Answer:
a) 226.6 grams of Cl₂
b) 19.2 grams of C
c) 303.2 grams of TiCl₄ and 70.4 grams of CO₂
Explanation:
The balanced chemical reaction is the following:
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?
From the chemical equation, 1 mol of TiO₂ reacts with 2 moles of Cl₂. So, the stoichiometric ratio is 2 mol Cl₂/1 mol TiO₂. We multiply this ratio by the moles of TiO₂ we have to calculate the moles of Cl₂ we need:
1.60 mol TiO₂ x 2 mol Cl₂/1 mol TiO₂ = 3.2 mol Cl₂
Now, we convert from moles to mass by using the molecular weight (MW) of Cl₂:
MW(Cl₂) = 35.4 g/mol x 2 = 70.8 g/mol
mass of Cl₂= 3.2 mol x 70.8 g/mol = 226.6 g
<em>Therefore, 226.6 grams of Cl₂ are needed to react with 1.6 mol of TiO₂. </em>
(b) What mass of C is needed to react with 1.60 mol of TiO₂?
From the chemical equation, 1 mol of TiO₂ reacts with 1 moles of C(s). So, the stoichiometric ratio is 1 mol C/1 mol TiO₂. We multiply this ratio by the moles of TiO₂ we have to calculate the moles of C(s) we need:
1.60 mol TiO₂ x 1 mol C(s)/1 mol TiO₂ = 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)
<em>Therefore, a mass of 19.2 grams of C is needed to react with 1.60 mol of TiO₂. </em>
(c) What is the mass of all the products formed by reaction with 1.60 mol of TiO₂?
From the chemical equation, we can notice that 1 mol of TiO₂ produces 1 mol of TiCl₄ and 1 mol of CO₂. So, from 1.60 moles of TiO₂, 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(TiCl₄) = 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(CO₂) = 12 g/mol C + (16 g/mol x 2 O) = 44 g/mol
1.60 mol x 44 g/mol = 70.4 g
<em>Therefore, from the reaction of 1.60 mol of TiO₂ are formed 303.2 grams of TiCl₄ and 70.4 grams of CO₂.</em>
