Problem 61 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Calculate the molarity of a solution that contains 0.175 mol \(\mathrm{ZnCl}_{2}\) in exactly \(150 \mathrm{~mL}\) of solution. (b) How many moles of protons are present in \(35.0 \mathrm{~mL}\) of a \(4.50 \mathrm{M}\) solution of nitric acid? (c) How many milliliters of a \(6.00 \mathrm{M} \mathrm{NaOH}\) solution are needed to provide 0.350 mol of \(\mathrm{NaOH} ?\)

Step-by-Step Solution

Answer

(a) The molarity of the ZnCl₂ solution is 1.17 M. (b) There are 0.1575 moles of protons present in 35.0 mL of a 4.50 M solution of nitric acid. (c) To provide 0.350 mol of NaOH, 58.3 mL of a 6.00 M NaOH solution is needed.

Step 1: Identify the given values

We are given the number of moles of ZnCl₂ (0.175 mol) and the volume of the solution (150 mL). We need to calculate the molarity of the solution.

Step 2: Convert the volume to liters

Since molarity requires the volume to be in liters, we need to convert 150 mL to liters. Recall that 1 L = 1000 mL. Therefore, the volume in liters is: \(V (L) = \frac{150}{1000} = 0.15 L\)

Step 3: Calculate the molarity

Now, use the formula M = n/V to calculate the molarity of the solution: \(M = \frac{n}{V} = \frac{0.175 \text{ mol}}{0.15 \text{ L}} = 1.17 \text{ M}\) Part (b)

Step 1: Identify the given values

We are given the volume of nitric acid solution (35.0 mL) and its molarity (4.50 M). We need to find the number of moles of protons present in the solution.

Step 2: Convert the volume to liters

Convert the volume of the nitric acid solution from milliliters to liters: \(V (L) = \frac{35.0}{1000} = 0.035 L\)

Step 3: Find the number of moles of protons

Now, we can use the formula M = n/V to find the number of moles of protons in the solution: \(n = M \times V = 4.50 \text{ M} \times 0.035 \text{ L} = 0.1575 \text{ mol}\) There are 0.1575 moles of protons present in 35.0 mL of a 4.50 M solution of nitric acid. Part (c)

Step 1: Identify the given values

We are given the molarity of the NaOH solution (6.00 M) and the number of moles of NaOH (0.350 mol). We need to find the volume of the NaOH solution in milliliters.

Step 2: Calculate the volume in liters

Use the formula M = n/V to find the volume of the NaOH solution in liters: \(V (L) = \frac{n}{M} = \frac{0.350 \text{ mol}}{6.00 \text{ M}} = 0.0583 \text{ L}\)

Step 3: Convert the volume to milliliters

Now, convert the volume of the NaOH solution from liters to milliliters: \(V (mL) = 0.0583 \text{ L} \times 1000 = 58.3 \text{ mL}\) To provide 0.350 mol of NaOH, 58.3 mL of a 6.00 M NaOH solution is needed.

Key Concepts

Solution concentration

Solution concentration refers to the measure of how much solute is present in a given volume of solvent. It's typically expressed in terms of molarity, which is the number of moles of solute per liter of solution. Understanding this concept is crucial in chemistry because it enables chemists to know exactly how strong or dilute a solution is. It helps predict how the solution will behave in chemical reactions.
To calculate molarity, we apply the formula: \[ M = \frac{n}{V} \]\(M\) is the molarity, \(n\) is the number of moles, and \(V\) is the volume in liters. Knowing this formula allows us to adjust concentrations for various applications, like increasing reactant concentrations or diluting solutions for safe handling.
For example, if you have a 0.175 mol quantity of \(\mathrm{ZnCl}_{2}\) in 0.15 L, the molarity is \(1.17 \mathrm{M}\). This information tells you that in every liter of this solution, there are 1.17 moles of \(\mathrm{ZnCl}_{2}\).

Volume conversion

Volume conversion is a necessary step in chemistry problems, as measurements can be given in different units. For molarity calculations, knowing how to convert volumes from milliliters to liters is essential, because molarity is defined using liters.

To convert milliliters to liters, remember that 1 liter is equal to 1000 milliliters. Hence, you divide the number of milliliters by 1000. This basic conversion is a key skill for solving chemical equations and performing experiments accurately.
For instance, in calculating the molarity of a solution, converting 150 mL to liters involves dividing by 1000, resulting in 0.15 L. This converted volume can then be accurately used to determine solution concentration.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It's a foundational concept in chemistry that provides the quantitative relationships between substances as they undergo chemical changes.
By using the mole concept and balanced chemical equations, stoichiometry allows chemists to predict yields of reactions, determine limiting reagents, and find out the quantities of reactants required for a reaction to occur.
For example, when dealing with a nitric acid solution with a molarity of 4.50 M and a volume of 35.0 mL, you can calculate the number of moles of protons using stoichiometry. By converting the volume to liters (0.035 L), and applying the molarity formula, you find there are 0.1575 moles of protons present.

Chemical reactions

Chemical reactions describe processes where substances (reactants) transform into new substances (products). Understanding the nature of reactions is essential for predicting outcomes and controlling conditions for desired results.
Chemical equations provide a visual representation of what happens when substances react. The coefficients in front of molecules indicate the proportions of each substance involved. Balancing these equations is crucial for applying stoichiometry.
For instance, when determining how many milliliters of a 6.00 M \(\mathrm{NaOH}\) solution are needed for 0.350 mol \(\mathrm{NaOH}\), the reaction might involve NaOH as a reactant. Using the molarity concept, first calculate the volume in liters, which is \(0.0583 \text{ L}\). Convert this to milliliters (58.3 mL) for practical usage in experiments. This precise measurement ensures you have the correct amount of reactant for the desired chemical reaction.