Question

The enthalpy of neutralization for the reaction of a strong acid with a strong base is \(-56 \mathrm{~kJ} / \mathrm{mol}\) water produced. How much energy will be released when \(200.0 \mathrm{~mL}\) of \(0.400 \mathrm{M} \mathrm{HCl}\) is mixed with \(150.0 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{NaOH}\) ?

Short answer

The energy released when \(200.0 \mathrm{~mL}\) of \(0.400 \mathrm{M} \mathrm{HCl}\) is mixed with \(150.0 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{NaOH}\) can be calculated in the following steps: 1. Calculate the moles of HCl and NaOH: moles of HCl = \(0.400 \times 0.200 = 0.080 \mathrm{~mol}\) moles of NaOH = \(0.500 \times 0.150 = 0.075 \mathrm{~mol}\) 2. Find the limiting reactant: HCl is the limiting reactant as it has fewer moles compared to NaOH. 3. Calculate moles of water produced: moles of water produced = 0.080 mol (equal to mol of the limiting reactant, HCl) 4. Calculate energy released: Q = n × ΔH = \(0.080 \mathrm{~mol} \times -56 \mathrm{~kJ/mol} = -4.48 \mathrm{~kJ}\) Therefore, \(4.48 \mathrm{~kJ}\) of energy will be released when \(200.0 \mathrm{~mL}\) of \(0.400 \mathrm{M} \mathrm{HCl}\) is mixed with \(150.0 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{NaOH}\).

Step-by-step solution

Calculate moles of HCl and NaOH

First, we need to find out how many moles of HCl and NaOH are present in the given solutions. We can do that using the formula: moles = concentration × volume Where the volume needs to be in liters. For HCl: moles = 0.400 M × 200.0 mL × (1 L / 1000 mL) For NaOH: moles = 0.500 M × 150.0 mL × (1 L / 1000 mL)

Find the limiting reactant

Next, we need to identify the limiting reactant, which is the reactant that will be completely consumed in the reaction. The balanced reaction is: HCl + NaOH → NaCl + H2O Since the stoichiometry is 1:1 for both HCl and NaOH, we can compare the moles of each reactant to determine which one is the limiting reactant.

Calculate moles of water produced

Now, we need to find out the number of moles of water produced. This will be equal to the number of moles of the limiting reactant, because of the 1:1 stoichiometry. moles of water produced = moles of limiting reactant

Calculate energy released

Finally, we can calculate the energy (Q) released in the reaction by using the enthalpy of neutralization (ΔH) and the number of moles of water produced (n): Q = n × ΔH Since ΔH = -56 kJ/mol for this reaction, we can plug in the values for n and ΔH to find the energy released during the reaction.

Key concepts

Acid-Base Reaction

An acid-base reaction is a chemical process where an acid and a base interact, typically resulting in the formation of water and a salt. These reactions are fundamental to chemistry and are characterized by the transfer of a proton (H+) from the acid to the base. A strong acid, like Hydrochloric acid (HCl), completely dissociates in water to release H+ ions, while a strong base, like Sodium hydroxide (NaOH), completely dissociates to provide OH- ions. When H+ from the acid combines with OH- from the base, they form H2O, which is water.

This reaction is also exothermic, meaning it releases energy in the form of heat. The amount of heat released during the neutralization of one mole of water is termed the enthalpy of neutralization. The typical enthalpy change for the neutralization of a strong acid with a strong base is approximately {-56 kJ/mol} of H2O produced. Understanding the concepts of acid-base reactions can significantly aid in grasping the enthalpy changes involved during such a process.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It's based on the laws of conservation of mass and fixed proportions, which state that in a chemical reaction, mass is conserved and elements combine in fixed ratios by mass.

In practical terms, stoichiometry allows us to predict the amounts of substances consumed and produced in a reaction. This is done through the balanced chemical equation, which gives us the mole ratios of reactants and products. For the acid-base reaction of HCl with NaOH, the balanced equation is: HCl + NaOH → NaCl + H2OThis indicates that one mole of HCl will react with one mole of NaOH to produce one mole of NaCl and one mole of water. The balanced equation is essential for all stoichiometric calculations, as it serves as the blueprint that dictates the proportions in which chemicals react.

Limiting Reactant

The concept of the limiting reactant is a key principle in stoichiometry. It refers to the reactant that will be entirely consumed first in a chemical reaction, thus limiting the amount of products that can be formed. Identifying the limiting reactant is crucial in determining the maximum amount of product that can be generated from a given amount of reactants.

In the reaction between HCl and NaOH, given the 1:1 mole ratio, we can compare the moles of each reactant to find which one is in short supply. The reactant present in the lesser molar quantity will be the limiting reactant. Knowing which reactant is limiting allows us to calculate the theoretical yield of products, in this case, water. When we understand which reactant is limiting, we ensure more effective planning and optimization of chemical processes and resources in practical applications.