Question

Silver nitrate solutions are 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 AgNO \(_{3}\) solution containing 3.4\(\%\) Ag hy mass? Assume that the density of the solution is 1.01 g/mL.

Short answer

The maximum amount of silver that can be plated out is 164.784 g.

Step-by-step solution

Calculate the total mass of the solution

To calculate the total mass of the AgNO3 solution, convert the volume from liters to milliliters and then multiply by the density. The volume in milliliters is 4.8 L * 1000 mL/L = 4800 mL. The total mass is therefore 4800 mL * 1.01 g/mL.

Calculate the mass of Ag in the solution

Use the percentage concentration (by mass) to find the mass of Ag. The mass of Ag is 3.4% of the total mass of the solution. Calculate this by multiplying the total mass of the solution by 3.4/100.

Convert the mass of Ag to grams

The mass obtained from Step 2 will be in grams, as the density was given in g/mL, and the solution volume was converted to mL.

Key concepts

Solution Concentration

Understanding solution concentration is crucial when working with chemical solutions, such as silver nitrate used in plating. Concentration is defined as the quantity of a solute that is contained in a certain quantity of solvent or solution. When you know the concentration of a solution, you can determine how much of a compound is present in a given volume of liquid.

For instance, the concentration of silver in the silver nitrate solution is described as 3.4% Ag by mass. This means that for every 100 grams of the solution, there are 3.4 grams of silver. To find out the amount of silver in the entire solution, we need to find the solution's total mass and then apply the percentage to ascertain the mass of silver alone. Understanding how to leverage the concept of solution concentration can simplify tasks, like calculating the maximum amount of silver that can be plated from a solution.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In plating silver, stoichiometry allows us to predict how much silver can be deposited from a silver nitrate solution on a metal surface.

The stoichiometric calculations generally start by determining the molar amounts of reactants or products involved. However, in the example of silver plating, we are particularly interested in the mass of silver available in the solution, rather than the molar amount. Even then, understanding the underlying stoichiometric concepts ensures that the relationships between different substances in a chemical process are well-balanced and the calculations are based on accurate chemical principles.

Molarity and Molality

Molarity and molality are two measures of solution concentration that express the amount of solute in a solvent. Molarity (\( M \)) is defined as the number of moles of solute per liter of solution, whereas molality (\( m \)) is defined as the number of moles of solute per kilogram of solvent.

The key difference is that molarity is volume-based and affected by temperature since it involves liters of solution, while molality is mass-based and not affected by temperature, as it involves kilograms of solvent. In the context of silver nitrate plating, the specific concentration measurement may not be provided directly, but understanding these concepts can aid in the precise preparation of solutions required for consistent and quality plating results.