Question

What are the concentrations of \(\mathrm{Cu}^{2+}\), \(\mathrm{NH}_{3},\) and \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\) at equilibrium when \(18.8 \mathrm{~g}\) of \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) are added to \(1.0 \mathrm{~L}\) of a \(0.400 \mathrm{M}\) solution of aqueous ammonia? Assume that the reaction goes to completion and forms \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\)

Short answer

Question: Given an initial amount of Cu(NO3)2 dissolved in 1.0 L of water, and a concentration of aqueous ammonia (NH3), determine the equilibrium concentrations of Cu²⁺, NH3, and Cu(NH3)₄²⁺ when the reaction reaches completion and forms Cu(NH3)₄²⁺.

Step-by-step solution

Find the concentration of \(\mathrm{Cu(NO}_3)_2\)

First, we need to find the concentration of \(\mathrm{Cu(NO}_3)_2\) in the solution after dissolving the given mass in 1.0L of water. Determine the molar mass of \(\mathrm{Cu(NO}_3)_2\): the atomic mass of Cu is 63.5 g/mol, N is 14.0 g/mol, and O is 16.0 g/mol. So, the molar mass of \(\mathrm{Cu(NO}_3)_2\) is \((63.5 + 2(14.0 + 3(16.0)))\) g/mol. Calculate the concentration of \(\mathrm{Cu(NO}_3)_2\) by dividing the mass by the molar mass and the volume of the solution in L.

Find the initial concentration of \(\mathrm{Cu}^{2+}\) ions

Since \(\mathrm{Cu(NO}_3)_2\) dissociates entirely in water, the initial concentration of \(\mathrm{Cu}^{2+}\) ions is equal to the concentration of \(\mathrm{Cu(NO}_3)_2\).

Determine the balanced reaction equation for the formation of \(\mathrm{Cu(NH}_3)_4^{2+}\)

We need to write the balanced chemical equation for the reaction we are considering: $$\mathrm{Cu}^{2+}(aq) + 4\mathrm{NH}_3(aq) \rightleftharpoons \mathrm{Cu(NH}_3)_4^{2+}(aq)$$

Find the change in concentration of reactants and products

Now, we will use stoichiometry to determine the change in concentration of \(\mathrm{Cu}^{2+}\), \(\mathrm{NH}_3\), and \(\mathrm{Cu(NH}_3)_4^{2+}\) when the reaction goes to completion (since the reaction goes to completion, this process is called stoichiometry). For every 1 mole of \(\mathrm{Cu}^{2+}\) consumed, 4 moles of \(\mathrm{NH}_3\) will be consumed, and 1 mole of \(\mathrm{Cu(NH}_3)_4^{2+}\) will be formed. Calculate the concentration of \(\mathrm{NH}_3\) consumed, then subtract it from the initial concentration to get the equilibrium concentration. Also, calculate the concentration of \(\mathrm{Cu(NH}_3)_4^{2+}\) produced.

Calculate the equilibrium concentrations of all species

Once we determine the changes in concentration for all reactants and products, we can calculate the equilibrium concentrations. Our final answers for the equilibrium concentrations are: - The concentration of \(\mathrm{Cu}^{2+}\): as all \(\mathrm{Cu}^{2+}\) is consumed to form \(\mathrm{Cu(NH}_3)_4^{2+}\), its equilibrium concentration is close to 0 M. - The equilibrium concentration of \(\mathrm{NH}_3\) - The equilibrium concentration of \(\mathrm{Cu(NH}_3)_4^{2+}\)

Key concepts

Chemical Equilibrium

Chemical equilibrium represents a state in a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no overall change in the concentration of reactants and products over time. However, it's crucial to understand that being in equilibrium does not mean that the reactants and products are present in equal concentrations, just that their concentrations have stabilized.

In the context of the problem provided, we assume the reaction goes to completion, which may seem counterintuitive when discussing equilibrium. Reaching completion means the reactants are fully consumed to form products under the given conditions. Nevertheless, under different conditions, the same reaction might not go to completion and an equilibrium state with all reactants and products could be established. Knowing how to calculate equilibrium concentrations is essential for students, as it allows them to understand dynamic processes where concentrations remain constant, a common occurrence in biological systems and industrial processes.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is a core concept in chemistry that involves using balanced chemical equations to calculate the quantities of reactants and products involved in a chemical reaction.

In our exercise, stoichiometry comes into play when predicting the amount of product formed from a given amount of reactants. By understanding the molar ratios from the balanced equation, \(\mathrm{Cu}^{2+}(aq) + 4\mathrm{NH}_3(aq) \rightleftharpoons \mathrm{Cu(NH}_3)_4^{2+}(aq)\), students can analyze how many moles of ammonia (\(\mathrm{NH}_3\)) are necessary to fully react with copper (\(\mathrm{Cu}^{2+}\)) ions. This concept also helps them determine the equilibrium concentrations by relating the amounts of compounds reacted or formed.

Molar Mass Calculation

Calculating molar mass is fundamental in stoichiometry; it's the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For students to solve problems like the one provided, they need to understand how to derive the molar mass of compounds based on the atomic masses of the elements they contain.

For example, the molar mass of \(\mathrm{Cu(NO}_3)_2\) is determined by adding the atomic masses of one copper (Cu) atom, two nitrogen (N) atoms, and six oxygen (O) atoms. A precise calculation is crucial for the following steps, where the mass of \(\mathrm{Cu(NO}_3)_2\) is converted to moles, as this will determine the concentration of \(\mathrm{Cu}^{2+}\) ions in the solution, ultimately affecting the equilibrium concentration of each species in the reaction.