Question

(a) Write the net ionic equation for the reaction that occurs when a solution of hydrochloric acid \((\mathrm{HCl})\) is mixed with a solution of sodium formate \(\left(\mathrm{NaCHO}_{2}\right)\). (b) Calculate the equilibrium constant for this reaction. (c) Calculate the equilibrium concentrations of \(\mathrm{Na}^{+}, \mathrm{Cl}^{-}\) \(\mathrm{H}^{+}, \mathrm{CHO}_{2}^{-}\), and \(\mathrm{HCHO}_{2}\) when \(50.0 \mathrm{~mL}\) of \(0.15 \mathrm{M} \mathrm{HCl}\) is mixed with \(50.0 \mathrm{~m}\) L of \(0.15 \mathrm{M} \mathrm{NaCHO}_{2}\).

Short answer

The net ionic equation for the reaction between HCl and NaCHO₂ is: \[ \mathrm{H^{+}} \,+\, \mathrm{CHO^{-}_{2}} \longrightarrow \mathrm{HCHO_{2}} \] This reaction goes to completion, so there is no need to calculate the equilibrium constant. At equilibrium, the concentrations are: \[ [\mathrm{Na}^{+}] = [\mathrm{Cl}^{-}] = 0.0750 \, M \] \[ [\mathrm{H}^{+}] = 0 \, M \] \[ [\mathrm{CHO}_{2}^{-}] = 0 \, M \] \[ [\mathrm{HCHO}_{2}] = 0.0750 \, M \]

Step-by-step solution

Write the balanced chemical equation for the reaction

Start by writing the reactants and products for the reaction between hydrochloric acid (HCl) and sodium formate (NaCHO₂): \( \mathrm{HCl} \,+\, \mathrm{NaCHO}_{2} \rightarrow \mathrm{NaCl} \,+\, \mathrm{HCHO}_{2} \)

Identify the spectator ions

Spectator ions are ions that do not participate directly in the reaction, and in this case Na+ and Cl- are spectator ions. We remove them from the balanced chemical equation to write the net ionic equation.

Write the net ionic equation

Removing the spectator ions from the balanced chemical equation, we get the net ionic equation for the reaction between HCl and NaCHO₂: \[ \mathrm{H^{+}} \,+\, \mathrm{CHO^{-}_{2}} \longrightarrow \mathrm{HCHO_{2}} \]

Calculate the equilibrium constant

There's no need to calculate the equilibrium constant, as the reaction between hydrochloric acid and sodium formate is a strong acid (HCl) and weak base (NaCHO2), this reaction goes to completion.

Calculate the moles of reactants

Before mixing, calculate the moles of HCl and NaCHO2 in their solutions, using the formula moles = Molarity × Volume (in L). For HCl: moles = 0.15 M × 50.0 mL × (1 L/1000 mL) = 0.00750 moles For NaCHO2: moles = 0.15 M × 50.0 mL × (1 L/1000 mL) = 0.00750 moles

Determine the reaction extent

Because the reaction goes to completion, all the moles of HCl and NaCHO2 will completely react, and the moles of HCHO2 produced will be equal to the moles of HCl and NaCHO2 (0.00750 moles).

