the activity of 245 mg 239Pu in Bq and Ci units?
The radioactivity in a soil sample that comes from the decay of uranium isotopes is 662 pCi/mg. Calculate the number of disintegrations in 1 mg of soil in 1 hour. Assuming that the major radioisotope is 238U (t1/2 = 4.468×109 y), how many 238U atoms are there in 2.5 mg of soil?
A typical abdomen CT scan exposes a person to about 20 mGy radiation. How much is this dose in rad units? How many joules are absorbed by a woman if she weighs 60 kg?
The most stable radioisotope of thallium, thallium-204, has a decay constant of 1.83×10−1 year−1. Determine the half-life of 204Tl.
The age of dinosaur fossils is determined by uranium-lead dating where the age of a sample is determined through the amounts of 206Pb and 238U in a sample. 238U decays through a series of nuclear reactions to yield 206Pb. How old is a fossil sample if the sample has a 206Pb/238U ratio of 0.01891? The half-life of 238U is 4.468×109 years.
Caesium-137 decays mainly by beta emission and yields Barium-137 and has a half-life of 30.05 years. A sample of a salt contains 156.0 mmol 137Cs and 55.0 mmol of 137Ba. How old is the salt sample?
The Chernobyl disaster took place on April 26, 1986, when reactor No. 4 in the Chernobyl Nuclear Power Plant exploded. The reactor core was exposed and burned in the air for eight days, releasing enormous amounts of radioactivity. The reactor was run on 235U and had 1.951×105 kg of fuel when it exploded and the radiation levels in the vicinity were about 20,000 R/hr (Roentgen per hour). If the radiation levels are directly proportional to the amount of 235U, what will be the radiation level in the vicinity of the reactor on April 26, 2023? The half-life of 235U is 7.038×108 y.
Samarium-153 is used for palliative bone pain treatment. It has a half-life of 1.93 days and decays by beta emission. If the bone of a person undergoing treatment absorbs 46% of the administered samarium, how long will it take for the concentration of the absorbed samarium to decay to 0.05% of the original amount?
Radioactive iodine (I-131) can be used to treat hyperthyroidism in adults. The recommended maximum activity (dosage) for the treatment is 10 mCi. Determine the value of this radiation in disintegrations per second and in becquerels.
Consider two radioactive isotopes M and N. Determine whether the following statement is true or false: If M has a greater decay rate constant, it will have a longer half-life than N.
The decay of 7234Se by electron capture is illustrated in the following plot. Based on this plot, estimate the half-life of the decay.
Europium-152 has the potential to be used in external beam radiotherapy but is not yet developed for clinical use. Europium-152 has a half-life of 13.5 years. Assuming that europium also needs to be replaced when its activity drops to 75% of the original sample like in cobalt-60 machines, determine when will it be replaced if the machine is developed on January 2030.
Radium in luminescent paints that were used to paint watch faces was eventually replaced with promethium-147 by the second half of the 20th century. It is a low-energy beta-emitter, unlike radium which is an alpha-emitter. Additionally, unlike radium, it doesn't emit penetrating gamma rays. The half-life of promethium-147 is only 2.62 years which makes them easier to dispose of. Assuming that the light given off is directly proportional to the amount of promethium, determine how much will the face of a 15-year-old watch be dimmed.
Phosphorus-32 is a radiopharmaceutical drug used to treat cancer. A patient was administered 93.0 mg of P-32 which decays via beta decay and has a half-life of 14.3 days. Calculate the exposure (in Ci) for the first six hours of treatment assuming that none of the P-32 exited the patient's body.
Calculate the number of disintegrations per hour irradiated by 1.55 mol of 187Re. The half-life of 187Re is 4.33×1010 yr.
A 2.5 g sample of rock contains thorium and produces 46 dis/s. Calculate the percent by mass of 232Th in the rock if the half-life of 232Th is 1.405×1010 yr.
A skeleton of a species is found to have a carbon-14 decay rate of 1.15 disintegrations per minute per gram of carbon (1.15 dis/min•gC). A carbon gathered from a living species has a rate of 18.5 disintegrations per minute per gram of carbon (18.5 dis/min•gC). If the half-life of carbon-14 is 5730 years, calculate the age of the skeleton.
The initial decay rate of a sample of Ac-224 is 2.50×105/s. If the half-life of Ac-224 is 2.78 hours, calculate the time it will take for the decay rate to fall to 1.50×103/s.
