The thermite reaction, Fe2O31s2 + 2 Al1s2 ¡2 Fe1s2 + Al2O31s2, H = -851.5 kJ>mol, is one of the most exothermic reactions known. Because the heat released is sufficient to melt the iron product, the reaction is used to weld metal under the ocean. How much heat is released per mole of Al2O3 produced? How does this amount of thermal energy compare with the energy released when 2 mol of protons and 2 mol of neutrons combine to form 1 mol of alpha particles?

Video transcript

Hello everyone. Today, we have a following problem. The following reaction is a highly exothermic industrial reaction used to weld railroad tracks, calculate the heat released per mole of aluminum oxide formed. Then compare with the energy released when two mosle neutrons and two muzzle protons combined to generate one mole of alpha particles. So we need to first calculate the heat that is released Permal of aluminum per one mole of aluminum oxide. And that can be found taking the enthalpy of the reaction which is negative 3316.5 kilojoules and dividing that by how many moles of aluminum oxide formed, which was four. So we have four moles of aluminum oxy, this will equal 829.13 kilojoules. But if we multiply by a factor such that one kilojoule is equal to 10 to the third joules, our units of kilojoules will cancel out and we will arrive at 8.2913 times 10 to the fifth joules. Now we must then calculate the energy released when two moles of neutrons and two moles of protons combine to generate one mole of alpha particles. And we can do that using the equation that the energy is equal to MC squared. So M is the mass of a change mass change. The C is for the speed of light. So to find our M variable, we can just make this part a of our second part of this question, we have the mass of one helium which is an awful particle that has four and then two as the correct structure. And this mass is equal to 4.00260 atomic mass units. Now, if you plug this into, if you plug that into the ideal that the change in mass can be equal to two of our mass of individuals of helium. So the mass of helium on the periodic table where the isotope is 1.00866. And then we add that to two multiplied by the other isomer which is or the other isotope which is 1.00727 atomic mass units. And then we subtract that from the total atomic mass units, we arrive at 0.02926 atomic mass units for our change. And m now we can plug that into our equation for the energy is equal to 0.02926 grams as it is equal to atomic mass units, we can multiply by the conversion factor that tends to the third grams is equal to 1 kg. And then finally multiply this by three times 10 to the eighth, which is the speed of light and it was raised to the power of two. And this, when solving for this, this comes out to be 2.6334 times 10 to the 12th kilograms and supplied by meter square meters divided by seconds squared. And this kilograms times meters squared per second squared is actually equal to joules. So we can say that this is actually equal to 2.6334 times 10 to the 12th joules. No. Now we can compare the heat released per mole of aluminum oxide with the energy released when two multiple neutrons and two muscle protons combine to make the alpha particle. And so we can divide the larger value by the smaller value and see how, by how much of a factor is the heat released in the second reaction. So in this third part, we will take our 2.6334 times 10 to the 12 jewels. And we will divide that by the smaller number which is 8.2913 times 10 to the fifth jos to arrive an answer of 30 of 3,176,100 or which is jus or we can just write this. And so to have scientific notation such that we have a 3.1761 times 10 to the six or in other words, a value that is 3 million times greater. So that is by that is the factor in which the heat of the second reaction is larger than that of the first. And with that, we have solved the problem overall, I hope this helped. And until next time.