A compound of silver has the following analytical composition: \(63.50 \% \mathrm{Ag}, 8.25 \%\) \(\mathrm{N},\) and 28.25\(\%\) O. Calculate the empirical formula.

Short Answer

Expert verified
The empirical formula for the silver compound is \(AgNO_3\).

Step by step solution

01

Convert percentage to grams

The compound is composed of 63.50% Ag, 8.25% N and 28.25% O. As a starting point, assume the total compound weighs 100 grams, therefore the weight of each element would be: Ag - 63.5 grams, N - 8.25 grams, O - 28.25 grams.
02

Convert grams to moles

Convert these weights into moles using the molecular weights of each element (Ag - \(107.87 \, g/mol\), N - \(14.01 \, g/mol\), O - \(16.00 \, g/mol\)). Therefore, the number of moles of each element are: Ag - \(63.5 \, g\) / \(107.87 \, g/mol\) = \(0.588 \, mol\), N - \(8.25 \, g\) / \(14.01 \, g/mol\) = \(0.588 \, mol\), O - \(28.25 \, g\) / \(16.00 \, g/mol\) = \(1.766 \, mol\).
03

Determine the simplest mole ratio

In order to find the simplest whole number mole ratio, divide the number of moles of each element by the smallest value, which is \(0.588 \, mol\). Thus, the mole ratios are: Ag - \(0.588/0.588 = 1\), N - \(0.588/0.588 = 1\), O - \(1.766/0.588 = 3\). The smallest whole number ratio of Ag, N, and O in the compound is 1:1:3 respectively.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mole Concept
The mole concept is a fundamental principle in chemistry that helps us understand the relationship between mass and the number of particles in a substance. A mole is defined as the amount of substance that contains the same number of particles (usually atoms or molecules) as there are atoms in 12 grams of pure carbon-12. This number is known as Avogadro's number, which is approximately \(6.02 \times 10^{23}\) particles.

The mole concept allows us to calculate the number of entities in a bulk quantity of material through a process called stoichiometry. By converting grams of elements to moles, we can find out how many moles of each element are present in a given sample. This conversion is done using the formula:
\[\text{number of moles} = \frac{\text{mass in grams}}{\text{molar mass}}\]
This formula is used in our exercise to convert the mass of silver (Ag), nitrogen (N), and oxygen (O) to moles for further analysis to determine the empirical formula of the compound.
Chemical Compound Composition
Understanding a chemical compound's composition involves identifying the elements present and their relative proportions. The empirical formula of a compound is the simplest positive integer ratio of atoms present in a compound. Unlike the molecular formula, the empirical formula does not tell us the exact number of atoms but gives us the simplest ratio reflecting the relative numbers of each type of atom.

For example, glucose has a molecular formula of \(C_6H_{12}O_6\), but its empirical formula is CH2O, indicating that for every carbon atom, there are two hydrogen atoms and one oxygen atom. To determine an empirical formula, one must:
  • Convert the percentage composition to mass.
  • Convert the mass to moles.
  • Determine the simplest whole-number ratio of moles of each element.

In the exercise provided, we use these steps to find that the empirical formula for the silver compound consists of one atom of silver, one atom of nitrogen, and three atoms of oxygen, or AgNO3.
Molar Mass
Molar mass is a property of a chemical substance that is defined as the mass of a sample of that substance divided by the amount of substance in moles. It is expressed in units of grams per mole \(g/mol\). Every element has a distinct molar mass, which can be found on the periodic table and is critical for converting between grams and moles.

In the context of the textbook exercise, we use the molar mass of silver (Ag), which is \(107.87 \, g/mol\), of nitrogen (N), which is \(14.01 \, g/mol\), and of oxygen (O), which is \(16.00 \, g/mol\), to convert the mass of these elements into moles. The molar mass serves as the conversion factor in the formula mentioned in the mole concept section. Since the molar mass of each element is consistent, it allows for precise and universally applicable calculations across various chemical reactions and processes.

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