Problem 2
Question
If we can find the ratio of the number of moles of the elements in a compound to one another. we can find the formula of the compound. In a certain compound of copper and oxygen, \(\mathrm{Cu}_{x} \mathrm{O}_{y},\) we find that a sample weighing 0.9573 g contains 0.8503 g Cu. a. How many moles of Cu are there in the sample? $$\text { (Moles of }\left.\mathrm{Cu}=\frac{\text { mass of } \mathrm{Cu}}{\text { molar mass of } \mathrm{Cu}}\right)$$ b. How many grams of O are there in the sample? (The mass of the sample cquals the mass of Cu plus the mass of O.) c. How many moles of \(\mathrm{O}\) are there in the sample? d. What is the mole ratio (moles of Cu/moles of \(\mathbf{O}\) ) in the sample? 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?
Step-by-Step Solution
Verified Answer
The empirical formula is \( \text{Cu}_2\text{O} \), and its molar mass is 143.10 g/mol.
1Step 1: Calculate Moles of Cu
To find the moles of copper (Cu), use the formula \( \text{moles of Cu} = \frac{\text{mass of Cu}}{\text{molar mass of Cu}} \). The mass of Cu is 0.8503 g, and the molar mass of Cu is 63.55 g/mol. Thus, the moles of Cu = \( \frac{0.8503\, \text{g}}{63.55\, \text{g/mol}} \approx 0.01338 \) moles.
2Step 2: Calculate Mass of O
The mass of oxygen (O) in the compound can be calculated by subtracting the mass of copper from the total mass of the sample. So, mass of O = 0.9573 g (total mass) - 0.8503 g (mass of Cu) = 0.1070 g.
3Step 3: Calculate Moles of O
To find the moles of oxygen (O), use the formula \( \text{moles of O} = \frac{\text{mass of O}}{\text{molar mass of O}} \). The mass of O is 0.1070 g, and the molar mass of O is 16.00 g/mol. Thus, the moles of O = \( \frac{0.1070\, \text{g}}{16.00\, \text{g/mol}} \approx 0.00669 \) moles.
4Step 4: Calculate Mole Ratio Cu:O
To find the mole ratio of Cu to O, divide the moles of Cu by the moles of O: \( \text{Mole Ratio (Cu:O)} = \frac{0.01338 \text{ moles of Cu}}{0.00669 \text{ moles of O}} \approx 2:1 \).
5Step 5: Determine the Empirical Formula
The empirical formula is based on the smallest whole number ratio of moles of each element. Since the ratio of Cu to O is approximately 2:1, the empirical formula for the oxide of copper is \( \text{Cu}_2\text{O} \).
6Step 6: Calculate the Molar Mass of Cu2O
The molar mass of copper(I) oxide (\( \text{Cu}_2\text{O} \)) is calculated by adding twice the molar mass of copper to the molar mass of oxygen: \[ \text{Molar Mass of } \text{Cu}_2\text{O} = 2 \times 63.55 \text{ g/mol} + 16.00 \text{ g/mol} = 143.10 \text{ g/mol} \].
Key Concepts
Mole CalculationCopper OxideMolar Mass CalculationElemental Analysis
Mole Calculation
Understanding moles is crucial in chemistry as it acts as a bridge between the microscopic world of atoms and the macroscopic world we observe. The mole is a standard unit of measurement in chemistry that allows us to count atoms or molecules. One mole represents Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles. To perform a mole calculation, you need the mass of the element and its molar mass. The molar mass is the mass of one mole of a substance and is typically expressed in grams per mole (g/mol).
To find the number of moles, use the formula:
In our exercise, we calculated the moles of copper (Cu) by dividing its mass (0.8503 g) by its molar mass (63.55 g/mol), resulting in approximately 0.01338 moles. This calculation is essential for determining the composition of the compound.
To find the number of moles, use the formula:
- \( ext{Moles} = \frac{\text{Mass of Substance (g)}}{\text{Molar Mass (g/mol)}} \)
In our exercise, we calculated the moles of copper (Cu) by dividing its mass (0.8503 g) by its molar mass (63.55 g/mol), resulting in approximately 0.01338 moles. This calculation is essential for determining the composition of the compound.
Copper Oxide
Copper oxide is a compound formed by the chemical combination of copper and oxygen. In chemistry, oxides are compounds that contain at least one oxygen atom bonded to another element. Copper can form multiple oxides, with copper(I) oxide (\( \text{Cu}_2\text{O} \)) being one of the simplest forms.
Copper oxide exhibits various physical and chemical properties.
In the provided exercise, we determine the empirical formula of copper oxide from the ratios of copper and oxygen in the sample. Calculating these ratios helps confirm whether the sample is indeed \( \text{Cu}_2\text{O} \) or another form of copper oxide.
Copper oxide exhibits various physical and chemical properties.
- It is often used in catalysis or as a pigment due to its distinctive color.
- Understanding the composition of copper oxide helps in various applications, including electrical conductivity and material science.
In the provided exercise, we determine the empirical formula of copper oxide from the ratios of copper and oxygen in the sample. Calculating these ratios helps confirm whether the sample is indeed \( \text{Cu}_2\text{O} \) or another form of copper oxide.
Molar Mass Calculation
Molar mass calculation is vital to convert the mass of a substance into moles. To determine the molar mass, sum up the atomic masses of all atoms present in the compound's formula. This process helps predict how substances will react chemically, based on their weights.
The step-by-step approach for calculating molar mass includes:
For copper(I) oxide (\( \text{Cu}_2\text{O} \)), the molar mass is calculated as:
This conversion is critical to understand reaction stoichiometry and the molecular weight of compounds involved.
The step-by-step approach for calculating molar mass includes:
- Identifying and adding the atomic masses of all elements in the compound.
- Using a periodic table for accurate atomic mass values.
For copper(I) oxide (\( \text{Cu}_2\text{O} \)), the molar mass is calculated as:
- Twice the molar mass of copper (2 \( \times 63.55 \text{ g/mol} \)) plus the molar mass of oxygen (16.00 g/mol), totaling 143.10 g/mol.
This conversion is critical to understand reaction stoichiometry and the molecular weight of compounds involved.
Elemental Analysis
Elemental analysis is a technique used to determine the elemental composition of a compound. By analyzing the quantities of each element, we can deduce the empirical formula of the compound. This process can provide precise information about the elements present and their ratios to each other.
Steps of an elemental analysis include:
This integer ratio assists in determining the empirical formula. In our example, after calculating the moles of copper and oxygen, we found a ratio of approximately 2:1. Thus, allowing us to conclude that the empirical formula of the sample is \( \text{Cu}_2\text{O} \). Elemental analysis is a fundamental method in analytical chemistry for understanding compound structures and verifying the composition of unknown substances.
Steps of an elemental analysis include:
- Measuring the mass of each element in a sample.
- Converting these masses to moles using their respective molar masses.
- Determining the simplest integer ratio of moles of each element.
This integer ratio assists in determining the empirical formula. In our example, after calculating the moles of copper and oxygen, we found a ratio of approximately 2:1. Thus, allowing us to conclude that the empirical formula of the sample is \( \text{Cu}_2\text{O} \). Elemental analysis is a fundamental method in analytical chemistry for understanding compound structures and verifying the composition of unknown substances.