Question

A copper bar with a mass of \(12.340 \mathrm{~g}\) is dipped into \(255 \mathrm{~mL}\) of \(0.125 \mathrm{M} \mathrm{AgNO}_{3}\) solution. When the reaction that occurs has finally ceased, what will be the mass of unreacted copper in the bar? If all the silver that forms adheres to the copper bar, what will be the total mass of the bar after the reaction?

Short answer

The mass of unreacted copper will be calculated using the stoichiometry of the reaction and the molar masses of copper and silver. The total mass of the bar after the reaction will include the mass of unreacted copper plus the mass of the silver formed.

Step-by-step solution

Determine the limiting reactant

Using the provided molar concentration of silver nitrate (AgNO3), calculate the moles of AgNO3 using the volume of the solution. Assuming the reaction is \(2AgNO_3 + Cu \rightarrow 2Ag + Cu(NO_3)_2\), calculate the moles of copper needed for the reaction and identify the limiting reactant.

Calculate the moles of AgNO3

First, convert the volume of the AgNO3 solution from milliliters to liters. Using the molarity formula, \(Molarity = \frac{moles}{liters}\), calculate the moles of AgNO3.

Calculate the moles of unreacted copper

Since the reaction requires 1 mole of Cu to react with 2 moles of AgNO3, and Cu is in excess, all of the AgNO3 will be consumed. The remaining unreacted moles of Cu can be calculated by subtracting the moles of Cu that reacted from the initial moles of Cu present in the copper bar.

Calculate the mass of unreacted copper

Convert the moles of unreacted Cu back to grams using the molar mass of copper (63.546 g/mol).

Calculate the mass of formed silver

Using the stoichiometry of the reaction, calculate the moles of Ag formed from the moles of AgNO3 that reacted, and then convert these moles of Ag to grams using the molar mass of silver (107.8682 g/mol).

Calculate the total mass of the bar after the reaction

Add the mass of the unreacted copper from step 4 to the mass of the formed silver from step 5 to find the total mass of the bar after the reaction has ceased.

Key concepts

Limiting Reactant Calculation

Understanding the concept of a limiting reactant is crucial in the world of stoichiometry chemistry problems. It's similar to a recipe – if you're making sandwiches and run out of bread, it doesn't matter how much cheese or ham you have left; you can’t make more sandwiches. In chemistry, the limiting reactant is the substance that gets used up first in a chemical reaction, determining the amount of product that can be formed.

To identify the limiting reactant, you first need to know the amounts of reactants you have at the beginning. This often requires converting masses to moles, as in the exercise, we are given mass for copper and volume and concentration (which can be used to find moles) for the silver nitrate solution. After calculating moles, the next step involves using the stoichiometric coefficients from the balanced chemical equation to compare the mole ratios of the reactants. The reactant which does not provide enough moles to react with the other is the limiting reactant.

Molar Mass Conversion

One of the most fundamental skills in stoichiometry is converting between mass and moles using molar mass as the conversion factor. The molar mass of a substance, expressed in grams per mole (g/mol), is numerically equivalent to its atomic or molecular weight. For instance, copper has a molar mass of 63.546 g/mol.

To convert from mass to moles, you divide the mass of the sample by the molar mass of the substance. Conversely, to find the mass from the number of moles, you multiply the moles by the molar mass. In the context of our example, we would convert the mass of copper to moles by dividing by its molar mass. Additionally, to convert the moles of Ag formed to grams, multiply by the molar mass of Ag. This step is crucial for solving many stoichiometric problems, as it allows the comparison of quantities of different substances involved in a chemical reaction.

Stoichiometric Calculations

Stoichiometric calculations are the bread and butter of chemical equations. They involve using the stoichiometric coefficients from balanced equations to relate moles of reactants to moils of products. For every chemical process, the ratios of reactants and products are dictated by these coefficients, allowing chemists to predict the amounts of substances produced or consumed in a reaction.

In the exercise provided, the balanced chemical reaction shows that one mole of copper reacts with two moles of silver nitrate to produce copper(II) nitrate and silver. To calculate the mass of unreacted copper, or the mass of silver formed, we use stoichiometry to relate the quantities. By understanding these ratios, we determine not only how much reactant is needed for a reaction but also the maximum amount of product that can be formed - a concept that directly stems from the idea of the limiting reactant. With these core stoichiometric concepts, a deeper and computational understanding of chemical reactions can be fully grasped.