Question

How many grams of metallic copper are required to react with the number of moles of ${\mathrm{Cu}}^{2+}$ calculated in Problem 1 to form the CuCl? The overall reaction can be taken to be: $${\mathrm{Cu}}^{2+}(\mathrm{aq})+2{\mathrm{Cl}}^{-}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})\to 2\mathrm{CuCl}(\mathrm{s})$$

Short answer

To find the grams of metallic copper needed to react with the number of moles of ${\mathrm{Cu}}^{2+}$ calculated in Problem 1 to form CuCl, use the stoichiometric ratio of 1:1 between ${\mathrm{Cu}}^{2+}$ ions and metallic Cu. Since the given number of moles of ${\mathrm{Cu}}^{2+}$ is $x$ moles, the same number of moles of metallic Cu is also needed: $x$ moles. Convert the moles of metallic Cu to grams using the molar mass of Cu (63.55 g/mol): $\text{grams of metallic Cu}=x\text{moles}\times 63.55\frac{\text{g}}{\text{mol}}$. Substitute the given value of $x$ from Problem 1 to calculate the required grams of metallic copper.

Step-by-step solution

Identify the stoichiometric ratio

From the reaction equation, we can see that 1 mole of ${\mathrm{Cu}}^{2+}$ ions reacts with 1 mole of metallic Cu, so the stoichiometric ratio is 1:1.

Calculate the moles of metallic Cu required

Using the stoichiometric ratio, the number of moles of metallic Cu required to react with the given moles of ${\mathrm{Cu}}^{2+}$ ions is the same: $$\text{moles of metallic Cu}=x\text{moles}$$

Convert moles of metallic Cu to grams

Using the molar mass of Copper, which is approximately 63.55 g/mol, we can convert the moles of metallic Cu required to grams: $$\text{grams of metallic Cu}=\text{moles of metallic Cu}\times \text{molar mass of Cu}$$ $$\text{grams of metallic Cu}=x\text{moles}\times 63.55\frac{\text{g}}{\text{mol}}$$ Now, substitute the given number of moles of ${\mathrm{Cu}}^{2+}$ from Problem 1 as $x$ in the last equation, and you will have the answer for the grams of metallic Copper required to form the CuCl.

Key concepts

Understanding Chemical Reactions

Chemical reactions are processes where reactants transform into products through exchanges or sharing of electrons. The essence lies within the rearrangement of atoms and the conservation of mass, which states that matter is neither created nor destroyed in a closed system. Let's take the provided reaction:

$${\mathrm{Cu}}^{2+}(\mathrm{aq})+2{\mathrm{Cl}}^{-}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})\to 2\mathrm{CuCl}(\mathrm{s})$$

This reaction involves copper ions (${\mathrm{Cu}}^{2+}$) reacting with chloride ions (${\mathrm{Cl}}^{-}$) and solid copper ($\mathrm{Cu}$) to form solid copper(I) chloride ($\mathrm{CuCl}$). One must focus on the stoichiometry to understand the quantitative aspect of this transformation. This includes recognizing the mole-to-mole relationships established by the balanced chemical equation, which dictates the proportion of reactants that combine to form products.

Calculating Molar Mass

Molar mass is a critical concept in stoichiometry as it links the mass of a substance to the number of moles, hence revealing how much of a substance is needed or produced in a reaction. The molar mass of an element is the mass in grams of one mole of atoms of that element. For copper ($\mathrm{Cu}$), the molar mass is approximately 63.55 g/mol, reflecting that 63.55 grams of copper constitute one mole of copper atoms.

In the context of our exercise, once the moles of metallic copper needed for the reaction are known, molar mass can convert this quantity into a tangible mass—a vital step for practical application such as measuring out the copper for a real-world laboratory experiment.

Executing Stoichiometric Calculations

Stoichiometric calculations are at the heart of carrying out chemical reactions efficiently. These calculations allow us to predict how much of each substance is needed and are based on the stoichiometric coefficients from a balanced chemical equation. For example, the one-to-one ratio in our given reaction indicates that for every mole of copper(II) ions, one mole of solid copper is required.

Executing these calculations involves three major steps: identifying the stoichiometric ratios, converting those ratios into moles and then applying the molar mass to transition from moles to grams. In practical terms, if we are given the number of moles of ${\mathrm{Cu}}^{2+}$ from a prior calculation, we can use the stoichiometric ratio (step 1) to ascertain the same number of moles of metallic copper needed (step 2). Conclusively, we multiply by the molar mass of copper to find the mass in grams (step 3). Applying such a systematic approach is not just about getting the right answer; it's also crucial for establishing a clear and traceable thought process, which is immensely beneficial for complex problem-solving in chemistry.