Question

Copper reacts with dilute nitric acid according to the following equation: $$ \begin{array}{r} 3 \mathrm{Cu}(s)+8 \mathrm{HNO}_{3}(a q) \rightarrow 3 \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2 \mathrm{NO}(g)+ \\ 4 \mathrm{H}_{2} \mathrm{O}(l) \end{array} $$ If a copper penny weighing \(3.045 \mathrm{~g}\) is dissolved in a small amount of nitric acid and the resultant solution is diluted to \(50.0 \mathrm{~mL}\) with water, what is the molarity of the \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Short answer

The molarity of \( \text{Cu(NO}_3)_2 \) is 0.958 M.

Step-by-step solution

Calculate Moles of Copper

The first step is to calculate the number of moles of copper in the 3.045 g sample. The atomic weight of copper (Cu) is 63.55 g/mol. Therefore, we use the formula \( \text{moles of Cu} = \frac{\text{mass of Cu}}{\text{molar mass of Cu}} \).\[\text{moles of Cu} = \frac{3.045 \, \text{g}}{63.55 \, \text{g/mol}} \approx 0.0479 \, \text{mol} \]

Determine Moles of Produced Cu(NO3)2

According to the balanced chemical equation, 3 moles of Cu produce 3 moles of \( \text{Cu(NO}_3)_2 \). Thus, the moles of \( \text{Cu(NO}_3)_2 \) produced are equal to the moles of Cu initially used. So, \[\text{moles of Cu(NO}_3)_2 = 0.0479 \, \text{mol}\]

Calculate Molarity of Cu(NO3)2 Solution

Finally, we calculate the molarity of the \( \text{Cu(NO}_3)_2 \) solution using the formula \( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \). The solution volume is 50.0 mL, which is 0.0500 liters.\[\text{Molarity} = \frac{0.0479 \, \text{mol}}{0.0500 \, \text{L}} = 0.958 \, \text{M} \]

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves using a balanced chemical equation to determine the proportions of molecules that will react with one another, ensuring that the law of conservation of mass is upheld.

• Stoichiometric calculations allow chemists to predict the amounts of products created from given amounts of reactants.
• These calculations begin with a balanced chemical reaction equation, where the coefficients indicate the molar ratio between different substances.

Understanding stoichiometry is crucial when calculating the amounts of reactants required or products formed. In the given reaction, the molar ratio between copper and copper nitrate is 1:1, simplifying the calculation of product concentration based on initial reactants.

Copper and Nitric Acid Reaction

The reaction of copper with nitric acid is a well-known chemical process that yields copper nitrate, nitrogen monoxide, and water. The chemical equation for this reaction is:\[3 \mathrm{Cu}(s) + 8 \mathrm{HNO}_3(aq) \rightarrow 3 \mathrm{Cu}(\mathrm{NO}_3)_2(aq) + 2 \mathrm{NO}(g) + 4 \mathrm{H}_2\mathrm{O}(l)\]

• This equation illustrates that three moles of copper react with eight moles of nitric acid.
• The products include three moles of copper nitrate, two moles of nitrogen monoxide, and water.

This reaction is an example of redox chemistry, where copper is oxidized and nitric acid acts as the oxidizing agent. Understanding this helps in comprehending the stoichiometry of the reaction, allowing for accurate calculation of products.

Moles Calculation

Calculating moles is a foundational skill in chemistry. The number of moles of a substance is determined using its mass and molar mass. The formula used is:\[\text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]To find the moles of copper in the exercise:

• Mass of copper provided: 3.045 g
• Molar mass of copper: 63.55 g/mol

Plug these values into the formula:\[\text{Number of moles of Cu} = \frac{3.045}{63.55} \approx 0.0479 \text{ mol}\]This value is then used to predict the number of moles of copper nitrate produced, based on the balanced equation provided. Mastery of mole calculations is essential for any further quantitative chemical analysis.

Solution Preparation

Preparing a solution with a known molarity is an essential laboratory skill. The molarity of a solution is defined as the number of moles of solute per liter of solution. The formula for molarity is:\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\]In the provided exercise, we need to determine the molarity of copper nitrate after dilution:

• Moles of \( \text{Cu(NO}_3)_2 \): 0.0479 mol
• Volume of solution: 50.0 mL = 0.0500 L

Inserting these into the formula gives:\[\text{Molarity} = \frac{0.0479}{0.0500} = 0.958 \text{ M}\]This calculation shows that the concentration of the \( \text{Cu(NO}_3)_2 \) solution is 0.958 M, depending on the volumes measured accurately. Solution preparation with correct molarity ensures consistency and accuracy in experimental data.