Problem 93 - 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 \(\mathrm{As}^{3+}\) 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 \(_{3}\) $$\begin{aligned} 3 \mathrm{As}_{2} \mathrm{S}_{3}(\mathrm{s})+10 \mathrm{HNO}_{3}(\mathrm{aq})+4 \mathrm{H}_{2} \mathrm{O}(\ell) & \rightarrow \\ 6 \mathrm{H}_{3} \mathrm{AsO}_{4}(\mathrm{aq})+10 \mathrm{NO}(\mathrm{g})+9 \mathrm{S}(\mathrm{s}) \end{aligned}$$ Finally, the presence of arsenic is confirmed by adding \(\mathrm{AgNO}_{3}\) to the solution of \(\mathrm{H}_{3} \mathrm{AsO}_{4}\) to precipitate a reddish brown solid \(\mathrm{Ag}_{x} \mathrm{AsO}_{y} .\) The composition of this solid is As, \(16.199 \%\) and \(\mathrm{Ag}, 69.964 \%\) (a) What are the oxidation numbers of As, \(S,\) and \(N\) in the reaction of \(\mathrm{As}_{2} \mathrm{S}_{3}\) with nitric acid? (b) What is the formula of the reddish brown solid \(\mathrm{Ag}_{\mathrm{x}} \mathrm{A} \mathrm{s} \mathrm{O}_{\mathrm{y}} ?\)

Step-by-Step Solution

Answer

(a) As: +5, S: 0, N: +2. (b) The formula is \(\mathrm{Ag}_3\mathrm{AsO}_4\).

Step 1: Determine the Oxidation Numbers for As, S, and N

In the compound \(\mathrm{As}_2\mathrm{S}_3\), arsenic (As) is bonded to sulfur (S). Since sulfur typically has an oxidation state of -2, we can determine that each arsenic must be in the +3 oxidation state to balance the -6 total from the three sulfurs.In \(\mathrm{HNO}_3\), nitrogen's oxidation state is usually +5, as oxygen has an oxidation state of -2 and the hydrogen atom has +1. Hence, the compound HNO₃ balances to zero (1 + 5 - 6 = 0).The nitric acid reaction products include nitric oxide (NO), where nitrogen is in the +2 oxidation state.

Step 2: Understand the Reaction with Nitric Acid

The reaction given: \[3 \mathrm{As}_2\mathrm{S}_3(\mathrm{s}) + 10 \mathrm{HNO}_3(\mathrm{aq}) + 4 \mathrm{H}_2\mathrm{O}(\ell) \rightarrow 6 \mathrm{H}_3\mathrm{AsO}_4(\mathrm{aq}) + 10 \mathrm{NO}(\mathrm{g}) + 9 \mathrm{S}(\mathrm{s})\] In this reaction, arsenic (As) oxidizes from +3 to +5 in \(\mathrm{H}_3\mathrm{AsO}_4\), while nitrogen (N) reduces from +5 in \(\mathrm{HNO}_3\) to +2 in NO. The sulfur (S) is released as elemental sulfur with an oxidation state of zero.

Step 3: Calculate Molar Mass of the Reddish Brown Solid

The solid contains arsenic (As) and silver (Ag) in the formula \(\mathrm{Ag}_x\mathrm{AsO}_y\). From the mass percentages provided (As: 16.199 % and Ag: 69.964 %), assume a 100 g compound sample, resulting in 16.199 g of As and 69.964 g of Ag.Using the atomic masses (Ag: 107.87 u, As: 74.92 u), find the number of moles:- Moles of As = \( \frac{16.199}{74.92} = 0.216\, \text{mol} \)- Moles of Ag = \( \frac{69.964}{107.87} = 0.648\, \text{mol} \)Find the simplest mole ratio between As and Ag by dividing by the smallest value:- For As: \( \frac{0.216}{0.216} = 1 \)- For Ag: \( \frac{0.648}{0.216} = 3 \)

Step 4: Determine the Formula of the Compound

From the mole ratio, the empirical formula of the solid is \(\mathrm{Ag}_3\mathrm{AsO}_4\). This implies that three silver (Ag) atoms are combining with one \(\mathrm{AsO}_4\) group to form the solid.

Key Concepts

Chemical Reaction

Chemical reactions are processes where substances, known as reactants, transform into different substances, called products. One vital concept in chemical reactions is the oxidation-reduction (redox) reaction. Redox reactions involve the transfer of electrons between substances, changing their oxidation states.
In our example, when arsenic sulfide \(\mathrm{As}_2\mathrm{S}_3\) reacts with nitric acid \(\mathrm{HNO}_3\), we witness a redox reaction. The arsenic (As) in \(\mathrm{As}_2\mathrm{S}_3\) undergoes oxidation. It changes from an oxidation state of +3 to +5 in \(\mathrm{H}_3\mathrm{AsO}_4\). Meanwhile, the nitrogen in nitric acid is reduced from +5 to +2 in nitric oxide \(\mathrm{NO}\).
Understanding these electron exchanges is crucial, as it helps in predicting products and balancing the equation.

Arsenic Chemistry

Arsenic, denoted as As, is an intriguing element found in the Group 15 of the periodic table, often referred to as a semimetal. Arsenic exhibits several oxidation states, with +3 and +5 being most common in compounds.
In analytical chemistry, detecting arsenic involves specific reactions due to its unique chemical properties. The exercise describes how to confirm arsenic presence in a mixture with antimony. First, both are precipitated as sulfide compounds — \(\mathrm{As}_2\mathrm{S}_3\) for arsenic being yellow. Arsenic is then separated because only \(\mathrm{Sb}_2\mathrm{S}_3\) dissolves in hydrochloric acid, leaving behind arsenic sulfide.
Arsenic compounds often require careful handling due to their toxicity, yet they are significant in varied applications such as electronics and even medicine.

Empirical Formula Determination

Empirical formulas provide the simplest whole-number ratio of atoms in a compound. It represents the primary composition of a compound without detailing its structure.
To find an empirical formula, we start with the mass percentages of each element in the compound. For instance, in the reddish brown compound \(\mathrm{Ag}_x\mathrm{AsO}_y\), the problem gives 16.199% arsenic and 69.964% silver. By considering a 100 g sample, we can directly assume we have 16.199 g of arsenic and 69.964 g of silver.
Next, we convert these masses to moles:

• Moles of As: divide its mass by its atomic mass (74.92 u).
• Moles of Ag: divide its mass by the atomic mass of silver (107.87 u).

The simplest mole ratio then dictates the empirical formula. In this case, the ratio indicates \(\mathrm{Ag}_3\mathrm{AsO}_4\).