Challenge Titanium is a transition metal used in many alloys...

Challenge Titanium is a transition metal used in many alloys because it is extremely strong and lightweight. Titanium tetrachloride $(\mathrm{TiCl_{4 }})$ is extracted from titanium oxide $\left(\mathrm{TiO}_{2}\right)$ using chlorine and coke (carbon). $$\mathrm{TiO}_{2}(\mathrm{s})+\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{TiCl}_{4}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ \begin{equation} \mathrm{a. Cl}_{2} \text { gas is needed to react with } 1.25 \text { mol of } \mathrm{TIO}_{2} ? \end{equation} \begin{equation} \begin{array}{l}{\text { b. What mass of } C \text { is needed to react with } 1.25 \text { mol of TiO_{2} ? }} \\ {\text { c. What is the mass of all of the products formed by reaction with } 1.25 \text { mol of TiO_{2} ? }}\end{array} \end{equation}

Challenge Titanium is a transition metal used in many alloys because it is extremely strong and lightweight. Titanium tetrachloride $(\mathrm{TiCl_{4 }})$ is
extracted from titanium oxide $\left(\mathrm{TiO}_{2}\right)$ using chlorine and coke (carbon).
$$\mathrm{TiO}_{2}(\mathrm{s})+\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{TiCl}_{4}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$
\begin{equation}
\mathrm{a. Cl}_{2} \text { gas is needed to react with } 1.25 \text { mol of } \mathrm{TIO}_{2} ?
\end{equation}
\begin{equation}
\begin{array}{l}{\text { b. What mass of } C \text { is needed to react with } 1.25 \text { mol of TiO_{2} ? }} \\ {\text { c. What is the mass of all of the products formed by reaction with } 1.25 \text { mol of TiO_{2} ? }}\end{array}
\end{equation}

Key Concepts

Balanced Chemical Equations

A balanced chemical equation accurately represents the chemical reaction by showing the same number of atoms for each element on both the reactant and product sides. This ensures the law of conservation of mass is met and provides the stoichiometric coefficients that are used to calculate the precise proportions of reactants and products involved in the reaction.

Stoichiometry

Stoichiometry involves using the relationships between reactants and products as given by the balanced equation to determine the quantities of substances consumed and produced. It allows one to convert between moles of reactants and moles of products, thereby facilitating calculations for quantities such as masses, volumes, or numbers of particles.

Mole Concept

The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. It provides a bridge between the microscopic scale of atoms and molecules and the macroscopic scale of grams and liters, allowing chemists to count entities by weighing samples, given that one mole contains Avogadro's number of particles.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule and is essential for converting between the mass of a substance and the number of moles, which is particularly useful in stoichiometric calculations.

Conservation of Mass

The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction. This principle underpins stoichiometric calculations by ensuring that the total mass of the reactants must equal the total mass of the products, allowing chemists to verify the consistency and correctness of their calculations.

Transcript

00:01 Even the balanced equation of the reaction between titanium for dioxide, carbon and chlorine, to produce titanium tetrachloride and carbon dioxide.

00:30 Okay? given this balanced equation, we need to determine the mass of chlorine, okay? that is necessary to react with 1 .25 moles of titanium for oxide.

00:54 These are the two substances involved.

00:58 Therefore, these are the two that you're going to use to establish your mole ratio.

01:05 So we have one more of titanium for oxide reacting reacting with two moles of chlorine.

01:17 So to calculate, we say one mole of titanium four oxide reacts with two moles of chlorine.

01:31 Therefore, when 1 .25 moles of titanium for oxide react, how many moles of chlorine do we get? or how many moles of chlorine react? and the answer is 2 .5.

01:51 So 2 times 1 .25 the way right 1 is 2 .5 moles of chlorine.

02:00 And now we need to convert the moles into grams.

02:06 For that we multiply by the molar mass of chlorine, which is 2 times 35 .5 or 35 .45 which is the atomic weight of chlorine atom okay grams per mole and the answer is a hundred so the whole 2 .5 moles times 2 times 35 .35 moles cancelled the answer is 177.

03:02 0 .25 grams of chlorines are needed.

03:10 Okay question b we need to figure out the mass of carbon that we react with this amount of titanium for oxide for that we establish the ratio between titanium for oxide and carbon because you're know clothing you can also use clothing because you already know clothing you'll determine clothing here so this is our unknown now and the mole ratio is one to one okay so you right away know that here x is 1 .25 moles because the ratio is 1 to 1 therefore 1 .25 to 1 .25 moles of carbon but they're asking us for the mass in grams okay so we need to convert these moles to grams by multiplying by the atomic mass of carbon which is 12 grams per mole okay moles will cancel and then we just multiply 12 times 1 .25 and the answer is 15 grams of carbon are needed to react with 1 .25 mode of titanium 4 oxide and the last question is to determine the mass of all the products that are formed when 1 .25 most of the 104 oxide react.

05:07 So we need to calculate the mass of titanium tetrachloride and the mass of carbon dioxide.

05:15 These are the only two products that we know.

05:18 So the ratio is then going to be titanium four oxide to the titanium four oxide and titanium four oxide to carbon dioxide...

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