Question

Silver chloride, used in silver plating, contains 75.27% Ag. Calculate the mass of silver chloride in grams required to make 4.8 g of silver plating.

Short answer

Approximately 6.38 grams of silver chloride are required to make 4.8 grams of silver plating.

Step-by-step solution

Understand the Percentage Composition

First, understand that if silver chloride contains 75.27% silver (Ag), it means that for every 100 grams of silver chloride, there are 75.27 grams of silver.

Set Up the Proportion

Set up a proportion to determine how many grams of silver chloride are needed to obtain 4.8 grams of silver. The proportion will be based on the percentage composition: \( \frac{75.27\text{ g of Ag}}{100\text{ g of AgCl}} = \frac{4.8\text{ g of Ag}}{x\text{ g of AgCl}} \).

Solve for the Mass of Silver Chloride

Cross-multiply to solve for the unknown mass of silver chloride (\(x\)): \(100\text{ g of AgCl} \cdot 4.8\text{ g of Ag} = 75.27\text{ g of Ag} \cdot x\text{ g of AgCl} \). This gives us \(4.8 \cdot 100 = 75.27 \cdot x \), or \(480 = 75.27 \cdot x \).

Calculate the Mass of Silver Chloride

Divide both sides of the equation by 75.27 to isolate \(x\) and find the mass of silver chloride required: \(x = \frac{480}{75.27} \approx 6.38\text{ g} \).

Key concepts

Chemical Stoichiometry

Chemical stoichiometry is the branch of chemistry that involves the quantitative relationships between the reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed. This means that the mass of the reactants must equal the mass of the products.

For instance, when calculating how much silver chloride (AgCl) is needed to produce a certain amount of silver (Ag) for plating, stoichiometry allows us to use the percentage composition of silver in silver chloride to set up a ratio. This ratio helps determine how much of one compound is needed to obtain a specific amount of another compound. In the given problem, we know that silver chloride contains 75.27% silver, and we use this information to calculate the required mass of silver chloride to produce 4.8 grams of silver. Understanding this fundamental concept of stoichiometry is crucial for performing accurate chemical calculations.

Molar Mass Calculations

Molar mass, often referred to as molecular weight, is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule, as per the periodic table. For instance, the molar mass of silver chloride (AgCl) is calculated by adding the atomic mass of silver (Ag) and chlorine (Cl).

Knowing the molar mass is essential for converting between mass, moles, and number of particles, making it a fundamental part of stoichiometric calculations. The percentage composition of a compound, like the 75.27% silver in silver chloride, is also related to the molar mass. It provides the fraction of the total mass of a compound that comes from a particular element, which can be useful when you need to calculate the mass of individual elements within a compound.

Stoichiometric Calculations

Stoichiometric calculations are the mathematical operations used to predict the amounts of reactants or products involved in a chemical reaction. These calculations are based on the balanced chemical equation and the stoichiometric coefficients, which tell us the ratio of moles of each substance that react or are produced.

In the context of the problem set, stoichiometric calculations involve using the percentage composition to determine the required mass of silver chloride for silver plating. By setting up a proportion (step 2), and solving for the unknown mass (steps 3 and 4), we're applying stoichiometry to find the exact amount of AgCl needed. These calculations are crucial in real-world applications such as chemical manufacturing, where precise amounts of materials are necessary for product consistency and safety.