Problem 55 - Chemistry A Molecular Approach

Question

Silver nitrate solutions are often used to plate silver onto other metals. What is the maximum amount of silver (in grams) that can be plated out of \(4.8 \mathrm{~L}\) of an \(\mathrm{AgNO}_{3}\) solution containing \(3.4 \%\) Ag by mass? Assume that the density of the solution is \(1.01 \mathrm{~g} / \mathrm{mL}\).

Step-by-Step Solution

Answer

The maximum amount of silver that can be plated out of 4.8 L of the AgNO3 solution is 164.832 grams.

Step 1: Calculate the mass of the silver nitrate solution

First, determine the total mass of the silver nitrate solution using its volume and density. The volume of the solution is given as 4.8 L (which is equivalent to 4800 mL because 1 L = 1000 mL). Since the density is given as 1.01 g/mL, the total mass of the solution is the product of its volume and density: Total mass = Volume × Density = 4800 mL × 1.01 g/mL = 4848 g.

Step 2: Calculate the mass of silver

Next, calculate the mass of silver in the solution. Given the solution has 3.4% silver by mass, you can find the mass of silver by multiplying the total mass of the solution by the percent of silver (expressed as a decimal):Mass of Ag = Total mass of solution × Percentage of Ag (in decimal form) = 4848 g × 0.034 = 164.832 g.

Step 3: Convert the mass of silver to grams

The mass of silver calculated in Step 2 is already expressed in grams, so no further conversion is necessary. The mass of silver that can be plated out of the solution is 164.832 grams.

Key Concepts

Chemistry of Silver Plating

Silver plating is a fascinating application of chemistry where a thin layer of silver is deposited onto the surface of another material, often a metal. This process involves the reduction of silver ions to elemental silver and is a classic example of a redox reaction, a fundamental type of chemical reaction where electrons are transferred between species. When silver nitrate (AgNO_3)) is used, the silver ions (Ag^+) in the solution are reduced, and elemental silver (Ag) is deposited onto a surface. To understand the extent to which silver can be plated, it's crucial to know how much silver is present in a given solution, which can be determined by calculations of molarity and stoichiometry.

Molarity Calculation

The molarity of a solution represents its concentration, defined as the number of moles of solute per liter of solution. To calculate molarity, the mass percentage and the density of the solution are often used. Molarity is crucial for quantitative analysis in chemistry, including understanding how much substance can be obtained from a solution. For silver plating, molarity tells us how much silver there actually is in a given volume of AgNO_3 solution. It is calculated using the formula:

M = (mass of solute in grams / molar mass of solute) / volume of solution in liters

However, in the given exercise, percentage by mass is used instead of molarity, but understanding how to calculate molarity is fundamental for similar problems where concentration terms might be interchanged.

Stoichiometry in Silver Plating

Stoichiometry is the method used to calculate the quantities of reactants and products in chemical reactions. In the context of silver plating, stoichiometry allows you to determine the maximum amount of silver that can be plated from a silver nitrate solution. The process involves several steps:

• Determining the total mass of the silver nitrate solution.
• Finding the mass of silver using the percentage by mass.
• Using the molar mass of silver to convert from moles to grams if necessary.

Although in this problem we directly used the mass percentage to find the mass of silver available, stoichiometry more commonly would require you to convert the mass of silver nitrate to moles, and then use the stoichiometry of the chemical reaction to find the moles of silver that could be plated out. Finally, you'd convert the moles back to grams to find the maximum mass of silver for plating.