Problem 2 - Chemical Principles in the Laboratory

Question

If one can find the ratio of the number of moles of the elements in a compound to one another, one can find the formula of the compound. In a certain compound of copper and oxygen, \(\mathrm{Cu}_{x}\) o, we find that a sample weighing 0.6349 g contains 0.5639 g Cu. a. How many moles of Cu are there in the sample? $$\left(\text {No. moles} =\frac{\text { mass Cu }}{\text { molar mass } \mathrm{Cu}}\right)$$ ______________ moles b. How many grams of O are there in the sample? (The mass of the sample equals the mass of Cu plus the mass of O.) ______________ g c. How many moles of O are there in the sample? ______________ moles d. What is the mole ratio (no. moles Cu/no. moles O) in the sample? ______________ : 1 e. What is the formula of the oxide? (The atom ratio equals the mole ratio, and is expressed using the smallest integers possible.) ______________ f. What is the molar mass of the copper oxide? ______________ g/mol

Step-by-Step Solution

Answer

a. 0.00887 moles Cu; b. 0.0710 g O; c. 0.00444 moles O; d. 2:1; e. Cu extsubscript{2}O; f. 143.10 g/mol.

Step 1: Calculate Moles of Cu

First, we need to determine the number of moles of copper (Cu) in the sample. We are given the mass of Cu as 0.5639 g. Using the molar mass of Cu, which is approximately 63.55 g/mol, we use the formula: \[ \text{No. moles of Cu} = \frac{\text{Mass of Cu}}{\text{Molar mass of Cu}} = \frac{0.5639 \, \text{g}}{63.55 \, \text{g/mol}} \approx 0.00887 \, \text{moles}. \]

Step 2: Calculate Mass of Oxygen

Now, calculate the mass of oxygen (O) in the sample. The total mass of the sample is 0.6349 g, composed of Cu and O. Therefore, the mass of O is: \[ \text{Mass of O} = \text{Total mass} - \text{Mass of Cu} = 0.6349 \, \text{g} - 0.5639 \, \text{g} = 0.0710 \, \text{g}. \]

Step 3: Calculate Moles of O

Next, we'll find the moles of oxygen. The molar mass of oxygen (as an atom) is approximately 16.00 g/mol. The number of moles is calculated by: \[ \text{No. moles of O} = \frac{\text{Mass of O}}{\text{Molar mass of O}} = \frac{0.0710 \, \text{g}}{16.00 \, \text{g/mol}} \approx 0.00444 \, \text{moles}. \]

Step 4: Determine Mole Ratio of Cu and O

Now, we need to find the mole ratio of Cu to O. This is calculated as: \[ \text{Mole Ratio} = \frac{\text{No. moles of Cu}}{\text{No. moles of O}} = \frac{0.00887}{0.00444} \approx 2.00. \] Thus, the mole ratio of Cu to O is approximately 2:1.

Step 5: Determine the Empirical Formula

Based on the mole ratio calculated, the empirical formula for the compound, which reflects the simplest whole-number ratio, is Cu extsubscript{2}O. This represents two moles of copper for every mole of oxygen.

Step 6: Calculate Molar Mass of Copper Oxide

Finally, we calculate the molar mass of the compound Cu extsubscript{2}O. Since there are 2 moles of Cu and 1 mole of O in the formula: \[ \text{Molar Mass of Cu extsubscript{2}O} = (2 \times 63.55) + (1 \times 16.00) = 127.10 + 16.00 = 143.10 \, \text{g/mol}. \]

Key Concepts

Molar Mass Calculations

When dealing with chemical compounds, understanding the concept of molar mass is essential. Molar mass is the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol). It helps us convert between the mass of a substance and the number of moles, a crucial operation in chemistry known as "mole conversion." The periodic table provides us with the atomic masses of elements, which are used to calculate the molar mass of compounds.

In our example, we needed to determine the moles of copper (Cu) in a given sample. First, we identified that the molar mass of Cu is approximately 63.55 g/mol. Using this information, we can calculate the number of moles by dividing the mass of Cu in the sample (0.5639 g) by its molar mass:

• Number of moles of Cu = \( \frac{0.5639 \, \text{g}}{63.55 \, \text{g/mol}} \approx 0.00887 \, \text{moles} \).

This calculation is the first step towards finding the composition of the compound.

Mole Concept

The mole is a fundamental concept in chemistry that helps us quantify substances based on the number of atoms, molecules, or formula units. One mole is defined as exactly \(6.022 \times 10^{23}\) entities, also known as Avogadro's number. This allows scientists to relate microscopic quantities, like atoms and molecules, to macroscopic amounts that we can measure and handle in labs.

In our example, after finding the moles of copper, we also determined the moles of oxygen in the compound. The mass of oxygen was found to be 0.0710 g. The molar mass of oxygen is approximately 16.00 g/mol, enabling us to calculate the moles of oxygen:

• Number of moles of O = \( \frac{0.0710 \, \text{g}}{16.00 \, \text{g/mol}} \approx 0.00444 \, \text{moles} \).

Having moles calculated for both copper and oxygen allows us to understand their relative quantities in the compound, establishing their stoichiometric relationship.

Chemical Stoichiometry

Chemical stoichiometry involves using the quantitative relationships among substances as they participate in chemical reactions and form compounds. This is based on the law of conservation of mass, meaning the mass of reactants equals the mass of products.

In practice, stoichiometry helps us determine how much of each element is present in a compound by using mole ratios derived from empirical formulas. For our copper oxide compound, we found the mole ratio of copper to oxygen by dividing the number of moles of copper by the number of moles of oxygen:

• Mole Ratio = \( \frac{0.00887}{0.00444} \approx 2.00 \).

This indicates for every 2 moles of Cu, there is 1 mole of O, giving the empirical formula Cu₂O. Stoichiometry also allowed us to calculate the molar mass of the compound, which is essential for understanding its composition and reactivity in further chemical interactions. The molar mass calculated for Cu₂O was 143.10 g/mol, reflecting its molecular structure.