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Titanium is a transition metal used in many alloys because it is extremely strong and lightweight. Titanium tetrachloride (TiCl4) is extracted from titanium oxide using chlorine and coke (carbon). TiO2(s) + C(s) + 2 Cl2(g) TiCl4(s) + CO2(g) (a) What mass of Cl2 gas is needed to react with 1.60 mol TiO2? g (b) What mass of C is needed to react with 1.60 mol of TiO2? g (c) What is the mass of all the products formed by reaction with 1.60 mol of TiO2? g

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Answer:

a) 226.6 grams of Clâ‚‚

b) 19.2 grams of C

c) 303.2 grams of TiClâ‚„ and 70.4 grams of COâ‚‚

Explanation:

The balanced chemical reaction is the following:

TiO₂(s) + C(s) + 2 Cl₂(g) → TiCl₄(s) + CO₂(g)

(a) What mass of Clâ‚‚ gas is needed to react with 1.60 mol TiOâ‚‚?

From the chemical equation, 1 mol of TiOâ‚‚ reacts with 2 moles of Clâ‚‚. So, the stoichiometric ratio is 2 mol Clâ‚‚/1 mol TiOâ‚‚. We multiply this ratio by the moles of TiOâ‚‚ we have to calculate the moles of Clâ‚‚ we need:

1.60 mol TiOâ‚‚ x 2 mol Clâ‚‚/1 mol TiOâ‚‚ = 3.2 mol Clâ‚‚

Now, we convert from moles to mass by using the molecular weight (MW) of Clâ‚‚:

MW(Clâ‚‚) = 35.4 g/mol x 2 = 70.8 g/mol

mass of Clâ‚‚= 3.2 mol x 70.8 g/mol = 226.6 g

Therefore, 226.6 grams of Clâ‚‚ are needed to react with 1.6 mol of TiOâ‚‚.

(b) What mass of C is needed to react with 1.60 mol of TiOâ‚‚?

From the chemical equation, 1 mol of TiOâ‚‚ reacts with 1 moles of C(s). So, the stoichiometric ratio is 1 mol C/1 mol TiOâ‚‚. We multiply this ratio by the moles of TiOâ‚‚ we have to calculate the moles of C(s) we need:

1.60 mol TiOâ‚‚ x 1 mol C(s)/1 mol TiOâ‚‚ = 1.60 mol C(s)

So, we convert the moles of C(s) to grams as follows:

MW(C) = 12 g/mol

1.60 mol x 12 g/mol = 19.2 g C(s)

Therefore, a mass of 19.2 grams of C is needed to react with 1.60 mol of TiOâ‚‚.

(c) What is the mass of all the products formed by reaction with 1.60 mol of TiOâ‚‚?

From the chemical equation, we can notice that 1 mol of TiOâ‚‚ produces 1 mol of TiClâ‚„ and 1 mol of COâ‚‚. So, from 1.60 moles of TiOâ‚‚, 1 mol of each product will be produced:

1 mol TiO₂/1 mol TiCl₄ ⇒ 1.60 mol TiO₂/1.60 mol TiCl₄

1 mol TiO₂/1 mol CO₂ ⇒ 1.60 mol TiO₂/1.60 mol CO₂

Finally, we convert the moles to grams by using the molecular weight of each compound:

MW(TiClâ‚„) = 47.9 g/mol Ti + (35.4 g/mol x 4 Cl) = 189.5 g/mol

1.60 mol x 189.5 g/mol = 303.2 g

MW(COâ‚‚) = 12 g/mol C + (16 g/mol x 2 O) = 44 g/mol

1.60 mol x 44 g/mol = 70.4 g

Therefore, from the reaction of 1.60 mol of TiOâ‚‚ are formed 303.2 grams of TiClâ‚„ and 70.4 grams of COâ‚‚.

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