Titanium metal is obtained from the mineral rutile, TiO2. The process requires multiple steps, as shown in the following reactions:
TiO₂(s) + 2 Cl₂(g) + 2 C(s) → TiCl₄(s) + 2 CO(g)
TiCl₄(s) + 2 Mg(s) → Ti(s) + 2 MgCl₂(s)
c. How many kilograms of rutile are needed to produce 95 kg of Ti?

Question

Titanium metal is obtained from the mineral rutile, TiO2. The process requires multiple steps, as shown in the following reactions:

TiO₂(s) + 2 Cl₂(g) + 2 C(s) → TiCl₄(s) + 2 CO(g)

TiCl₄(s) + 2 Mg(s) → Ti(s) + 2 MgCl₂(s)

c. How many kilograms of rutile are needed to produce 95 kg of Ti?

Accepted Answer

Welcome back everyone. Iron ore hematite also spelled as hematite contains iron. Three oxide iron can be extracted from iron three oxide using a blast furnace. According to the following reactions, we need to calculate the mass in kilograms of solid carbon required to obtain 100 kg of iron. So our first reaction is solid carbon reacting with oxygen gas to form carbon dioxide gas. Our second reaction is carbon dioxide gas reacting with solid carbon to form two moles of carbon monoxide gas. And our third reaction is iron, three oxide solid reacting with three moles of carbon monoxide to form two moles of liquid iron and three moles of carbon dioxide gas. We're going to begin with what we are given which is 100 kg. So 100 kilograms of iron and we're going to convert from kilograms to units of grams. So we're going to multiply by a conversion factor where we have kilograms of iron in our denominator and grams of iron in our numerator. Recall that our prefix kilo tells us that we have an equivalence of 10 to the third power of our base unit gram, canceling out kilograms of iron. We have grams of iron, which is one of our products in reaction three. And we're going to now multiply to convert from grams of iron in the denominator to moles of iron in the numerator. This is where we will utilize our molar mass of iron. Where from the product table for one mole of iron, we find a mass of 55.85 g of iron, canceling out grams of iron. And now converting from moles of iron, we want to multiply next by a molar ratio between moles of our product. From reaction three iron to moles of carbon monoxide, which is one of our products as well as a reactant in reaction two and in reaction three. So we're going to utilize molar ratios here from reaction three, we have a ratio of two moles of iron with which is formed from three moles of carbon monoxide. So we have a 3 to 2 molar ratio where we can now cancel out our moles of iron and move from moles of carbon monoxide to multiply by our next conversion factor to go from moles of carbon monoxide to an equation which would be our second equation which relates carbon monoxide to carbon. So we would go from moles of carbon monoxide in the denominator to moles of carbon in the numerator. From our second equation in the prompt, we're given a molar ratio of two moles of carbon monoxide produced from one mole of carbon canceling out moles of carbon monoxide. We then want to end up with mass of carbon as our final unit. So we're going to multiply by our fifth conversion factor where we would go from moles of carbon in the denominator to grams of carbon in the numerator where we would utilize our molar mass of carbon from the periodic table which tells us that we have 12.1 g of carbon per mole of carbon. So canceling out moles of carbon, we would then go from grams of carbon in the denominator to kilograms of carbon in the numerator for our final unit. In which as before, for our prefix kilo, we're told that we have for one g of carbon and equivalent of 10 to the negative third kilograms of carbon. So canceling out grams of carbon kilograms of carbon for our mass is our final unit and our quotient is going to simplify so that we find a mass of 16.1 kg of carbon obtained from 100 g of iron. So 16.1 kms of carbon is going to be our final answer. I hope this made sense and let us know if you have any questions.

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Key Concepts

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Titanium metal is obtained from the mineral rutile, TiO2. The process requires multiple steps, as shown in the following reactions:TiO2(s) + 2 Cl2(g) + 2 C(s) → TiCl4(s) + 2 CO(g)TiCl4(s) + 2 Mg(s) → Ti(s) + 2 MgCl2(s) c. How many kilograms of rutile are needed to produce 95 kg of Ti?

Verified video answer for a similar problem:

Key Concepts

Stoichiometry

Molar Mass

Chemical Reactions