Problem 88 - Chemistry: The Central Science in SI Units, Global Edition

Question

A solution is made by mixing \(1.5 \mathrm{~g}\) of \(\mathrm{LiOH}\) and \(23.5 \mathrm{~mL}\) of \(1.000 \mathrm{M}\) HNO3. (a) Write a balanced equation for the reaction that occurs between the solutes. (b) Calculate the concentration of each ion remaining in solution. (c) Is the resulting solution acidic or basic?

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction between LiOH and HNO3 is: \( LiOH + HNO_3 \rightarrow LiNO_3 + H_2O \). After the reaction, there are 1.668 M OH- ions, and 1.000 M Li+ and NO3- ions remaining in the solution. As there are no H+ ions remaining and the presence of OH- ions, the solution is basic.

Step 1: Write the balanced chemical equation

The reaction between LiOH (a base) and HNO3 (an acid) is an acid-base neutralization reaction, which produces water and a salt. The balanced chemical equation for the reaction is: \( LiOH + HNO_3 \rightarrow LiNO_3 + H_2O \)

Step 2: Convert given amount of reactants into moles

As we are given mass of LiOH and the volume and concentration of HNO3, we have to convert these amounts into moles. Given, mass of LiOH = 1.5 g Molar mass of LiOH = 6.94 (Li) + 15.999 (O) + 1.008 (H) = 23.942 g/mol Moles of LiOH = mass/molar mass Moles of LiOH = 1.5 g / 23.942 g/mol = 0.0627 mol Given, volume of HNO3 = 23.5 mL = 0.0235 L Concentration of HNO3 = 1.000 M Moles of HNO3 = concentration × volume Moles of HNO3 = 1.000 M × 0.0235 L = 0.0235 mol

Step 3: Determine the limiting reactant

Let's compare the mole ratio of reactants based on the balanced equation and the mole ratio from the given amounts of reactants. From the balanced equation: 1 mol LiOH : 1 mol HNO3 Given amounts: 0.0627 mol LiOH : 0.0235 mol HNO3 Since the given amounts of LiOH : HNO3 are greater than the mole ratio in the balanced equation, HNO3 is the limiting reactant. The reaction will consume all of the HNO3 and only a portion of the LiOH.

Step 4: Calculate the remaining amounts of reactants and products

As HNO3 is the limiting reactant, it will be completely consumed. This means that in the resulting solution, there will be no HNO3 left and no H+ ions (from the consumed HNO3). Moles of LiOH remaining = Initial moles of LiOH - moles of consumed LiOH Moles of LiOH remaining = 0.0627 mol - 0.0235 mol = 0.0392 mol Moles of LiNO3 produced = moles of HNO3 consumed = 0.0235 mol

Step 5: Calculate the concentration of each remaining ion

The total volume of the solution (assuming it does not change significantly due to the reaction) = 23.5 mL = 0.0235 L Concentration of remaining OH- ions (from LiOH) = moles of LiOH remaining / total volume Concentration of OH- ions = 0.0392 mol / 0.0235 L = 1.668 M Concentration of remaining Li+ and NO3- ions (from LiNO3) = moles of LiNO3 produced / total volume Concentration of Li+ and NO3- ions = 0.0235 mol / 0.0235 L = 1.000 M

Step 6: Determine whether the solution is acidic or basic

Since there are no H+ ions remaining in the solution but there are OH- ions present, the solution will be basic. This is because a higher concentration of OH- ions compared to H+ ions will result in a pH greater than 7.

Key Concepts

Balanced Chemical Equation

When mixing an acid and a base, a specific type of chemical reaction takes place called an acid-base neutralization. For the given exercise, you combine lithium hydroxide (LiOH) and nitric acid (HNO3). The products formed are lithium nitrate (LiNO3) and water (H2O). The balanced chemical equation for this reaction is:\( \text{LiOH} + \text{HNO}_3 \rightarrow \text{LiNO}_3 + \text{H}_2\text{O} \)This equation is considered "balanced" because the number of atoms of each element on the reactant side equals the number on the product side. Balancing chemical equations is crucial to show that matter is conserved in a reaction. When writing a balanced equation, ensure that the number of atoms of each type is the same before and after the reaction.

Limiting Reactant

To fully understand the extent of a reaction, identifying the limiting reactant is vital. The limiting reactant is the substance that controls the amount of product formed. In every chemical reaction, one reactant is usually used up before the others.Here, we first determine the moles for each reactant:

• For LiOH: Given mass is 1.5 g with a molar mass of 23.942 g/mol results in \( 0.0627 \) mol LiOH.
• For HNO3: Volume is 23.5 mL (which converts to 0.0235 L), and using the molarity of 1.000 M, you find \( 0.0235 \) mol HNO3.

According to the balanced equation (1:1 ratio), since there is less HNO3 than LiOH, nitric acid is the limiting reactant. It is this reactant that ultimately determines how much product is formed and when the reaction will stop. This concept is essential as it suggests which reactant will have a residue and which one will completely react.

Ion Concentration

After identifying the limiting reactant, calculating the remaining ions' concentration is the next step. Once the reaction is complete, only some reactants contribute to the ion concentration in the solution.For the given reaction:

• OH- ions will focus on remaining LiOH. Moles of remaining LiOH = initial \( 0.0627 \) moles - consumed HNO3, \( 0.0235 \) moles = \( 0.0392 \) moles.
• The concentration of OH- ions is the moles remaining divided by total volume \( 0.0235 \) L, giving \( 1.668 \) M.
• The resulting Li+ and NO3- ions from LiNO3 give a concentration of \( 1.000 \) M, same as the initial concentration of HNO3.

Calculating ion concentration gives insight into the chemical makeup of the solution after the reaction. These concentrations determine important properties, such as the pH of the solution, and help in understanding the solution's nature.

pH of Solution

The pH level of a solution indicates whether it is acidic, neutral, or basic. It's a measure of the hydrogen ion (H+) concentration, and in this scenario, it answers the question of the solution's nature. After the reaction:

• The absence of H+ ions, as they were neutralized by OH- ions, leaves no contribution to acidity from HNO3.
• A considerable concentration of OH- ions remains, marking the solution as basic.

The pH value is specifically greater than 7 for basic solutions due to the higher presence of OH- ions over H+ ions. Calculating pH typically involves analyzing the concentration of these ions, though for basic solutions, we often consider pOH first and convert it if necessary. This fundamental understanding of pH helps students grasp the characteristics of solutions after acid-base reactions.