Problem 125 - Chemistry Matter and Change

Question

A single-replacement reaction occurs between copper and silver nitrate. When 63.5 g of copper reacts with 339.8 g of silver nitrate, 215.8 g of silver is produced. Write a balanced chemical equation for this reaction. What other product formed? What is the mass of the second product?

Step-by-Step Solution

Answer

The balanced chemical equation for the single-replacement reaction between copper and silver nitrate is: Cu + 2AgNO3 -> Cu(NO3)2 + 2Ag The other product formed in the reaction is copper nitrate (Cu(NO3)2), and its mass is 187.56 g.

Step 1: Write the unbalanced chemical equation

We are given that the single-replacement reaction occurs between copper (Cu) and silver nitrate (AgNO3). The typical single-replacement reactions follow this pattern: A + BC -> AC + B. In this case, copper replaces silver in the silver nitrate compound. This gives us the following unbalanced chemical equation: Cu + AgNO3 -> Cu(NO3)2 + Ag

Step 2: Balance the chemical equation

Now we need to balance the chemical equation so that there are the same number of atoms of each element on both sides. The balanced chemical equation is: Cu + 2AgNO3 -> Cu(NO3)2 + 2Ag

Step 3: Determine the other product formed

We now have the balanced chemical equation: Cu + 2AgNO3 -> Cu(NO3)2 + 2Ag The product that is not silver is copper nitrate (Cu(NO3)2). This is the other product formed in the reaction.

Step 4: Calculate the mass of the second product

We are given that 63.5 g of copper reacts with 339.8 g of silver nitrate, and 215.8 g of silver is produced. We can use stoichiometry to find the mass of the second product, copper nitrate (Cu(NO3)2). First, we will convert the given masses to moles using the molar mass of each substance: Molar mass of Cu = 63.55 g/mol Molar mass of AgNO3 = 169.88 g/mol Molar mass of Ag = 107.87 g/mol Moles of Cu = mass of Cu / molar mass of Cu = 63.5 g / 63.55 g/mol = 1 mol Moles of AgNO3 = mass of AgNO3 / molar mass of AgNO3 = 339.8 g / 169.88 g/mol = 2 mol Moles of Ag = mass of Ag / molar mass of Ag = 215.8 g / 107.87 g/mol = 2 mol From the balanced chemical equation, we can see that 1 mole of Cu reacts with 2 moles of AgNO3 to produce 1 mole of Cu(NO3)2 and 2 moles of Ag. Since we have 1 mole of Cu reacting, we can conclude that 1 mole of Cu(NO3)2 is produced. Now, we can convert the moles of Cu(NO3)2 to mass using its molar mass: Molar mass of Cu(NO3)2 = 187.56 g/mol Mass of Cu(NO3)2 = moles of Cu(NO3)2 x molar mass of Cu(NO3)2 Mass of Cu(NO3)2 = 1 mol x 187.56 g/mol = 187.56 g The mass of the second product, copper nitrate (Cu(NO3)2), is 187.56 g.

Key Concepts

Chemical Equations

In the study of chemistry, a chemical equation is a symbolic representation of a chemical reaction, where reactants are transformed into products. The copper and silver nitrate reaction discussed in the single-replacement problem is depicted by a balanced chemical equation to ensure that the law of conservation of mass is honored, meaning that atoms are neither created nor destroyed in the reaction.

The balancing act involves making sure that there are an equal number of each type of atom on both the reactant and product sides. For instance, the balanced equation for the reaction between copper and silver nitrate is:
\[ \text{Cu} + 2\text{AgNO}_3 \rightarrow \text{Cu(NO}_3\text{)}_2 + 2\text{Ag} \]
This equation indicates that one copper atom reacts with two silver nitrate molecules to produce one copper nitrate molecule and two silver atoms. Always ensure that coefficients in front of the compounds and elements reflect the stoichiometry necessary to balance the atoms. Mastering the art of balancing chemical equations is essential for further understanding chemical reactions and stoichiometry.

Stoichiometry

Moving on to stoichiometry, this branch of chemistry concerns the calculation of reactants and products in chemical reactions. An intimate understanding of stoichiometry allows us to predict the amounts of substances consumed and produced in a reaction.

In the case of our copper and silver nitrate reaction, stoichiometry involves utilizing the balanced chemical equation to deduce the proportion of reactants to products. Since the balanced equation tells us that one mole of copper reacts with two moles of silver nitrate to produce two moles of silver and one mole of copper nitrate, we can determine the exact amount of each substance involved in the reaction.

For example, if 63.5 grams of copper reacts, the stoichiometry of the reaction allows us to calculate the resultant mass of copper nitrate that forms. Proper use of stoichiometry takes into account the molar mass of the reactants and products, and employs dimensional analysis to convert between grams and moles, ensuring accurate predictions of chemical quantities.

Molar Mass

Lastly, the concept of molar mass is a cornerstone in solving stoichiometry problems. The molar mass is the weight of one mole (6.022 x 10²³ particles) of a given substance and its unit is grams per mole (g/mol). It's crucial when converting the mass of substances to moles and vice versa, as seen in our reaction.

For instance, to compute the mass of the second product, copper nitrate, we first need its molar mass which is 187.56 g/mol. Knowing that one mole of copper nitrate forms from the reaction (according to the balanced chemical equation), we can determine its mass by multiplying the number of moles by the molar mass:
\[ \text{Mass of Cu(NO}_3\text{)}_2 = 1 \text{ mol} \times 187.56 \text{ g/mol} = 187.56 \text{ g} \]
Knowing how to calculate molar mass is imperative, as it connects the mass of a substance to its amount in moles, thus bridging the gap between the macroscopic and microscopic worlds of chemistry. Understanding molar mass empowers students to accurately calculate quantities necessary for chemical reactions and to elucidate the intricate relationships between reactants and products.