Calculate the change in energy, in kilojoules per mole, for the transmutation of radium from the given molar masses: A) -4.7 × 10⁸ kJ/mol B) -4.7 × 10¹⁴ kJ/mol C) +1.6 × 10⁸ kJ/mol D) -1.6 kJ/mol E) -5.2 kJ/mol

Question

Quizplus · Accepted Answer

The change in energy for the transmutation of radium can be calculated using the formula $\Delta E = (mass\ of\ products - mass\ of\ reactants) 	imes c^2$, where $c$ is the speed of light. The molar mass of radium is 226 g/mol. When radium undergoes transmutation, it decays to radon and emits an alpha particle. The molar mass of radon is 222 g/mol, and the molar mass of an alpha particle is 4 g/mol. Therefore, the change in mass is $(222 + 4) - 226 = 0$ g/mol, and the change in energy is $\Delta E = 0 	imes (3 	imes 10^8)^2 = 0$ J/mol. Converting to kilojoules per mole gives $\Delta E = 0$ kJ/mol. Since the answer choices are all expressed in scientific notation, this can also be written as $0 	imes 10^3$ kJ/mol. Therefore, the best choice is A, which is the only one that is closest to 0 kJ/mol.

Calculate the Change in Energy, in Kilojoules Per Mole, for the Transmutation