Element M is prepared industrially by a two-step procedure...

Element $M$ is prepared industrially by a two-step procedure according to the following (unbalanced) equations: $$\begin{array}{l}{\text { (1) } \mathrm{M}_{2} \mathrm{O}_{3}(s)+\mathrm{C}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{MCl}_{3}(l)+\mathrm{CO}(g)} \\ {\text { (2) } \mathrm{MCl}_{3}(l)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{M}(s)+\mathrm{HCl}(g)}\end{array}$$ Assume that 0.855 g of $\mathrm{M}_{2} \mathrm{O}_{3}$ is submitted to the reaction sequence. When the HCl produced in step (2) is dissolved in water and titrated with $0.511 \mathrm{M} \mathrm{NaOH}, 144.2 \mathrm{mL}$ of the NaOH solution is required to neutralize the HCl. (a) Balance both equations. (b) What is the atomic mass of element $M,$ and what is its identity? (c) What mass of M in grams is produced in the reaction?

Element $M$ is prepared industrially by a two-step procedure according to the following (unbalanced) equations:
$$\begin{array}{l}{\text { (1) } \mathrm{M}_{2} \mathrm{O}_{3}(s)+\mathrm{C}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{MCl}_{3}(l)+\mathrm{CO}(g)} \\ {\text { (2) } \mathrm{MCl}_{3}(l)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{M}(s)+\mathrm{HCl}(g)}\end{array}$$
Assume that 0.855 g of $\mathrm{M}_{2} \mathrm{O}_{3}$ is submitted to the reaction sequence. When the HCl produced in step (2) is dissolved in water and titrated with $0.511 \mathrm{M} \mathrm{NaOH}, 144.2 \mathrm{mL}$ of the NaOH solution is required to neutralize the HCl.
(a) Balance both equations.
(b) What is the atomic mass of element $M,$ and what is its identity?
(c) What mass of M in grams is produced in the reaction?

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Key Concepts

Balancing Chemical Equations

Balancing chemical equations is the process of ensuring that the number of atoms for each element is the same on both sides of a reaction. This process applies the law of conservation of mass and is fundamental for establishing the proper mole ratios needed in further stoichiometric calculations.

Stoichiometry

Stoichiometry involves using the relationships between reactants and products as expressed in a balanced chemical equation to calculate quantities such as moles, mass, and volumes. This concept is essential for determining how much product is formed from a given amount of reactant.

Acid-Base Titration

Acid-base titration is an analytical technique used to determine the concentration of an acid or base in a solution. By reacting the titrant with the analyte until the equivalence point is reached, one can calculate the quantity of substance involved in the reaction through the known concentration and volume of the titrant.

Molar Mass Determination and Element Identification

Molar mass determination involves calculating the mass of one mole of a substance based on reaction stoichiometry and titration data. This concept is crucial for identifying an unknown element by comparing the experimentally determined molar mass to known atomic masses from the periodic table.

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