Problem 36 - Chemistry The Central Science

Question

Calculate the following quantities: $$ \begin{array}{l}{\text { (a) mass, in grams, of } 1.50 \times 10^{-2} \text { mol CdS }} \\ {\text { (b) number of moles of } \mathrm{NH}_{4} \mathrm{Cl} \text { in } 86.6 \mathrm{g} \text { of this substance }} \\ {\text { (c) number of molecules in } 8.447 \times 10^{-2} \mathrm{mol} \mathrm{C}_{6} \mathrm{H}_{6}} \\ {\text { (d) number of } \mathrm{O} \text { atoms in } 6.25 \times 10^{-3} \mathrm{mol} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}}\end{array} $$

Step-by-Step Solution

Answer

The short answer for this question is as follows: (a) The mass of 1.50x10^{-2} mol CdS is 2.1712 g. (b) The number of moles of NH4Cl in 86.6 g is 1.00029 mol. (c) The number of molecules in 8.447x10^{-2} mol C6H6 is 5.081x10^{22} molecules. (d) The number of O atoms in 6.25x10^{-3} mol Al(NO3)3 is 3.387x10^{22} O atoms.

Step 1: Find the molar mass of CdS

To find the mass of CdS, we first need to find the molar mass of CdS. The molar mass of an element is the mass of one mole of that substance, expressed in grams per mole. The molar mass of CdS can be calculated by adding the molar mass of Cd (cadmium) with the molar mass of S (sulfur). Molar mass of cd=112.41g/mol and S=32.07g/mol

Step 2: Calculate the mass of CdS

Now that we have the molar mass, we can calculate the mass by using the given moles. Use this formula: mass = moles x molar_mass Mass = 1.5x10^{-2} mol CdS * (112.41g/mol + 32.07g/mol) = 2.1712 g Part (b) - Number of moles of NH4Cl in 86.6 g

Step 3: Find the molar mass of NH4Cl

We need to find the molar mass of NH4Cl. The molar mass of NH4Cl can be calculated by adding the molar masses of N (nitrogen), H (hydrogen) x 4, and Cl (chlorine). Molar mass of NH4Cl = 14.01g/mol + 1.01g/mol * 4 + 35.45g/mol

Step 4: Calculate the number of moles of NH4Cl

Now that we have the molar mass, use the formula: moles = mass / molar_mass Moles = 86.6 g / (14.01g/mol + 1.01g/mol * 4 + 35.45g/mol) = 1.00029 mol NH4Cl Part (c) - Number of molecules in 8.447x10^{-2} mol C6H6

Step 5: Use Avogadro's number to find the number of molecules

We are given the moles, and now we want to find the number of molecules. To do this, we will use Avogadro's number, which is 6.022x10^{23} molecules/mol. Then, use this formula: molecules = moles * Avogadro's_number Molecules = 8.447x10^{-2} mol C6H6 * 6.022x10^{23} molecules/mol = 5.081x10^{22} molecules C6H6 Part (d) - Number of O atoms in 6.25x10^{-3} mol Al(NO3)3

Step 6: Determine the moles of O atoms

In each molecule of Al(NO3)3, there are three nitrate ions, and each nitrate ion (NO3) has one oxygen atom. Therefore, there are three oxygen atoms for each molecule of Al(NO3)3. To find the moles of oxygen atoms in 6.25x10^{-3} mol Al(NO3)3, use this formula: moles_O = (moles_Al(NO3)3) * (number of oxygen atoms per molecule) Moles_O = 6.25x10^{-3} mol Al(NO3)3 * 3 * 3 = 0.05625 mol O

Step 7: Calculate the number of O atoms

Now that we have the moles of oxygen atoms, use Avogadro's number again to find the number of O_atoms: O_atoms = moles_O * Avogadro's_number O_atoms = 0.05625 mol O * 6.022x10^{23} molecules/mol = 3.387x10^{22} O atoms

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry. It tells us the mass of one mole of a substance in grams per mole (g/mol). To calculate it, we add up the molar mass of all the elements present in a substance. For instance, Cadmium Sulfide (CdS) has two elements: cadmium and sulfur. The molar mass is found by adding the molar mass of Cadmium (112.41 g/mol) and Sulfur (32.07 g/mol), giving CdS a molar mass of 144.48 g/mol. This allows us to calculate the mass of a substance when given the number of moles.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry. It's the number of particles in one mole of a substance, which equals approximately \(6.022 \times 10^{23}\). This constant helps us convert between moles and the number of atoms, ions, or molecules. For example, if you have 0.08447 moles of benzene (C₆H₆), you multiply by Avogadro's number to find the number of molecules: \(0.08447\, \text{mol} \times 6.022 \times 10^{23}\, \text{molecules/mol} = 5.081 \times 10^{22}\) molecules of C₆H₆. Using Avogadro's number provides a link between the microscopic and macroscopic worlds.

Chemical Formula Analysis

Analyzing a chemical formula is crucial to understanding the composition and reactions of compounds. Chemical formulas tell us the types and numbers of atoms in a molecule. For instance, Aluminum nitrate is represented as Al(NO₃)₃, indicating one aluminum atom and three nitrate ions. Each nitrate ion (NO₃) contains three oxygen atoms. So, in Al(NO₃)₃, there are a total of nine oxygen atoms. When calculating the number of specific atoms in a sample, it's vital to understand the structure of the compound through its chemical formula. This allows us to calculate precise quantities, such as the number of oxygen atoms in a given number of moles of Al(NO₃)₃.