Problem 101 - Chemistry and Chemical Reactivity

Question

The presence of arsenic in a sample that may also contain another Group 5 A element, antimony, can be confirmed by first precipitating the As \(^{3+}\) and \(\mathrm{Sb}^{3+}\) ions as yellow solid \(\mathrm{As}_{2} \mathrm{S}_{3}\) and orange solid \(\mathrm{Sb}_{2} \mathrm{S}_{3} .\) If aqueous HCl is then added, only \(\mathrm{Sb}_{2} \mathrm{S}_{3}\) dissolves, leaving behind solid \(\mathrm{As}_{2} \mathrm{S}_{3} .\) The \(\mathrm{As}_{2} \mathrm{S}_{3}\) can then be dissolved using aqueous HNO \(_{3}.\) $$3 \mathrm{As}_{2} \mathrm{S}_{3}(\mathrm{s})+10 \mathrm{HNO}_{3}(\mathrm{aq})+4 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow6 \mathrm{H}_{3} \mathrm{AsO}_{4}(\mathrm{aq})+10 \mathrm{NO}(\mathrm{g})+9 \mathrm{S}(\mathrm{s})$$ Finally, the presence of arsenic is confirmed by adding AgNO_to the solution of \(\mathrm{H}_{3} \mathrm{AsO}_{4}\) to precipitate a reddish brown solid \(\mathrm{Ag}_{\mathrm{x}} \mathrm{AsO}_{\mathrm{y}}\). The composition of this solid is As, \(16.199 \%\) and \(\mathrm{Ag}\) \(69.964 \%.\) (a) What are the oxidation numbers of As, S, and \(\mathrm{N}\) in the reaction of \(\mathrm{As}_{2} \mathrm{S}_{3}\) with nitric acid? (b) What is the formula of the reddish brown solid \(\mathrm{Ag}_{\mathrm{x}} \mathrm{AsO}_{\mathrm{y}} ?\)

Step-by-Step Solution

Answer

(a) As: +5, S: 0, N: +2; (b) Ag3AsO4.

Step 1: Determine oxidation states in As2S3

In the compound \(As_2S_3\), arsenic (As) has a typical oxidation state of \(+3\) since it forms a compound with sulfur (S), which usually has an oxidation state of \(-2\). Hence, each As holds a \(+3\) state while each S maintains its \(-2\) state.

Step 2: Identify oxidation states in HNO3

In the nitric acid \(HNO_3\), the oxygen (O) typically has an oxidation state of \(-2\) and hydrogen (H) has \(+1\). Considering a neutral HNO3 molecule, nitrogen (N) needs an oxidation state of \(+5\) to balance the compound.

Step 3: Determine oxidation states in reactants and products

Following the reaction \(3 As_2S_3(s) + 10 HNO_3(aq) + 4 H_2O(l) \rightarrow 6 H_3AsO_4(aq) + 10 NO(g) + 9 S(s)\), arsenic changes from \(+3\) in \(As_2S_3\) to \(+5\) in \(H_3AsO_4\), indicating oxidation. Sulfur remains \(0\) in the elemental form \(S(s)\). Nitrogen is reduced from \(+5\) to \(+2\) in \(NO(g)\).

Step 4: Calculate molar ratios using given mass percentages

The compound \(Ag_xAsO_y\) has 16.199% As and 69.964% Ag. Converting these percentages to moles, assuming a 100 g sample, gives \(16.199 \, g\) of As, \(69.964 \, g\) of Ag, and consequently \(13.837 \, g\) of O. Divide each by their atomic/molar mass to ascertain their stoichiometric coefficients.

Step 5: Finding empirical formula ratios

For As: \(16.199/74.92 \approx 0.216\) moles. For Ag: \(69.964/107.87 \approx 0.648\) moles. For O: \(13.837/16.00 \approx 0.864\) moles. Calculate the simplest ratio by dividing each mole value by the smallest among them, which is \(0.216\) moles.

Step 6: Obtain the empirical formula

Divide each component’s mole number by the smallest one \(0.216\): As: \(1\), Ag: \(3\), O: \(4\). Thus, the formula is \(Ag_3AsO_4\).

Key Concepts

Oxidation States

In chemistry, oxidation states are essential for understanding how atoms share or transfer electrons in reactions. This concept is integral when investigating a reaction's redox nature, where electron transfer occurs.

• In the compound \(As_2S_3\), arsenic holds an oxidation state of \(+3\) since each sulfur typically exhibits \(-2\). With two arsenic and three sulfur atoms, the compound maintains electrical neutrality.


• For nitric acid, \(HNO_3\), hydrogen is \(+1\), oxygen is \(-2\), leading nitrogen to have a \(+5\) oxidation state in this context.


• During the described reaction, arsenic undergoes oxidation, transitioning from an oxidation state of \(+3\) in \(As_2S_3\) to \(+5\) in \(H_3AsO_4\).


• Nitrogen, in turn, is reduced from \(+5\) in \(HNO_3\) to \(+2\) in \(NO(g)\), indicating an electron gain.


• Such changes are central to identifying the movement of electrons, fundamental to redox (reduction-oxidation) reactions.

Understanding these oxidation changes can greatly illuminate chemical reaction pathways and substance transformation.

Chemical Reactions

Chemical reactions are processes that result in the conversion of one set of chemical substances to another. In this context, they play a crucial role in arsenic detection by facilitating precipitation and oxidation-reduction.

• The reaction of \(As_2S_3\) with \(HNO_3\) not only dissolves arsenic from its sulfide form but also transforms it into \(H_3AsO_4\), arsenic acid, via oxidation.


• This reaction process is typical of oxidation-reduction (redox) reactions, involving electron transfer; here, arsenic loses electrons.


• The breakdown of \(HNO_3\) results in the evolution of \(NO(g)\) as a product, a clear indicator of nitrogen reduction within this reaction scheme.


• Moreover, the added silver nitrate \(AgNO_3\) reacts with the dissolved arsenic to create a distinct precipitate here in determining the arsenic’s presence.

Observing these reactions not only confirms arsenic but exemplifies the chemistry of separation and detection techniques used.

Empirical Formula Calculation

Determining empirical formulas is a method in chemistry used to find the simplest whole-number ratios of atoms in a compound. This process is crucial when confirming the components' percentages in a reaction product.

• The goal is to convert mass percentages into moles to deduce stoichiometric ratios. For \(Ag_xAsO_y\), convert each element’s given mass percentage into moles by dividing by their respective atomic masses.


• In this exercise: \(16.199\%\) of arsenic corresponds to \(0.216\) moles, \(69.964\%\) of silver equals \(0.648\) moles, and the remaining oxygen makes \(0.864\) moles.


• To find the simplest ratio, divide by the smallest number of moles, here \(0.216\): resulting in \(1:3:4\) for As, Ag, and O, respectively.


• The empirical formula is then derived as \(Ag_3AsO_4\), showing the simplest whole-number ratios, crucial for deducing molecular quantities.

This calculation helps translate experimental data into a clear, interpretable chemical formula, which is foundational in identifying unknown substances in chemical analysis.