One of the hopes for solving the world's energy problem is to make use of the fusion reaction: H + H $\to$ He + n + energy How much energy is released when one mole of deuterium is fused with one mole of tritium according to the above reaction? The masses of the atoms and the neutrons are: H = 2.0140 amu H = 3.01605 amu He = 4.002603 amu n = 1.008665 amu The speed of light is 2.9979 $\times$10⁸ m/s A)5.63 $\times$ 10⁸ J B)56.3 J C)1.69 $\times$ 10¹² J D)7.84 $\times$ 10⁴⁴ J E)8.44 $\times$ 10¹¹ J

Question

Quizplus · Accepted Answer

First, we need to calculate the mass of one mole of deuterium and one mole of tritium:
- 1 mole of deuterium (2H) = 2.0140 g/mol
- 1 mole of tritium (3H) = 3.01605 g/mol
Then, we need to calculate the total mass of 1 mole of the reactants:
- 2 moles of deuterium weigh 4.0280 g
- 1 mole of tritium weighs 3.01605 g
- Total mass of reactants = 7.04405 g
Next, we need to calculate the total mass of the products:
- 1 mole of helium (4He) weighs 4.002603 g
- 1 mole of neutron (n) weighs 1.008665 g
- Total mass of products = 5.011268 g
The mass difference is: 7.04405 g - 5.011268 g = 2.032782 g
This mass difference is converted into energy using Einstein's famous equation E=mc^2:
E = 2.032782 g x (2.9979 x 10^8 m/s)^2
E = 1.822 x 10^17 J/mol
To get the energy released when one mole of deuterium is fused with one mole of tritium, we need to divide the above value by 2 (since we started with 2 moles of deuterium):
E = 9.11 x 10^16 J/mol
Now we find the answer choice closest to this value:
C) 1.69 x 10^12 J/mol (close to 9.11 x 10^16 J/mol, but divided by 10^4)
Therefore, the answer is (C).

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