Q24.93P - Chemistry: Molecular Nature Of Matter And Change

Question

The reaction that will probably power the first commercial fusion reactor is

${}_{\mathbf{\text{1}}}{}^{\mathbf{\text{3}}}{\mathbf{\text{H + }}}_{\mathbf{\text{1}}}^{\mathbf{\text{2}}}\mathbf{\text{H}}{\mathbf{\to }}_{\mathbf{\text{2}}}^{\mathbf{\text{4}}}{\mathbf{\text{He + }}}_{\mathbf{\text{0}}}^{\mathbf{\text{1}}}\mathbf{\text{n}}$ 

How much energy would be produced per mole of reaction?

(Masses of atoms: ${}_{\mathbf{\text{1}}}{}^{\mathbf{\text{3}}}\mathbf{\text{H = 3.01605amu;}}_{\mathbf{\text{1}}}^{\mathbf{\text{2}}}\mathbf{\text{H = 2.0140amu}}$;

${}_{\mathbf{\text{2}}}{}^{\mathbf{\text{4}}}\mathbf{\text{He = 4.00260 amu;mass of }}_{\mathbf{\text{0}}}^{\mathbf{\text{1}}}\mathbf{\text{n = 1.008665 amu}}$ .)

Step-by-Step Solution

Answer

The energy per mole of the given reaction is  $\text{1689654573 }\frac{\text{kJ}}{\text{mol}}$.

Step 1: Definition of Concept

Electronegativity: An atom's chemical behavior in which it attracts the shared electron pair to itself is known as electronegativity. As the number of energy levels grows larger, electronegativity decreases.

Step 2: Find the energy per mole of the given reaction

Considering the given reaction:

${}_{\text{1}}{}^{\text{3}}{\text{H + }}_{\text{1}}^{\text{2}}\text{H}{\to }_{\text{2}}^{\text{4}}{\text{He + }}_{\text{0}}^{\text{1}}\text{n}$ 

The total masses of both reactants and products must first be determined.

Mass of the reactants:

$\text{3.01605 + 2.0140} \text{ = } \text{5.03005 amu}$ 

The product's mass is:

$\begin{array}{rcl}\text{4.00260 + 1.008665}& =& \text{5.011265 amu}\\ \text{4m}& =& \text{5.03005 amu - 5.011265 amu}\\ & =& \text{0.0188 amu}\end{array}$ 

To calculate the amount of energy released, we must use Einstein's equation:

$\begin{array}{rcl}\text{E}& =& {\text{4mc}}^{\text{2}}\\ \text{E}& =& \left[\frac{\text{0.0188 g}}{\text{mol}}\right]\left[\frac{\text{1 kg}}{\text{1000 g}}\right]{\left[{\text{2.99792×10}}^{\text{8}}\frac{\text{m}}{\text{s}}\right]}^2\left[\frac{\text{1.J}}{\frac{{\text{kg.m}}^{\text{2}}}{{\text{s}}^{\text{2}}}}\right]\left[\frac{\text{1 kJ}}{\text{1000.J}}\right]\\ & =& \text{1689654573 }\frac{\text{kJ}}{\text{mol}}\end{array}$ 

Therefore, the required value is $\text{1689654573 }\frac{\text{kJ}}{\text{mol}}$.