Problem 113 - Chemistry The Central Science

Question

The arsenic in a \(1.22-\) g sample of a pesticide was converted to \(\mathrm{AsO}_{4}^{3-}\) by suitable chemical treatment. It was then titrated using \(\mathrm{Ag}^{+}\) to form \(\mathrm{Ag}_{3} \mathrm{AsO}_{4}\) as a precipitate. (a) What is the oxidation state of As in AsO \(_{4}^{3-2}(\mathbf{b})\) Name \(\mathrm{Ag}_{3} \mathrm{AsO}_{4}\) by analogy to the corresponding compound containing phosphorus in place of arsenic. (c) If it took 25.0 \(\mathrm{mL}\) of 0.102 \(\mathrm{MAg}^{+}\) to reach the equivalence point in this titration, what is the mass percentage of arsenic in the pesticide?

Step-by-Step Solution

Answer

The oxidation state of As in AsO4^(3-) is +5. The compound Ag3AsO4 can be named as silver arsenate by analogy to the corresponding compound containing phosphorus (silver phosphate). The mass percentage of arsenic in the pesticide is 5.22%.

Step 1: Determine oxidation state of As in AsO4^(3-)#

To determine the oxidation state of arsenic in AsO4^(3-), we can use the general rule that the sum of oxidation states of all the elements in a compound is equal to the charge of the compound. In AsO4^(3-), we have As and 4 oxygen atoms, so we can write: x + 4(-2) = -3 Where x represents the oxidation state of As and -2 is the known oxidation state of O in this compound. Solving for x, x = -3 + 8 x = +5 Thus, the oxidation state of As in AsO4^(3-) is +5.

Step 2: Naming Ag3AsO4 by analogy to the corresponding compound containing phosphorus#

In order to find the name of Ag3AsO4 by analogy to the corresponding compound containing phosphorus, we must first identify the analogous phosphorus compound. The phosphorus compound will have the same structure but with arsenic (As) replaced by phosphorus (P). The phosphorus compound is Ag3PO4, which is known as silver phosphate. By analogy, Ag3AsO4 can be named as silver arsenate.

Step 3: Calculate moles of Ag+ at the equivalence point#

From the given titration data, it takes 25.0 mL of 0.102 M Ag+ solution to reach the equivalence point. To compute the moles of Ag+ ions at the equivalence point, we can use the formula: n(Ag+) = M x V n(Ag+) = (0.102 mol/L) x (25.0 mL) x (1 L/1000 mL) = 0.00255 mol

Step 4: Calculate moles of As in the pesticide sample#

Since 3 moles of Ag+ reacts with 1 mole of AsO4^(3-) to form Ag3AsO4, the mole ratio of Ag+:As is 3:1. We can now use the stoichiometry to compute the moles of As in the pesticide sample as: n(As) = n(Ag+) / 3 = 0.00255 mol / 3 = 0.00085 mol

Step 5: Calculate mass percentage of arsenic in the pesticide#

Now that we have the moles of arsenic, we can calculate its mass in the pesticide sample: mass(As) = n(As) × molar mass(As) = 0.00085 mol × 74.92 g/mol = 0.06369 g To find the mass percentage of arsenic in the pesticide, we can use the formula: mass percentage = (mass(As) / mass of pesticide sample) × 100 % mass percentage = (0.06369 g / 1.22 g) × 100 % = 5.22 % Thus, the mass percentage of arsenic in the pesticide is 5.22%.

Key Concepts

Oxidation State

The oxidation state of an element in a compound denotes the degree of oxidation (loss of electrons) of the respective element. For arsenic in the arsenate ion \( \text{AsO}_4^{3-} \), we can determine its oxidation state by applying the rule that the sum of the oxidation states must equal the charge of the ion. In this case:

• Oxygen typically has an oxidation state of \(-2\).
• Arsenic's oxidation state needs to be found by setting up the equation:\( x + 4(-2) = -3 \).
• Solving yields \( x = +5 \).

Therefore, the oxidation state of arsenic in \( \text{AsO}_4^{3-} \) is \(+5\). This indicates that arsenic has lost five electrons in the formation of this ion.

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It enables us to determine the amounts of substances consumed and produced. In the reaction forming silver arsenate \( \text{Ag}_3\text{AsO}_4 \), three moles of \( \text{Ag}^+ \) are needed for every mole of \( \text{AsO}_4^{3-} \). Here's how stoichiometry was applied:

• Using the molarity and volume of the titrant \( \text{Ag}^+ \), moles of silver can be calculated with: \[ n(\text{Ag}^+) = M \times V \] where \( M \) is molarity and \( V \) is volume in liters.
• This yields \( 0.00255 \) moles of \( \text{Ag}^+ \).
• The stoichiometric ratio provides the moles of arsenic:\[ n(\text{As}) = \frac{n(\text{Ag}^+)}{3} \] resulting in \( 0.00085 \) moles of arsenic.

Stoichiometry is crucial for correctly predicting the amounts involved in chemical reactions, ensuring accurate experimental outcomes.

Mass Percentage

Mass percentage is a way of expressing the concentration of an element in a compound or mixture. It tells us what fraction of the total mass is accounted for by the element of interest. The formula is:

• \[\text{mass percentage} = \left( \frac{\text{mass of element}}{\text{total mass of sample}} \right) \times 100\%\]
• In this exercise, \( 0.06369 \text{ g} \) of arsenic was found in a \( 1.22 \text{ g} \) pesticide sample.
• Substituting these values, the mass percentage of arsenic is calculated:\( \frac{0.06369 \text{ g}}{1.22 \text{ g}} \times 100\% = 5.22\% \).

Using mass percentage is helpful in evaluating the purity of compounds or assessing compliance with safety regulations.

Silver Arsenate

Silver arsenate \( \text{Ag}_3\text{AsO}_4 \) is a compound composed of silver and the arsenate ion. It is formed as a precipitate during the titration process in this exercise. Below are some important points about silver arsenate:

• It is an ionic compound.
• Arsenate ion has a formula unit of \( \text{AsO}_4^{3-} \), where arsenic shares oxygen atoms similarly to phosphorus in phosphate ions.
• By analogy to silver phosphate \( \text{Ag}_3\text{PO}_4 \), \( \text{Ag}_3\text{AsO}_4 \) is named silver arsenate.
• It is often used in chemical analyses involving arsenic to form stable precipitates.

Understanding compounds like silver arsenate is essential for grasping broader chemical reaction mechanisms.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of bonds, leading to different molecular structures. In the context of this problem, a chemical reaction occurs when arsenic in the pesticide is converted to arsenate ions, which then react with silver ions:

• The reaction \( \text{AsO}_4^{3-} + 3 \text{Ag}^+ \rightarrow \text{Ag}_3\text{AsO}_4 \) represents a typical ionic reaction, forming a precipitate.
• Chemical reactions are governed by principles like mass conservation and stoichiometry, ensuring that atom counts are balanced on both sides of the equation.
• Molecules interact through ionic, covalent, or metallic bonds, each with unique properties influencing reaction conditions and products.

Understanding these principles underpins the practical and theoretical approaches to laboratory techniques and chemical research.