Question

Write a balanced equation that corresponds to the following word equation for a reaction in aqueous solution: copper \(+\) silver nitrate \(\longrightarrow\) copper(II) nitrate \(+\) silver

Short answer

The balanced equation for the given chemical reaction in aqueous solution is: \(Cu + 2AgNO_3 \longrightarrow Cu(NO_3)_2 + 2Ag\)

Step-by-step solution

Write Down the Chemical Formulas

Translate the words into chemical symbols to form a chemical equation. Copper is represented by \(Cu\), Silver Nitrate by \(AgNO_3\), Copper(II) nitrate by \(Cu(NO_3)_2\) and Silver by \(Ag\). The equation, therefore, will be initially written as: \(Cu + AgNO_3 \longrightarrow Cu(NO_3)_2 + Ag\).

Balance the Chemical Equation

It's necessary to always balance a chemical equation to obey the law of conservation of mass. Compare the number of atoms for each element on the reactant and product side. Notice that the number of \(Ag\) and \(NO_3\) groups are imbalanced. Balancing the equation gives: \(Cu + 2AgNO_3 \longrightarrow Cu(NO_3)_2 + 2Ag\)

Verify the Balanced Equation

Always verify the balanced equation by making sure the number of atoms for each element are the same on both sides of the equation. Once balanced, the equation should show: one \(Cu\), two \(NO_3\), and two \(Ag\) on both sides, thus the equation is balanced.

Key concepts

Chemical Formulas

Understanding chemical formulas is the cornerstone of engaging with the world of chemistry. A chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound or molecule. It uses established standard abbreviations for the chemical elements and employs figures to indicate the number of atoms involved. For instance, in the copper and silver nitrate reaction, copper is represented by the symbol \(Cu\), while silver nitrate is denoted by \(AgNO_3\).

In this context, the appropriateness of chemical symbols and their combinations in formulas thus dictates the subsequent steps in balancing the equation. Learners should become comfortable with these symbols and numerical subscripts that indicate the quantity of atoms present in a compound. These building blocks of chemical notation are not just random codes; they carry significant meaning about the substances involved, such as the types of atoms and the ratios in which they combine.

Conservation of Mass

The principle of conservation of mass is a fundamental concept in chemistry and one that is crucial when balancing chemical equations. This principle states that in a closed system, mass is neither created nor destroyed during a chemical reaction, meaning that the mass of reactants must equal the mass of products. From this standpoint, our equation involving copper and silver nitrate must be scrutinized to ensure there is an equal number of atoms for each element on both sides.

When the initial equation, \(Cu + AgNO_3 \longrightarrow Cu(NO_3)_2 + Ag\), is assessed, it's clear that the number of silver \(Ag\) and nitrate \(NO_3\) entities are not equal on both reactant and product sides. The adjustment made to balance the number of these atoms is a direct application of the conservation of mass. By adding a coefficient of 2 before the silver nitrate, the equation is balanced, truly reflecting that matter is conserved across the reaction.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is a quantitative reflection of chemical formulas and the conservation of mass. This aspect of chemistry is essential in predicting the quantities of substances consumed and produced in a given reaction. Through stoichiometry, chemists can calculate the amounts in moles, mass, or volume, facilitating the proper scaling of reactions for practical use.

In practice, by balancing the equation \(Cu + 2AgNO_3 \longrightarrow Cu(NO_3)_2 + 2Ag\), not only are we ensuring the adherence to the principle of conservation of mass, but we are also setting the stage for stoichiometric computations. With the balanced equation, we can now accurately determine, for instance, how much silver \(Ag\) will be produced when a certain amount of silver nitrate \(AgNO_3\) reacts with copper \(Cu\). This vital part of the chemical equation balancing process extends beyond theory and into applications ranging from industrial synthesis to medication dosage calculation.