Domanda del libro di testo
Write the nuclear equation for the most likely mode of decay for each unstable nuclide. b. Ra-216
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Ch.21 - Radioactivity & Nuclear Chemistry
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving117
- Ch.2 - Atoms & Elements106
- Ch.3 - Molecules and Compounds128
- Ch.4 - Chemical Reactions and Chemical Quantities56
- Ch.5 - Introduction to Solutions and Aqueous Solutions84
- Ch.6 - Gases112
- Ch.7 - Thermochemistry96
- Ch.8 - The Quantum-Mechanical Model of the Atom60
- Ch.9 - Periodic Properties of the Elements86
- Ch.10 - Chemical Bonding I: The Lewis Model91
- Ch.11 - Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory85
- Ch.12 - Liquids, Solids & Intermolecular Forces51
- Ch.13 - Solids & Modern Materials48
- Ch.14 - Solutions93
- Ch.15 - Chemical Kinetics114
- Ch.16 - Chemical Equilibrium68
- Ch.17 - Acids and Bases137
- Ch.18 - Aqueous Ionic Equilibrium154
- Ch.19 - Free Energy & Thermodynamics91
- Ch.20 - Electrochemistry105
- Ch.21 - Radioactivity & Nuclear Chemistry74
- Ch.22 - Organic Chemistry141
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371Non è quello che usi tu?Cambia libro di testo
Capitolo 21, Problema 83
Radium-226 (atomic mass = 226.025402 amu) decays to radon-222 (a radioactive gas) with a half-life of 1.6⨉103 years. What volume of radon gas (at 25.0 °C and 1.0 atm) does 25.0 g of radium produce in 5.0 days? (Report your answer to two significant digits.)
Guida verificata passo dopo passo1
Convert the mass of radium-226 to moles using its atomic mass: \( \text{moles of } \text{Ra} = \frac{25.0 \text{ g}}{226.025402 \text{ amu}} \).
Determine the fraction of radium that decays in 5.0 days using the half-life formula: \( N_t = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} \), where \( t = 5.0 \text{ days} \) and \( t_{1/2} = 1.6 \times 10^3 \text{ years} \).
Calculate the moles of radon-222 produced, which is equal to the moles of radium-226 that decayed.
Use the ideal gas law \( PV = nRT \) to find the volume of radon gas, where \( P = 1.0 \text{ atm} \), \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \), and \( T = 25.0 \degree C = 298.15 \text{ K} \).
Solve for \( V \) in the ideal gas law equation to find the volume of radon gas produced.
Concetti chiave
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Radioactive Decay and Half-Life
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. The half-life is the time required for half of the radioactive atoms in a sample to decay. For Radium-226, with a half-life of 1.6 × 10^3 years, this means that after this period, half of the original amount will have transformed into Radon-222.
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Percorso guidato
01:49
Method 1 of Radioactive Half-Life
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. Here, P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law is essential for calculating the volume of gas produced from the decay of Radium-226 into Radon-222 under specified conditions.
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Percorso guidato
01:15Ideal Gas Law Formula
Stoichiometry of Radioactive Decay
Stoichiometry in the context of radioactive decay involves calculating the amount of product formed from a given amount of reactant based on the decay process. In this case, knowing the initial mass of Radium-226 allows us to determine how much Radon-222 is produced after a certain time, using the decay constant derived from the half-life.
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Percorso guidato
03:00Rate of Radioactive Decay