Problem 1
Question
Suppose the \(\mathrm{Cu}^{2+}\) ions in this experiment are produced by the reaction of \(1.06 \mathrm{g}\) of copper turnings with excess nitric acid. How many moles of \(\mathrm{Cu}^{2+}\) are produced? _____________mol
Step-by-Step Solution
Verified Answer
0.0167 mol of \(\mathrm{Cu}^{2+}\) are produced.
1Step 1: Find the Molar Mass of Copper
Copper (Cu) has an atomic mass of approximately 63.55 g/mol. To convert grams of copper to moles, you need to know its molar mass.
2Step 2: Use the Molar Mass to Convert Grams to Moles
The number of moles of copper is calculated by dividing the mass of copper by its molar mass:\[ \text{moles of Cu} = \frac{1.06 \, \text{g}}{63.55 \, \text{g/mol}} \]
3Step 3: Perform the Calculation
Substitute the values and calculate:\[ \text{moles of Cu} = \frac{1.06}{63.55} \approx 0.0167 \, \text{mol} \]
4Step 4: Determine Moles of Cu^{2+} Ions
Since each copper atom forms one \(\text{Cu}^{2+}\) ion, the number of moles of \(\text{Cu}^{2+}\) ions is equal to the number of moles of copper moles present, which is approximately 0.0167 mol.
Key Concepts
Molar MassMole ConceptChemical Reactions
Molar Mass
Understanding molar mass is key to solving many chemistry problems. Molar mass refers to the mass of one mole of a substance and is expressed in grams per mole (g/mol). For elements, the molar mass can be found on the periodic table as the atomic weight. In our exercise, the molar mass of copper is 63.55 g/mol. This means that one mole of copper atoms weighs 63.55 grams.
To convert between grams and moles, you'd use the molar mass as a conversion factor. For example, given 1.06 grams of copper, you divide by its molar mass (63.55 g/mol) to find the number of moles:
\[ \text{moles of Cu} = \frac{1.06 \text{ g}}{63.55 \text{ g/mol}} \approx 0.0167 \text{ mol} \]
Understanding this calculation helps in predicting how much of a substance you have. It's the relationship between the mass of the sample and the number of particles it contains.
To convert between grams and moles, you'd use the molar mass as a conversion factor. For example, given 1.06 grams of copper, you divide by its molar mass (63.55 g/mol) to find the number of moles:
\[ \text{moles of Cu} = \frac{1.06 \text{ g}}{63.55 \text{ g/mol}} \approx 0.0167 \text{ mol} \]
Understanding this calculation helps in predicting how much of a substance you have. It's the relationship between the mass of the sample and the number of particles it contains.
Mole Concept
The mole concept simplifies the way we count particles in chemistry. A mole is a unit that represents a large quantity of particles, whether they are atoms, molecules, or ions. One mole corresponds to Avogadro's number, \(6.022 \times 10^{23}\) particles, which is a convenient way to count when dealing with atoms and molecules because they're so small.
In the context of the exercise, we used the concept of moles to understand how many individual copper ions were generated from the copper turnings. By converting the mass of copper into moles, we translated weight into a countable number of atoms. This helps chemists to predict and measure the outcome of chemical reactions precisely.
In the context of the exercise, we used the concept of moles to understand how many individual copper ions were generated from the copper turnings. By converting the mass of copper into moles, we translated weight into a countable number of atoms. This helps chemists to predict and measure the outcome of chemical reactions precisely.
- One mole of any substance contains the same number of particles.
- It's like a dozen but with a much larger number.
- The mole bridges the gap between the atom scale (very small) and the lab scale (more manageable).
Chemical Reactions
Chemical reactions involve the transformation of reactants into products. In these processes, atoms are rearranged as bonds break and form new ones, but the total number of each kind of atom remains the same due to the conservation of mass.
In our example exercise, copper reacted with nitric acid to yield \(\mathrm{Cu}^{2+}\) ions among other products. This illustrates a typical chemical reaction where an element reacts with a compound: one of the simplest yet fundamentally important scenarios in chemistry. During the reaction, copper atoms lose electrons, and each copper atom becomes a \(\mathrm{Cu}^{2+}\) ion, which carries a positive charge because of the loss of electrons.
Knowing the moles of copper used helps us determine the moles of \(\mathrm{Cu}^{2+}\) ions produced. Since each copper atom provides one \(\mathrm{Cu}^{2+}\) ion, the moles of \(\mathrm{Cu}^{2+}\) ions created are equal to the moles of copper used. This direct relationship is a core idea in stoichiometry, which links the quantities of reactants and products in chemical reactions.
In our example exercise, copper reacted with nitric acid to yield \(\mathrm{Cu}^{2+}\) ions among other products. This illustrates a typical chemical reaction where an element reacts with a compound: one of the simplest yet fundamentally important scenarios in chemistry. During the reaction, copper atoms lose electrons, and each copper atom becomes a \(\mathrm{Cu}^{2+}\) ion, which carries a positive charge because of the loss of electrons.
Knowing the moles of copper used helps us determine the moles of \(\mathrm{Cu}^{2+}\) ions produced. Since each copper atom provides one \(\mathrm{Cu}^{2+}\) ion, the moles of \(\mathrm{Cu}^{2+}\) ions created are equal to the moles of copper used. This direct relationship is a core idea in stoichiometry, which links the quantities of reactants and products in chemical reactions.