Problem 2
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, \(\mathrm{Cu}_{x} \mathrm{O}_{y},\) we find that a sample weighing \(0.5424 \mathrm{g}\) contains \(0.4831 \mathrm{g} \mathrm{Cu}\). a. How many moles of Cu are there in the sample? $$\text { (No. moles }\left.=\frac{\text { mass } \mathrm{Cu}}{\text { molar mass } \mathrm{Cu}}\right)$$ ________ 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 \(\mathrm{O}\) ) 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? _______ \(g\)
Step-by-Step Solution
Verified Answer
a. The number of moles of Cu in the sample is \(=\frac{0.4831\,\mathrm{g}}{63.55\,\mathrm{g/mol}}=0.0076\,\text{moles}\).
b. The mass of O in the sample is \(0.5424\,\mathrm{g} - 0.4831\,\mathrm{g}=0.0593\,\mathrm{g}\).
c. The number of moles of O in the sample is \(=\frac{0.0593\,\mathrm{g}}{16.00\,\mathrm{g/mol}}=0.0037\,\text{moles}\).
d. The mole ratio of Cu and O in the sample is \(\frac{0.0076}{0.0037}=2:1\).
e. The formula of the copper oxide is \(\mathrm{Cu}_2 \mathrm{O}\).
f. The molar mass of the copper oxide is \(2\times63.55\,\mathrm{g/mol} + 1\times16.00\,\mathrm{g/mol}=143.10\,\mathrm{g/mol}\).
1Step 1: Calculate moles of Cu
Since the mass of copper (Cu) in the sample is given, to find the number of moles of Cu, use the formula:
Number of moles \(= \frac{\text{mass of Cu}}{\text{molar mass of Cu}}\)
The molar mass of Cu is 63.55 g/mol. Therefore, the number of moles of Cu in the sample is:
\(\text{no. of moles of Cu } = \frac{0.4831 \,\mathrm{g}}{63.55 \,\mathrm{g/mol}}\).
2Step 2: Calculate mass of O in the sample
The mass of the sample is the sum of the mass of copper (Cu) and the mass of oxygen (O). So, the mass of O in the sample can be calculated as:
Mass of O \(= \text{mass of sample} - \text{mass of Cu}\)
\(= 0.5424 \,\mathrm{g} - 0.4831 \,\mathrm{g}\).
3Step 3: Calculate moles of O in the sample
To find the number of moles of O in the sample, use the formula:
Number of moles \(= \frac{\text{mass of O}}{\text{molar mass of O}}\)
The molar mass of O is 16.00 g/mol. Therefore, the number of moles of O in the sample is:
\(\text{no. of moles of O } = \frac{\text{mass of O}}{16.00 \,\mathrm{g/mol}}\).
4Step 4: Determine mole ratio of Cu and O
The mole ratio of copper and oxygen in the compound can be found by dividing the number of moles of Cu by the number of moles of O:
\(\text{mole ratio} = \frac{\text{no. of moles of Cu}}{\text{no. of moles of O}}\).
5Step 5: Determine the formula of the oxide
The atom ratio equals the mole ratio and is expressed using the smallest integers possible. Therefore, you can write the formula of the oxide by simply expressing the ratio in the form:
\(\mathrm{Cu}_x \mathrm{O}_y\).
6Step 6: Calculate the molar mass of the copper oxide
To find the molar mass of the copper oxide, multiply the number of atoms of each element in the compound by their respective molar masses and sum them up:
\(\text{molar mass of Cu}_x \mathrm{O}_y = x \times \text{molar mass of Cu} + y \times \text{molar mass of O}\).
Key Concepts
Mole ConceptMolar Mass CalculationElemental AnalysisChemical Stoichiometry
Mole Concept
The mole concept is a fundamental idea in chemistry that helps us quantify the amount of a substance. One mole of a substance contains Avogadro's number of entities (like atoms, molecules, or ions), which is approximately \(6.022 \times 10^{23}\). This allows chemists to count particles by weighing them. In this exercise, we are determining the moles of copper (Cu) and oxygen (O) present in a sample of copper oxide. We start with the mass of Cu, given as \(0.4831 \, \text{g}\), and convert this mass into moles using the molar mass of Cu.
Molar Mass Calculation
Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). For elements, it is basically the atomic weight listed on the periodic table, expressed in g/mol. For example, copper (Cu) has a molar mass of \(63.55 \, \text{g/mol}\), while oxygen (O) has a molar mass of \(16.00 \, \text{g/mol}\).
To calculate the number of moles, you can use the formula:
\[\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}\]
In our case, to find the moles of Cu, we use:
\[\text{no. of moles of Cu} = \frac{0.4831 \, \text{g}}{63.55 \, \text{g/mol}}\]
To calculate the number of moles, you can use the formula:
\[\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}\]
In our case, to find the moles of Cu, we use:
\[\text{no. of moles of Cu} = \frac{0.4831 \, \text{g}}{63.55 \, \text{g/mol}}\]
Elemental Analysis
Elemental analysis involves determining the specific elements present in a compound and their relative amounts. In the copper oxide exercise, we know the total mass of the sample and the individual mass of copper. By subtracting the mass of copper from the total sample mass, we deduce the mass of oxygen in the compound.
The calculation is as follows:
This step allows us to carry forward into the calculation of moles, using the known molar mass of oxygen.
The calculation is as follows:
- Total mass of the sample: \(0.5424 \, \text{g}\)
- Mass of Cu: \(0.4831 \, \text{g}\)
- Mass of O: \(0.5424 - 0.4831 = 0.0593 \, \text{g}\)
This step allows us to carry forward into the calculation of moles, using the known molar mass of oxygen.
Chemical Stoichiometry
Chemical stoichiometry is concerned with the quantitative relationships between reactants and products in a chemical reaction. Here, it involves finding the mole ratio between Cu and O in the copper oxide compound. This ratio tells us the simplest whole number ratio of atoms in the compound, reflecting the chemical formula.
Steps involved:
The mole ratio serves as the basis to write the compound's chemical formula, such as \(\text{Cu}_x\text{O}_y\), where "x" and "y" are the smallest integers derived from the mole ratio.
Steps involved:
- Calculate moles of Cu and O using their respective masses and molar masses.
- Determine the mole ratio, \(\text{mole ratio} = \frac{\text{moles of Cu}}{\text{moles of O}}\).
- The smallest whole numbers representing the mole ratio give the empirical formula of the compound.
The mole ratio serves as the basis to write the compound's chemical formula, such as \(\text{Cu}_x\text{O}_y\), where "x" and "y" are the smallest integers derived from the mole ratio.