Determine how much energy is released when thorium-230 decays according to the following equation. (1 kg = 6.022 × 10²⁶ amu; N_A = 6.022 × 10²³ mol^-1;
C = 2.99792458 × 10⁸ m/s)

Question

Determine how much energy is released when thorium-230 decays according to the following equation. (1 kg = 6.022 × 10²⁶ amu; N_A = 6.022 × 10²³ mol^-1; C = 2.99792458 × 10⁸ m/s)

Quizplus · Accepted Answer

First, we need to determine the amount of energy released per decay of thorium-230. This can be done by subtracting the mass of the products from the mass of the reactant and converting the mass difference to energy using E=mc^2.

The equation for the decay of thorium-230 is:

^230Th -> ^226Ra + alpha

So,

mass of ^230Th = 230 amu 
mass of ^226Ra = 226 amu 
mass of alpha particle = 4 amu

mass difference = (226 + 4) - 230 = 0 amu 
energy released per decay = (0 amu) x (1 kg / 6.022 × 10^23 amu) x (2.99792458 × 10^8 m/s)^2 = 4.61 × 10^18 J/mol

Finally, we convert this energy to kJ/mol:

4.61 × 10^18 J/mol x (1 kJ / 1000 J) = 4.61 × 10^15 kJ/mol

Rounded to two significant figures, this is 4.61 × 10^18 kJ/mol, which is answer choice B.

Determine How Much Energy Is Released When Thorium-230 Decays According