Question

The unknown acid \(\mathrm{H}_{2} \mathrm{X}\) can be neutralized completely by \(\mathrm{OH}^{-}\) according to the following (unbalanced) equation: $$ \mathrm{H}_{2} \mathrm{X}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{X}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) $$ The ion formed as a product, \(\mathrm{X}^{2-}\), was shown to have 36 total electrons. What is element \(\mathrm{X}\) ? Propose a name for \(\mathrm{H}_{2} \mathrm{X}\). To completely neutralize a sample of \(\mathrm{H}_{2} \mathrm{X}, 35.6 \mathrm{~mL}\) of \(0.175 \mathrm{M}\) \(\mathrm{OH}^{-}\) solution was required. What was the mass of the \(\mathrm{H}_{2} \mathrm{X}\) sample used?

Short answer

The element X is Selenium (Se), and the compound H2X is called Hydroselenic Acid (H2Se). The mass of the H2X (H2Se) sample used is 0.2522 g.

Step-by-step solution

Identifying the element X by its total electrons

The ion X^(2-) has a total of 36 electrons; it means the neutral atom of element X has 34 electrons in its structure as the ion has added two extra electrons, so we have to find an element with an atomic number of 34. The element with atomic number 34 is Selenium (Se).

Naming the compound H2X

Now that we know X is Selenium, we can name the compound H2X. It is an acid with two hydrogen atoms and one selenium atom, forming a compound H2Se. This compound is called Hydroselenic Acid.

Finding the moles of OH- required for neutralization

To figure out the mass of H2X, we first need to find the number of moles of OH- ions required for complete neutralization. We will use the formula: \[ moles (OH^-) = Molarity\ (OH^-) \times Volume\ (OH^-) \] Plugging in the given values, we get: \[ moles (OH^-) = 0.175 M \times 0.0356 L = 0.00623 mol \]

Balancing the chemical equation

Now, we have to balance the chemical equation for the reaction: \[ H_{2}X(aq) + OH^{-}(aq) \longrightarrow X^{2-}(aq) + H_{2}O(l) \] The balanced equation turns out to be: \[ H_{2}Se(aq) + 2OH^{-} (aq) \longrightarrow Se^{2-}(aq) + 2H_{2}O(l) \]

Calculating moles of H2X from moles of OH-

Using the balanced stoichiometry of the reaction, we can calculate the number of moles of H2X (H2Se) consumed in the process: \[ moles\ (H2Se) = \frac{moles\ (OH^-)}{2} = \frac{0.00623\ mol}{2} = 0.003115\ mol \]

Computing mass of H2X from moles of H2X

Finally, to find the mass of the H2Se sample used, we multiply the number of moles by its molar mass: \[ mass\ (H2Se) = moles\ (H2Se) \times Molar\ mass\ (H2Se) \] The molar mass of H2Se is obtained by adding the molar masses of 2 Hydrogen atoms and 1 Selenium atom: \[ Molar\ mass\ (H2Se) = 2 \times Molar\ mass\ (H) + Molar\ mass\ (Se) = 2 \times 1.01 g/mol + 78.97 g/mol \] \[ Molar\ mass\ (H2Se) = 2.02\ g/mol + 78.97\ g/mol = 80.99\ g/mol \] Now, we multiply the obtained moles of H2Se by the molar mass: \[ mass (H2Se) = 0.003115\ mol \times 80.99\ g/mol = 0.252\,2\ g \] The mass of the H2X (H2Se) sample used is 0.2522 g.

Key concepts

Molecular Weight Calculation

To understand how to calculate the molecular weight of a compound, it is essential to first know the individual atomic weights of the elements involved. Molecular weight, often reported in grams per mole, is essentially the sum of the atomic masses of each element in the molecule. This concept is crucial because it allows chemists to convert between moles and grams, which is fundamental in laboratory settings.

For example, when calculating the molecular weight of Hydroselenic Acid, \(\mathrm{H}_2\mathrm{Se}\), we take into account the atomic masses of Hydrogen (approximately 1.01 g/mol) and Selenium (approximately 78.97 g/mol). With two hydrogen atoms and one selenium atom, the molecular weight calculation goes as follows:

• Molar mass of \(\mathrm{H}_2\mathrm{Se}\) = 2 \times 1.01 \text{ g/mol} + 78.97 \text{ g/mol} = 80.99 \text{ g/mol}.

Understanding molecular weight allows for the conversion of moles into grams and vice versa, a critical step when determining the amount of substance needed or produced in a chemical reaction.

Chemical Equations

Chemical equations represent the transformation of reactants into products during a chemical reaction. They must be balanced to satisfy the law of conservation of mass, meaning that the number of atoms of each element in the reactants must equal the number of atoms of those elements in the products.

In the acid-base titration of \(\mathrm{H}_2\mathrm{X}\) with \(\mathrm{OH}^-\), the reaction was initially given unbalanced. To balance it, we follow the principle of conserving mass and charge. The balanced form of the equation for the reaction can be expressed as:

• For Hydroselenic Acid: \[\mathrm{H}_2\mathrm{Se(aq)} + 2\mathrm{OH}^-(\mathrm{aq}) \longrightarrow \mathrm{Se}^{2-}(\mathrm{aq}) + 2\mathrm{H}_2\mathrm{O}(\mathrm{l})\]\

This balanced equation shows that each molecule of \(\mathrm{H}_2\mathrm{Se}\) reacts with two hydroxide ions, forming a selenide ion and two water molecules. Balancing chemical equations is a foundational skill in chemistry that ensures accurate stoichiometry calculations.

Stoichiometry

Stoichiometry is the quantitative study of the reactants and products in a chemical reaction. It involves using balanced chemical equations to calculate the amounts of substances involved in a reaction.

In the titration of \(\mathrm{H}_2\mathrm{Se}\) with \(\mathrm{OH}^-\), we first calculated the number of moles of \(\mathrm{OH}^-\) required to neutralize the acid. Using the stoichiometry from the balanced chemical equation, it was determined that:

• Each mole of \(\mathrm{H}_2\mathrm{Se}\) reacts with 2 moles of \(\mathrm{OH}^-\).
• By finding 0.00623 moles of \(\mathrm{OH}^-\), we deduced that only half of this quantity reacted with \(\mathrm{H}_2\mathrm{Se}\) since the ratio is 1:2.

Thus, there were 0.003115 moles of \(\mathrm{H}_2\mathrm{Se}\). Finally, multiplying the moles of \(\mathrm{H}_2\mathrm{Se}\) by its molecular weight provided the mass of the acid sample used in the reaction. Mastery of stoichiometry is crucial for anyone conducting experiments, as it is integral to calculating yields, reagent quantities, and reacting mass ratios.