Chapter 20, Problem 20.98QP

Interpretation Introduction

Interpretation:

Energy released when 1.00kg of Hydrogen-1 undergoes given fusion process and compare this energy with heat released when 1.00kg graphite burns to Carbon dioxide gas.

Answer to Problem 20.98QP

• Energy released when 1.00kg of hydrogen-1 undergoes given fission is $\text{-5}{\text{.92×10}}^{\text{11}}\text{J}$.
• The energy released in fusion process is high than the energy released by combustion of Carbon.

Explanation of Solution

Given:

${\text{Nuclear mass of }}_2^4\text{He= 4}\text{.00260 amu-(2×0}\text{.000549amu)=4}\text{.001502amu}$

Write the appropriate nuclear mass below each nuclide symbol and calculate change in mass.

$\begin{array}{l}4{}_1^{\text{1}}\text{H }\stackrel{}{\to }{}_2^4\text{He }\text{+ }{\text{2}}_1^0\text{e }\\ \text{Masses: 1}\text{.00728}4.\text{001502}0.\text{000549}\text{amu}\\ \\ \text{Δm =}\left[\text{4}\text{.001502+(2×000549-(4}\times \text{1}\text{.00728)}\right]\text{amu}\\ \\ \text{= - 0}\text{.026520 amu}\end{array}$

When 4 mol ${}_{\text{1}}^{\text{1}}\text{H}$ are fused, the change in mass is $\text{-0}\text{.026520 g}$. Therefore, for 1.00kg ${}_{\text{1}}^{\text{1}}\text{H}$, the mass change is

$\text{1}{\text{.00×10}}^{\text{3}}\text{g×}\frac{{\text{1mol }}_{\text{1}}^{\text{1}}\text{H}}{\text{1}{\text{.00728g }}_{\text{1}}^{\text{1}}\text{H}}\text{×}\frac{\text{-0}\text{.026520}}{\text{1}{\text{.00728g}}_{\text{1}}^{\text{1}}\text{H}}\text{= -6}\text{.5820g}$

Converting mass to energy gives,

$\begin{array}{l}{\text{ΔE=(Δm)c}}^{\text{2}}\text{=(-6}{\text{.5820×10}}^{\text{-3}}\text{kg)(2}{\text{.998×10}}^{\text{8}}{\text{m/s)}}^{\text{2}}\\ \\ \text{=-5}{\text{.9159×10}}^{\text{14}}\\ \\ \text{=-5}{\text{.92×10}}^{\text{14}}\text{J}\end{array}$

For the combustion of Carbon:

$\begin{array}{l}\text{C(graphite)}{\text{+ O}}_{\text{2(g)}}\stackrel{}{\to }{\text{CO}}_{\text{2(g)}}\\ \text{ΔH}\text{0}\text{0}\text{-394kJ/mol}\\ \text{Forthereaction,}\\ \text{ΔH=ΔE=-394kJ/mol}\\ \\ \text{1}{\text{.00×10}}^{\text{3}}\text{g×}\frac{\text{1molC}}{\text{12}\text{.01gC}}\text{×}\frac{\text{-394kJ}}{\text{1mol}\text{C}}\text{= -3}{\text{.280×10}}^4\text{kJ}\\ =-3.28{\text{×10}}^4\text{kJ}\end{array}$

In the fusion process the energy released from $\text{1}\text{.00kg}$ Hydrogen-1 ( $\text{5}{\text{.92×10}}^{\text{11}}\text{kJ)}$ is more than 18 million times larger than the energy released by combustion of $\text{1}\text{.00kg}$ of graphite which is equal to $\text{3}{\text{.28×10}}^4\text{kJ}$.

Conclusion

• Energy released when 1.00kg of hydrogen-1 undergoes given fission is $\text{-5}{\text{.92×10}}^{\text{11}}\text{J}$.
• The energy released in fusion process is high than the energy released by combustion of Carbon.