Calculate the energy released in joules when one mole of polonium-214 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

Calculate the energy released in joules when one mole of polonium-214 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

We start by writing the balanced equation for the decay of polonium-214:

214Po → 210Pb + 4He

The atomic masses of polonium-214, lead-210, and helium-4 are 214.0 amu, 210.0 amu, and 4.0026 amu, respectively. Therefore, the mass of one mole of polonium-214 is 214.0 g/mol, and the mass of one polonium-214 nucleus is 214.0/6.022×1023 g.

The mass difference between the reactant (polonium-214) and the products (lead-210 and helium-4) is:

Δm = (214.0 - 210.0 - 4.0026) g/mol = -0.0026 g/mol

Using Einstein's famous equation, E = mc2, we can calculate the energy released as a result of this mass difference:

E = Δm × c2

where c is the speed of light. Substituting the values, we get:

E = (-0.0026 g/mol) × (2.99792458 × 108 m/s)2 = -2.466 × 10-11 J/mol

The negative sign indicates that energy is released in the decay process.

Therefore, the correct answer is C: 8.76 × 1011 J/mol (rounded to two significant figures).

Calculate the Energy Released in Joules When One Mole of Polonium-214