Question

Challenge A sample of silver chromate has a mass of 25.8 g. a. Write the formula for silver chromate. b. How many cations are present in the sample? c. How many anions are present in the sample? d. What is the mass in grams of one formula unit of silver chromate?

Short answer

a. The formula for silver chromate is Ag2CrO4. b. There are 9.35 × 10^22 silver cations in the sample. c. There are 4.68 × 10^22 chromate anions in the sample. d. The mass of one formula unit of silver chromate is 5.51 × 10^-22 g.

Step-by-step solution

a. Writing the formula for silver chromate

Silver chromate is an ionic compound formed by the combination of silver ions (Ag+) and chromate ions (CrO4 2-). The chemical formula can be determined by balancing the charges of the ions. Silver has a +1 charge, and chromate has a -2 charge. Therefore, we need two silver ions to balance one chromate ion. The chemical formula is Ag2CrO4.

b. Calculating the number of cations in the sample

First, we need to find the molar mass of Ag2CrO4. Using the periodic table, we find the molar mass of silver (Ag) is 107.87 g/mol, chromium (Cr) is 51.99 g/mol, and oxygen (O) is 16.00 g/mol. Next, calculate the molar mass of Ag2CrO4: Molar mass = (2 × 107.87) + 51.99 + (4 × 16.00) = 331.73 g/mol Now let's determine the number of moles in the 25.8 g sample: Moles: \(\dfrac{25.8\,\text{g}}{331.73\,\text{g/mol}}\) = 0.0777 mol In one mole of Ag2CrO4, there are 2 moles of silver cations (Ag+). Therefore, in 0.0777 moles of Ag2CrO4, there are: Cations: \(0.0777\,\text{mol} \times 2\) = 0.1554 mol To find the number of silver cations, multiply by Avogadro's number (6.022 × 10^23): Silver cations: \(0.1554\,\text{mol} \times 6.022 \times 10^{23}\,\text{particles/mol}\) = 9.35 × 10^22

c. Calculating the number of anions in the sample

In one mole of Ag2CrO4, there is one mole of chromate anion (CrO4 2-). Therefore, in 0.0777 moles of Ag2CrO4, there are: Anions: \(0.0777\,\text{mol} \times 1\) = 0.0777 mol To find the number of chromate anions, multiply by Avogadro's number (6.022 × 10^23): Chromate anions: \(0.0777\,\text{mol} \times 6.022 \times 10^{23}\,\text{particles/mol}\) = 4.68 × 10^22

d. Calculating the mass of one formula unit of silver chromate

We have already found the molar mass of Ag2CrO4 to be 331.73 g/mol. To find the mass of one formula unit, we have to divide the molar mass by Avogadro's number (6.022 × 10^23): Mass of one formula unit: \(\dfrac{331.73\,\text{g/mol}}{6.022 \times 10^{23}\,\text{particles/mol}}\) = 5.51 × 10^-22 g In summary: a. The formula for silver chromate is Ag2CrO4. b. There are 9.35 × 10^22 silver cations in the sample. c. There are 4.68 × 10^22 chromate anions in the sample. d. The mass of one formula unit of silver chromate is 5.51 × 10^-22 g.

Key concepts

Silver Chromate Formula

Silver chromate is an ionic compound. Ionic compounds are formed through the combination of positively charged ions, known as cations, and negatively charged ions, called anions. Silver chromate consists of silver ions (Ag⁺) and chromate ions (CrO₄^2-). To correctly write the chemical formula for silver chromate, we must balance the overall charge of the compound to be neutral. Silver has a +1 charge, and chromate has a -2 charge.

To balance the charges, we need two silver ions for every chromate ion. This gives us the formula: Ag₂CrO₄. The subscript in the formula indicates that there are two silver ions present with each chromate ion in the compound. This balance ensures the net charge of the compound is zero, which is a key characteristic of stable ionic compounds.

Ions in Compounds

In an ionic compound such as silver chromate, understanding the roles and calculations related to ions is crucial. Ions are atoms or molecules that have gained or lost one or more electrons, thus acquiring an electric charge. In Ag₂CrO₄, it is composed of:

• Silver ions (Ag⁺) which serve as the cations.
• Chromate ions (CrO₄^2-) which serve as the anions.

The formula Ag₂CrO₄ clearly shows the fixed ratio of ions: two silver ions for each chromate ion. Such ratios are essential to maintaining electrical neutrality in compounds.

When calculating the number of ions in a sample, understanding how many ions are present per formula unit helps in determining total quantities when provided with a sample's mass, using stoichiometry and Avogadro's number. This foundational concept is critical when engaging in quantitative chemical analysis.

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a given substance. It is typically measured in grams per mole (g/mol) and can be calculated by summing the masses of all atoms in a formula unit of a compound.

For silver chromate, Ag₂CrO₄, its molar mass can be calculated as follows:

• The atomic mass of silver (Ag) is approximately 107.87 g/mol.
• The atomic mass of chromium (Cr) is about 51.99 g/mol.
• The atomic mass of oxygen (O) is roughly 16.00 g/mol.

The compound consists of two silver atoms, one chromium atom, and four oxygen atoms. Therefore, the molar mass is calculated by:\[(2 imes 107.87) + 51.99 + (4 imes 16.00) = 331.73 \, \text{g/mol}\]

Avogadro's Number

Avogadro's number is a constant used to denote the number of particles, such as atoms, molecules, or ions, in one mole of a substance. It is \(6.022 imes 10^{23}\), a very large number that helps bridge the gap between the atomic scale and macroscopic measurements.

When calculating the number of particles in a given quantity of substance, Avogadro's number is fundamental. For instance, to find how many silver cations (Ag⁺) or chromate anions (CrO₄^2-) are present in a sample of silver chromate, you would multiply the number of moles of the specific ion by Avogadro's number. This calculation allows chemists to quantify amounts of substances in a mole-based systematic method, essential for precisely executing stoichiometric calculations.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with quantitative relationships between reactants and products in chemical reactions. It is crucial for calculating the ratios of various compounds and determining how much of each is needed or produced in a reaction.

For compounds like silver chromate (Ag₂CrO₄), stoichiometry helps chemists calculate the number of ions or molecules in a sample given its mass. Using the molar mass calculated earlier, we can convert between grams and moles, and then use Avogadro's number to convert between moles and individual ions. This involves:

• Finding the moles of a substance from its mass.
• Using the established mole ratios from the compound's formula.
• Utilizing Avogadro's number to convert moles to actual units.

These principles are fundamental for executing precise measurements and adjustments in chemical experiments.