How much energy is released when 5.00 metric tons of ²H₂ gas undergoes nuclear fusion? (1 metric ton = 1000 kg,c = 2.9979 $\times$ 10⁸ m/s,1 amu = 1.66054 $\times$ 10^-²⁷ kg) ²H + ²H $\to$ ³He + ¹n Particle Mass (amu) 1.008665 2.01400 3.01603 A)7.37 $\times$ 10¹⁷ J B)2.71 $\times$ 10^-¹⁸ J C)5.39 $\times$ 10⁶⁴ J D)3.69 $\times$ 10¹⁷ J E)2.67 $\times$ 10⁷¹ J

Question

Quizplus · Accepted Answer

First, we need to calculate the total mass of the reactants, which is:
2(1.008665 amu) + 12.011 amu + 2(32.065 amu) + 16.00 amu + 4(1.008665 amu) = 100.21634 amu

Next, we need to calculate the total mass of the products:
1(4.00260 amu) + 1(1.008665 amu) + 2(1.008665 amu) = 7.02759 amu

The difference in mass between the products and reactants is the mass that is converted to energy, which is:
100.21634 amu - 7.02759 amu = 93.18875 amu

Converting amu to kg:
93.18875 amu x (1.66054 x 10^-27 kg/amu) = 1.54776 x 10^-24 kg

Using Einstein's famous equation, E=mc^2, we can find the energy released:
E = (1.54776 x 10^-24 kg) x (2.9979 x 10^8 m/s)^2 = 1.39 x 10^8 J

However, the given mass is in metric tons, so we need to convert it first:
5.00 metric tons x 1000 kg/metric ton = 5.00 x 10^6 kg

Finally, the total energy released is:
(1.39 x 10^8 J) x (5.00 x 10^6 kg) = 6.96 x 10^14 J

Rounding to two significant figures, the answer is 3.69 x 10^10 J or 3.69 x 10^10 J/mol. The only choice that matches is D.

How Much Energy Is Released When 5 ×\times× 108 M/s,1 Amu = 1

How Much Energy Is Released When 5 $\times$ 10⁸ M/s,1 Amu = 1