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 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

Element X is selenium (Se), and the compound \(\mathrm{H}_{2} \mathrm{X}\) is named hydrogen selenide. The mass of the hydrogen selenide sample used in the reaction is approximately 0.252 g.

Step-by-step solution

Determine the number of protons in element X

Since the ion X^2- has 36 total electrons, it must have lost 2 electrons to the \(\mathrm{H}_{2} \mathrm{X}\) molecule. Therefore, the neutral atom X has 34 electrons. As the number of protons in an atom is equal to the number of electrons in its neutral state, element X has 34 protons.

Identify the element X

Checking the periodic table, we find that the element with 34 protons is selenium (Se).

Propose a name for H₂X

Since element X is selenium, the compound \(\mathrm{H}_{2} \mathrm{X}\) can be named as hydrogen selenide.

Calculate the moles of OH⁻ used in the reaction

To find the moles of OH⁻ used in the reaction, we need to use the volume and molarity of the OH⁻ solution that was used to completely neutralize the sample. $$ \text{moles of OH}^{-} = \text{volume} \times \text{molarity}\\ = 35.6\,\mathrm{mL} \times 0.175\,\mathrm{M}\\ = 0.00623\,\mathrm{mol} $$

Calculate the moles of H₂X used in the reaction

From the balanced equation of the reaction, we can see that: $$ 2\, \mathrm{H}_{2} \mathrm{X}(a q)+2\, \mathrm{OH}^{-}(a q) \longrightarrow 2\, \mathrm{X}^{2-}(a q)+4\, \mathrm{H}_{2} \mathrm{O}(l) $$ Since it takes 2 moles of OH⁻ to neutralize 1 mole of H₂X completely: $$ \text{moles of} \,\mathrm{H}_{2} \mathrm{X} = \frac{0.00623\,\mathrm{mol}}{2} = 0.003115\,\mathrm{mol} $$

Calculate the molar mass of H₂X

The molar mass of H₂X can be calculated by adding the molar masses of two hydrogen atoms (H) and one selenium atom (Se). $$ \text{Molar mass of}\,\mathrm{H}_{2} \mathrm{X} = 2 \times \text{Molar mass of H} + \text{Molar mass of Se}\\ = 2 \times 1.00784\,\mathrm{g/mol} + 78.971\,\mathrm{g/mol}\\ = 80.98668\,\mathrm{g/mol} $$

Calculate the mass of H₂X sample used

Now we can use the moles of H₂X and its molar mass to calculate the mass of the H₂X sample used in the reaction. $$ \text{mass of}\,\mathrm{H}_{2} \mathrm{X} = \text{moles of}\,\mathrm{H}_{2} \mathrm{X} \times \text{molar mass of}\,\mathrm{H}_{2} \mathrm{X}\\ = 0.003115\,\mathrm{mol} \times 80.98668\,\mathrm{g/mol}\\ = 0.25237\,\mathrm{g} $$ So, the mass of the H₂X sample used in the reaction is approximately 0.252 g.

Key concepts

Understanding Acid-Base Neutralization

An acid-base neutralization is a type of chemical reaction where an acid and a base react to form water and a salt. This process is essential in many areas of chemistry and has practical applications, such as titrations.

In the provided exercise, an unknown acid \( \mathrm{H}_{2} \mathrm{X} \) is neutralized by hydroxide ions \( \mathrm{OH}^{-} \) in an aqueous solution. This reaction illustrates a common neutralization process where the hydrogen ions, H+, from the acid combine with the hydroxide ions, OH−, from the base to form water, H2O. The resulting product along with water is a salt, which in this case, is \( \mathrm{X}^{2-} \).

Assessing a neutralization reaction involves balancing the chemical equation, as shown in the solution. This balance ensures that the number of atoms for each element is the same on both sides of the equation, adhering to the law of conservation of mass. The balanced equation also allows us to understand the stoichiometry of the reaction—namely, the mole ratios of reactants that react and products formed.

Calculating Molar Mass in Chemical Equations

The molar mass calculation is an essential step in working with chemical formulas and equations. The molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). It is determined by summing the weights of the component atoms, based on their atomic weights from the periodic table.

In the context of the exercise, the unknown compound \( \mathrm{H}_{2} \mathrm{X} \) is determined to contain selenium (Se), with hydrogen being the other element. To find the molar mass of \( \mathrm{H}_{2} \mathrm{X} \) we must add the atomic weights of two hydrogen atoms with that of selenium. Knowing the molar mass is crucial for the final step of the exercise, which involves converting moles of the compound to grams.

Stoichiometry in Action

Stoichiometry refers to the calculation of reactants and products in chemical reactions. It is a key concept in chemistry that involves using balances in equations to predict the outcomes of reactions.

In this exercise, stoichiometry is used to calculate how much of the unknown acid \( \mathrm{H}_{2} \mathrm{X} \) reacts with the hydroxide ions. First, we needed the balanced chemical equation to understand the mole ratio between \( \mathrm{H}_{2} \mathrm{X} \) and \( \mathrm{OH}^{-} \). With a mole ratio of 1:2, we then calculated the moles of \( \mathrm{H}_{2} \mathrm{X} \) that reacted based on the volume and molarity of the hydroxide solution.

Through these calculations, we discover that stoichiometry is not just about numbers and ratios. It provides a systematic approach to quantifying the changes that occur during chemical reactions, making it a foundational tool for anyone working with chemical processes.