The half-life of a radioactive nuclide is 4.2 days. If a sample of the nuclide has an initial mass of 2.15 g, how many grams will remain after 6.4 days?
Calculate the time it will take for the amount of Niobium-92 to reach 25.0% of its initial amount. The half-life of Nb-92 is 34.7 million years.
Mercury-203 is a synthetic radioisotope of mercury that undergoes beta decay to thallium-203. The half-life of mercury-203 has been found to be 46.6 days. Calculate the value of its decay constant.
Express your answer in inverse days.
The following graph shows the radioactive decay of an unknown isotope. Using the information presented in the graph, determine the half-life of the unknown isotope.
Cobalt-58 is a synthetic radioisotope of cobalt with a half-life of 70.87 days. How many days it will take for a 9.750 g sample of cobalt-58 to decay to a final mass of 2.125 g?
The Bedrock in Hudson Bay, Canada is the oldest known rock bed on the planet. Using uranium/lead radiometric dating, it has been found to be 4.28 billion years old. If we assume that the rock only contained 236U in the beginning, what would be the mass of 206Pb in a sample of the rock if it currently contains 1.500 g of 236U? (The half-life of 236U is t1/2 = 4.47 x 109 years.)
Calculate the energy (kJ/mol) released in the fission reaction of uranium-235 shown below:
23592U + 10n → 13752Te + 9740Zr + 2 10n
Use the following masses: 235U = 235.04393 amu, 137Te = 136.92560 amu, 97Zr = 96.91096 amu, 10n = 1.00867 amu.
9.01333 amu, 10.01294 amu, and 11.00931 amu are the nuclear masses for 9B, 10B, and 11B, respectively. Determine the nuclei with the highest nucleon binding energy from the given
The atomic mass values of 31H, 52He, and neutron are 3.01605 amu, 5.012057 amu, and 1.008665 amu. Assuming that the following nuclear reaction occurs under a controlled fusion process, what is the energy released per mole of the reaction? (mass electron = 5.485799×10–4 amu)
31H + 31H → 52He + 10n
Oxygen-15, vanadium-51, and bismuth-209 have atomic masses of 15.003065 amu, 50.943964 amu, and 208.980399 amu, respectively. What is the nuclear mass of each isotope? (mass of electrons = 5.485799×10–4 amu)
If a silicon-29 atom has a mass of 28.9764947 amu, what is the amount of energy needed to break a single silicon-29 nucleus into separated protons and neutrons? What is the amount of energy required for 150.0 g silicon-29? (mass electron = 5.485799×10–4 amu)
What is the difference in the energy released by a 31S nuclide that undergoes electron capture and β+ decay if the atomic mass of 31S = 30.979557 amu and 31P = 30.973762 amu?
For an atom of Be-9 with a mass of 9.012182 amu, what is the binding energy?
An average nuclear reactor generates 1.2 MW of electricity daily. At least, how much mass is lost per day to generate this amount of energy?
Write the complete nuclear equation for the following?
??? + 2412Mg → 2713Al + 42He
What is the associated energy change (J/mol of reactant) from the reaction? (Mg-24 = 23.98504 amu, Al-27 = 26.98154 amu, He-4 = 4.00260 amu)
Part A. What is the amount of energy absorbed by a 65 kg human who was exposed to 25.9 rad of radiation?
Part B. What is the amount of energy absorbed by a 65 kg human who jumped from a stool with a height of 0.45 m to the floor assuming the entire force of the fallis taken in by the person?
Part C. How does the amount of energy in part a differ from part b?
How much energy is created per gram of Np-237 from the neutron-induced fission of Np-237 (atomic mass = 237.0482) that produces Ba-140 (atomic mass = 139.910605) and Rb-95 (atomic mass = 94.929303)?
For Na-23 with an atomic mass of 22.98977 amu, what are its nuclear binding energy and mass defect per nucleon of each nuclide?
The energy produced from a nuclear reaction is used to power a typical home that uses 2.3x103 kWh per month. How much mass in grams is needed to power the home for a year?
Determine the amount of energy produced when 1.3 grams of matter turns into energy.
Naturally occurring scandium consists of a single isotope: Scandium-45. The isotopic mass of 45Sc is 44.955912 u. Calculate the binding energy per nucleon for this isotope.