Question

Titanium(III) chloride is used in the manufacture of polyethylene. It is produced by the reaction (at high temperatures) between TiCl4 gas and H2. 2TiCl4(g) 1 H2(g) 9: 2TiCl3(s) 1 2HCl(g) Assume 100% yield and constant temperature and pressure. (a) How many liters of HCl gas can be produced by mixing 3.72 L of TiCl4 and 4.50 L of H2? (b) How many liters of reactant in excess are present after the reaction is complete? 35\. Nitric acid can be prepared by b

Short answer

Question: In a chemical reaction, 3.72 L of titanium(IV) chloride (TiCl4) gas reacts with 4.50 L of hydrogen (H2) gas to produce titanium(III) chloride (TiCl3) and hydrogen chloride (HCl) gas. Calculate (a) the volume of HCl gas produced and (b) the volume of the reactant in excess after the reaction is complete. Answer: (a) 3.72 L of HCl gas can be produced, (b) 2.64 L of reactant (H2) in excess are present after the reaction is complete.

Step-by-step solution

Identify the balanced chemical equation

The balanced chemical equation is given by: 2TiCl4(g) + H2(g) → 2TiCl3(s) + 2HCl(g)

Calculate the moles of reactants present

Since the reaction is happening at constant temperature and pressure, we can directly use the volume ratio provided in the balanced equation (assuming ideal gas behavior). We are given the initial volumes of TiCl4 and H2: Volume of TiCl4 = 3.72 L Volume of H2 = 4.50 L

Determine the limiting reactant

To find the limiting reactant, we need to compare the volume ratio of the reactants with the stoichiometric ratio: Volume ratio (TiCl4 : H2) = 3.72 L : 4.50 L Stoichiometric ratio (TiCl4 : H2) = 2 : 1 Divide the volume of each reactant by its stoichiometric coefficient: Ratio for TiCl4 = 3.72 L / 2 = 1.86 L Ratio for H2 = 4.50 L / 1 = 4.50 L Since the ratio for TiCl4 is smaller, TiCl4 is the limiting reactant.

Calculate the volume of HCl gas produced

Based on the stoichiometric ratio and the volume of the limiting reactant (TiCl4), we can find the volume of HCl produced: Stoichiometric ratio (TiCl4 : HCl) = 2 : 2 Volume of HCl produced = (Volume of TiCl4) * (HCl ratio / TiCl4 ratio) = 3.72 L * (2 / 2) = 3.72 L

Calculate the volume of reactant in excess (H2) after the reaction is complete

To find the amount of H2 remaining after the reaction is complete, subtract the amount consumed by the reaction from the initial volume: Volume of H2 consumed = (Volume of TiCl4) * (H2 ratio / TiCl4 ratio) = 3.72 L * (1 / 2) = 1.86 L Volume of H2 remaining after the reaction = Initial volume of H2 - Volume of H2 consumed = 4.50 L - 1.86 L = 2.64 L The answers to the exercise are: (a) 3.72 L of HCl gas can be produced (b) 2.64 L of reactant (H2) in excess are present after the reaction is complete.

Key concepts

Limiting Reactant

In a chemical reaction, the limiting reactant is the substance that is completely consumed first, determining the maximum amount of product that can be formed. This concept is vital for predicting the amounts of products formed and the reactants remaining after the reaction has ceased. To identify the limiting reactant, one must compare the molar or volume ratios of the reactants used to those required by the balanced chemical equation.

For example, consider the scenario with Titanium(III) chloride and hydrogen. To identify the limiting reactant, given volumes of reactants 3.72 L for TiCl4 and 4.50 L for H2 are compared to their stoichiometric coefficients. The calculation for TiCl4 gives a higher value per stoichiometric unit, indicating that hydrogen (H2) is in excess, and thus, TiCl4 is the limiting reactant. It is important to remember that this can only be done directly with volumes when dealing with gases at constant temperature and pressure, due to the ideal gas law.

Chemical Reaction

A chemical reaction is a process where reactants are transformed into products through the breaking and forming of chemical bonds. Reactions follow the Law of Conservation of Mass, which implies that matter is neither created nor destroyed. This means the number of atoms for each element must be the same in the reactants and products. In the case of Titanium(III) chloride production, the reaction at high temperature sees TiCl4 gas reacting with H2 gas to produce TiCl3 solid and HCl gas.

The equation provides not just the substances involved but also the phase state they are in, such as gases (g), solids (s), and so forth, which can influence reaction conditions. When carrying out a reaction, various factors such as temperature, pressure, catalysts, and concentration can impact the yield and rate at which products are formed.

Balanced Chemical Equation

A balanced chemical equation provides a symbolic representation of a chemical reaction where both sides have the same number of atoms for all elements involved. It adheres to the Law of Conservation of Mass. Each substance is denoted by its chemical formula, with coefficients used to balance the equation. For instance, in our exercise, the balanced equation is 2TiCl4(g) + H2(g) → 2TiCl3(s) + 2HCl(g).

When balancing an equation, it requires adjusting coefficients — the numbers placed before chemical formulas — but never by changing subscripts within chemical formulas since this would change the substances involved. Balancing equations is essential for finding the stoichiometry of a reaction, which subsequently allows for the calculation of the amounts of reactants and products. In the context of the provided exercise, the balanced equation shows the direct molar ratio between reactants and products, which can be translated into volume ratio under the ideal gas law, enabling us to solve for the volumes of products and reactants.