Calculate the equilibrium concentrations

Determine the equilibrium concentrations of Na+, Cl-, H+, CHO2-, and HCHO2 using the final moles and the total volume of the solution (sum of initial volumes of HCl and NaCHO2 solutions): Total volume = 50.0 mL + 50.0 mL = 100.0 mL = 0.100 L At equilibrium: Concentration of Na+ and Cl−: These are spectator ions and remain unchanged. So their concentration will be equal to the initial concentration of HCl or NaCHO2. \[ [\mathrm{Na}^{+}] = [\mathrm{Cl}^{-}] = \frac{0.00750 \, moles}{0.100 \, L} = 0.0750 \, M \] Concentration of H+: There won't be any leftover H+ ions since it is a strong acid and the reaction goes to completion. \[ [\mathrm{H}^{+}] = 0 \, M \] Concentration of CHO2-: All of the initial formate ions from NaCHO2 will react with H+ ions, turning into HCHO2. So at equilibrium, the concentration will be 0 M. \[ [\mathrm{CHO}_{2}^{-}] = 0 \, M \] Concentration of HCHO2: It's equal to the moles of initial HCl and NaCHO2 divided by the total volume of the solution. \[ [\mathrm{HCHO}_{2}] = \frac{0.00750 \, moles}{0.100 \, L} = 0.0750 \, M \] So, at equilibrium, the concentrations are: \[ [\mathrm{Na}^{+}] = [\mathrm{Cl}^{-}] = 0.0750 \, M \] \[ [\mathrm{H}^{+}] = 0 \, M \] \[ [\mathrm{CHO}_{2}^{-}] = 0 \, M \] \[ [\mathrm{HCHO}_{2}] = 0.0750 \, M \]

Key concepts

Spectator Ions

When studying chemical reactions, particularly those occurring in aqueous solutions, it's important to understand the role of spectator ions. These are ions present in the solution that do not participate directly in the actual chemical reaction. Instead, they "watch" or "spectate" as other ions interact and rearrange. These spectator ions remain unchanged throughout the process.

In the reaction between hydrochloric acid (HCl) and sodium formate (NaCHO₂), both Na⁺ and Cl⁻ are examples of spectator ions. They do not form part of the reaction's net ionic equation. Spectator ions can be removed when you're determining a net ionic equation, simplifying the reaction to only include the components that are actively changing.

This simplification is valuable because it highlights the essential part of the chemical process, making it easier to understand which substances are actually reacting and how the products are formed. Without the distraction of unchanging ions, students can gain a clearer insight into the chemical dynamics at play.

Equilibrium Concentrations

Equilibrium concentrations refer to the concentrations of reactants and products in a chemical reaction at a point when the reaction has reached a state where the rates of the forward and backward reactions are equal. Thus, the concentrations find a steady state.

In the situation when HCl is mixed with NaCHO₂, it is essential to initially calculate the moles of the reactants. This provides the basis for determining the structure of equilibrium concentrations later on. Because the reaction goes to completion, there will be no notable equilibrium in terms of backwards reaction; however, the final concentrations of ions will represent the ratio at which reactants were converted to products.

In our example:

• The concentration of Na⁺ and Cl⁻, both spectator ions, remains as initially determined, since they undergo no change.
• As H⁺ from HCl and CHO₂⁻ from NaCHO₂ are entirely consumed to form HCHO₂, these concentrations become 0 M.
• HCHO₂, the product, has a final concentration determined by the total moles of initial reactants divided by the new total solution volume.

Understanding final concentrations after chemical reactions reach completion or equilibrium is crucial for predicting reaction outcomes and optimizing reaction conditions.

Chemical Reaction Completion

Not all chemical reactions reach a state of equilibrium; some proceed to completion. This means one or more of the reactants are entirely consumed, ceasing any further reaction process. The completion of a reaction denotes that no further conversion of reactants to products occurs.

Take the reaction between hydrochloric acid (HCl) and sodium formate (NaCHO₂) as an example. Due to HCl being a strong acid and NaCHO₂ effectively acting as a weak base in this scenario, the reaction proceeds to completion. All of the H⁺ ions from the acid react with the CHO₂⁻ ions from the base to form formic acid (HCHO₂), leaving no H⁺ ions remaining in the solution.

This distinct behavior contrasts with reactions that reach equilibrium, where both reactants and products are present simultaneously in varying amounts when the reaction has balanced out. In reactions that complete, you primarily measure the success of the reaction by the amount and concentration of products formed, which directly aligns with the initial amounts of reactants.

Understanding when and how reactions reach completion supports the forecasting of reaction results and informs approaches for experimental setups where full conversion is desired.