To determine the percentage of silver in the coin sample, we can follow a series of logical steps involving stoichiometry and the properties of the compounds formed during the reaction. Let's break it down step by step.
Understanding the Reaction
When the silver coin is dissolved in concentrated nitric acid, silver (Ag) and copper (Cu) react to form their respective nitrates. The silver ions can then react with hydrochloric acid (HCl) to form silver chloride (AgCl), which is a precipitate. The mass of the silver chloride formed can help us backtrack to find the amount of silver in the original coin.
Calculating Moles of Silver Chloride
The first step is to calculate the number of moles of silver chloride produced. The molar mass of silver chloride (AgCl) can be calculated as follows:
- Molar mass of Ag = 107.87 g/mol
- Molar mass of Cl = 35.45 g/mol
- Total molar mass of AgCl = 107.87 g/mol + 35.45 g/mol = 143.32 g/mol
Now, using the mass of silver chloride obtained (1.050 g), we can calculate the number of moles:
Number of moles of AgCl = mass / molar mass = 1.050 g / 143.32 g/mol ≈ 0.00732 moles
Finding Moles of Silver
From the reaction, we know that one mole of silver chloride is produced from one mole of silver. Therefore, the number of moles of silver in the sample is also approximately 0.00732 moles.
Calculating Mass of Silver
Next, we can find the mass of silver in the sample using its molar mass:
Mass of silver = number of moles × molar mass of silver = 0.00732 moles × 107.87 g/mol ≈ 0.789 g
Determining the Percentage of Silver
Finally, to find the percentage of silver in the original coin sample, we use the formula:
Percentage of silver = (mass of silver / mass of coin) × 100
Substituting the values we have:
Percentage of silver = (0.789 g / 1.590 g) × 100 ≈ 49.5%
Final Thoughts
Thus, the percentage of silver in the coin sample is approximately 49.5%. This method demonstrates how chemical reactions and stoichiometric calculations can be applied to analyze the composition of a sample effectively.
