Answer :
Final answer:
The percentage yield of the reaction is 80.67%. The atom economy of the reaction is also 80.67%. For a yield of 81%, 328.47kg of Titanium Chloride would be needed.
Explanation:
Let's begin by calculating the percentage yield. The actual yield of the reaction was 51kg of titanium, but we need to determine the theoretical yield first. This is done by identifying the limiting reactant, which in this case is Titanium Chloride (TiCl4), as we have 250kg of it. The molar mass of TiCl4 is about 189.7 g/mol and that of Titanium (Ti) is about 47.9 g/mol. Therefore, 1 mol of TiCl4 produces 1 mol of Ti. Converting these amounts to kilograms, we learn that 189.7 kg of TiCl4 produces 47.9 kg of Ti. Thus, the theoretical yield from 250kg of TiCl4 would be (250kg TiCl4) * (47.9 kg Ti / 189.7 kg TiCl4) = 63.1 kg Ti. The percentage yield is then (actual yield / theoretical yield) * 100% = (51 kg / 63.1 kg) * 100% = 80.67%. The percentage yield is therefore 80.67%.
Next, let's calculate the atom economy. Atom economy is the mass of desired product divided by total mass of products. Here, the desired product is titanium (Ti), so the atom economy is (mass of Ti / mass of all products) * 100%. Since the only products are Ti and MgCl2, and the reaction produces 1 mol Ti for every 1 mol MgCl2, the atom economy is also 80.67%.
For the extension question, given that the yield is 81%, we first calculate the theoretical mass of TiCl4 needed to produce 141kg of Ti, then divide by 0.81 (as the yield is 81%) to find the actual mass of TiCl4 needed. So (141kg Ti) * (189.7 kg TiCl4 / 47.9 kg Ti) / 0.81 = 328.47kg of TiCl4.
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