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Chapter 4: Problem 159

The unknown acid \(\mathrm{H}_{2} \mathrm{X}\) can be neutralized completely by \(\mathrm{OH}^{-}\) according to the following (unbalanced) equation: $$\mathrm{H}_{2} \mathrm{X}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{X}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(i) $$ The ion formed as a product, \(X^{2-},\) 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

Expert verified
The unknown element X is selenium (Se), and the acid is named hydrogen selenide (\(H_2X\)). The mass of the hydrogen selenide sample used is 0.2524 grams.

Step by step solution

01

Identify the element X

In the ion \(X^{2-}\), there are 36 total electrons. Since the ion has a 2- charge, this means that it gains 2 extra electrons, and the element in its neutral state has 34 electrons. Since the number of electrons is equal to the number of protons for a neutral atom, we can look up an element in the periodic table with atomic number (number of protons) 34, which is selenium (Se).
02

Propose a name for \(H_2X\)

Since we determined that X is selenium (Se), we can propose a name for the unknown acid \(H_2X\). The compound \(H_2X\) has two hydrogen atoms and one selenium atom, so it's a selenide acid. Therefore, the name for \(H_2X\) is hydrogen selenide.
03

Find the moles of \(OH^-\) used

Since we know the volume and concentration of the \(OH^-\) solution used to neutralize \(H_2X\) (35.6 mL and 0.175 M), we can calculate the moles of \(OH^-\) by multiplying the volume (converted to liters) and concentration: Moles of \(OH^-\) = Volume (L) × Concentration (M) Moles of \(OH^-\) = (35.6 mL × (1 L/1000 mL)) × 0.175 M = 0.006236 mol
04

Determine the moles of \(H_2X\)

To get the balanced chemical equation, we need to add a coefficient in front of \(OH^-\) to make sure that the charge and number of atoms in the reactants and products are equal: \(H_2X(aq) + 2OH^-(aq) \longrightarrow X^{2-}(aq) + 2H_2O(l)\) According to the balanced equation, there is a 1:2 mole ratio between \(H_2X\) and \(OH^-\). Therefore, we can calculate the moles of \(H_2X\) by dividing the moles of \(OH^-\) by 2: Moles of \(H_2X\) = 0.006236 mol \(OH^-\) × (1 mol \(H_2X\) / 2 mol \(OH^-\)) = 0.003118 mol
05

Calculate the molar mass of \(H_2X\)

To calculate the molar mass of the hydrogen selenide \(H_2X\), we need to sum the molar masses of each element in the compound: Molar mass of \(H_2X\) = 2 × Molar mass of H + Molar mass of Se Molar mass of \(H_2X\) = 2 × 1.008 g/mol + 78.97 g/mol = 80.986 g/mol
06

Determine the mass of the \(H_2X\) sample used

Finally, we can determine the mass of the \(H_2X\) sample used by multiplying the moles of \(H_2X\) and its molar mass: Mass of \(H_2X\) = Moles of \(H_2X\) × Molar mass of \(H_2X\) Mass of \(H_2X\) = 0.003118 mol × 80.986 g/mol = 0.2524 g The mass of the \(H_2X\) sample used is 0.2524 grams.

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