Question

Although Cu is not sufficiently active to react with acids, it can be dissolved by concentrated nitric acid, which functions as an oxidizing agent according to the following equation: \(\mathrm{Cu}(s)+4 \mathrm{HNO}_{3}(a q) \longrightarrow\) $$\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2 \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ (a) Write the net ionic equation for this process. (b) Is \(35.0 \mathrm{~g}\) of \(\mathrm{HNO}_{3}\) sufficient to dissolve \(5.00 \mathrm{~g}\) of copper?

Short answer

35.0 g of \( \mathrm{HNO}_3 \) is sufficient to dissolve 5.00 g of \( \mathrm{Cu} \).

Step-by-step solution

Write the Balanced Net Ionic Equation

To write the net ionic equation, first identify the ions involved in the reaction. The complete reaction is: \[ \mathrm{Cu}(s) + 4 \mathrm{HNO}_3(aq) \longrightarrow \mathrm{Cu}(\mathrm{NO}_3)_2(aq) + 2 \mathrm{NO}_2(g) + 2 \mathrm{H}_2\mathrm{O}(l) \] \( \mathrm{Cu} \) and \( \mathrm{NO}_3^- \) ions are involved. Remove the spectator ions to get the net ionic equation: \[ \mathrm{Cu}(s) + 4 \mathrm{H^+}(aq) + 2 \mathrm{NO}_3^-(aq) \longrightarrow \mathrm{Cu}^{2+}(aq) + 2 \mathrm{NO}_2(g) + 2 \mathrm{H}_2\mathrm{O}(l) \] This is the balanced net ionic equation, with the elimination of the spectator ions (e.g., complexed \( \mathrm{NO}_3^- \) in the products).

Calculate the Moles of \( ext{HNO}_3 ext{ Required} o ext{Determine Moles of Cu that can be Dissolved} ",

Calculate the moles of \( \mathrm{Cu} \) using its molar mass: \[ 5.00 \text{ g Cu} \times \frac{1 \text{ mol Cu}}{63.55 \text{ g Cu}} = 0.0787 \text{ mol Cu} \] \( 4 \text{ mol of } \mathrm{HNO}_3 \) is needed to dissolve 1 mol of \( \mathrm{Cu} \). Therefore, the moles of \( \mathrm{HNO}_3 \) required for \( 0.0787 \text{ mol Cu} \) is: \[ 0.0787 \text{ mol Cu} \times \frac{4 \text{ mol } \mathrm{HNO}_3}{1 \text{ mol Cu}} = 0.3148 \text{ mol } \mathrm{HNO}_3 \]

Calculate the Mass of \\ \\ \( ext{HNO}_3 ext{ Required}\)

Convert the moles of \( \mathrm{HNO}_3 \) needed to mass using its molar mass (63.01 g/mol): \[ 0.3148 \text{ mol } \mathrm{HNO}_3 \times \frac{63.01 \text{ g } \mathrm{HNO}_3}{1 \text{ mol } \mathrm{HNO}_3} = 19.82 \text{ g } \mathrm{HNO}_3 \]

Compare with the Available Amount of \\\\\\ \( ext{HNO}_3 ext{ Given}\)

The problem states that we have 35.0 g of \( \mathrm{HNO}_3 \). Since 19.82 g is required to dissolve 5.00 g of \( \mathrm{Cu} \), 35.0 g of \( \mathrm{HNO}_3 \) is more than sufficient to dissolve the copper.

Key concepts

Chemical Reaction

A chemical reaction involves the transformation of reactants into products. In this case, copper (Cu) reacts with concentrated nitric acid (HNO₃) to form copper(II) nitrate, nitrogen dioxide (NO₂), and water.

• The reactants are Cu and HNO₃.
• The products are Cu(NO₃)₂, NO₂, and H₂O.

Chemical equations must be balanced to ensure the conservation of mass. This means the number of atoms for each element must be the same on both sides of the reaction. Balancing helps us understand the stoichiometry of the reaction and what amount of each reactant is necessary.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance and is expressed in g/mol. It is a crucial component in stoichiometry, allowing us to convert between grams and moles.
For copper, the molar mass is 63.55 g/mol. To find the number of moles in a sample, divide the mass of the sample by its molar mass:
\[ \text{Moles of Cu} = \frac{5.00 \text{ g Cu}}{63.55 \text{ g/mol}} = 0.0787 \text{ mol Cu} \]
Similarly, you can calculate the moles of HNO₃ needed by using its molar mass, 63.01 g/mol. This calculation helps determine how much of the reactant is needed to complete a reaction.

Oxidizing Agent

In a redox reaction, an oxidizing agent is the substance that gains electrons and is reduced.

• In this reaction, HNO₃ acts as the oxidizing agent.
• It causes copper to oxidize by accepting electrons from it.

As copper loses electrons and forms Cu²⁺, nitric acid is reduced to nitrogen dioxide (NO₂). Understanding oxidizing and reducing agents is essential in predicting how a reaction will proceed and what products will form.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses the coefficients in a balanced chemical equation to determine the proportional relationships between different substances.
In this particular exercise, stoichiometry helps us find out how much HNO₃ is needed to dissolve a given amount of Cu.

• 4 moles of HNO₃ are required to dissolve 1 mole of Cu.
• Calculations showed that 0.3148 moles of HNO₃ are needed for 0.0787 moles of Cu.

Applying stoichiometry ensures that we use the exact proportions of each reactant, avoiding waste and ensuring completeness of the reaction.