Problem 61 - Chemistry The Central Science

Question

(a) Calculate the molarity of a solution that contains \(0.175 \mathrm{~mol}\) \(\mathrm{ZnCl}_{2}\) in exactly \(150 \mathrm{~mL}\) of solution. (b) How many moles of \(\mathrm{HCl}\) are present in \(35.0 \mathrm{~mL}\) of a \(4.50 \mathrm{M}\) solution of nitric acid? (c) How many milliliters of \(6.00 \mathrm{M} \mathrm{NaOH}\) solution are needed to provide \(0.325 \mathrm{~mol}\) of \(\mathrm{NaOH} ?\)

Step-by-Step Solution

Answer

The short answers for the 3 parts of the question are: (a) The molarity of the ZnCl2 solution is\( 1.17\mathrm{~M} \). (b) There are \( 0.158\mathrm{~mol} \)of HCl in the solution. (c) We need \(54.2\mathrm{~mL} \)of \(6.00\mathrm{~M}\)NaOH solution to provide \(0.325\mathrm{~mol} \)of NaOH.

Step 1: Write down the formula to find molarity

Molarity (M) is the number of moles of solute per liter of solution. The formula is: \[M = \frac{\text{moles of solute}}{\text{liters of solution}}\]

Step 2: Convert volume from mL to L

We are given 150 mL of solution, so we need to convert it to liters: \[150 \mathrm{~mL} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}} = 0.15 \mathrm{~L}\]

Step 3: Calculate the molarity

Now, we can plug in the values into the formula: \[M = \frac{0.175 \mathrm{~mol}}{0.15 \mathrm{~L}} = 1.17 \mathrm{~M}\] The molarity of the ZnCl2 solution is 1.17 M. (b) Find the moles of HCl in the solution

Step 1: Write down the formula to find moles

We can rewrite the molarity formula as: \[\text{moles of solute} = M \times \text{liters of solution}\]

Step 2: Convert volume from mL to L

We are given 35.0 mL of solution, so we need to convert it to liters: \[35.0 \mathrm{~mL} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}} = 0.035 \mathrm{~L}\]

Step 3: Calculate the moles of HCl

Now, we can plug in the values into the formula: \[\text{moles of HCl} = 4.50 \mathrm{~M} \times 0.035 \mathrm{~L} = 0.158 \mathrm{~mol}\] There are 0.158 mol of HCl in the solution. (c) Find the volume of NaOH solution needed

Step 1: Write down the formula to find volume

We can rewrite the molarity formula as: \[\text{liters of solution} = \frac{\text{moles of solute}}{M}\]

Step 2: Calculate the volume of NaOH solution

Now, we can plug in the values into the formula: \[\text{liters of solution} = \frac{0.325 \mathrm{~mol}}{6.00 \mathrm{~M}} = 0.0542 \mathrm{~L}\]

Step 3: Convert volume from L to mL

We need to convert the volume from liters to milliliters: \[0.0542 \mathrm{~L} \times \frac{1000 \mathrm{~mL}}{1 \mathrm{~L}} = 54.2 \mathrm{~mL}\] We need 54.2 mL of 6.00 M NaOH solution to provide 0.325 mol of NaOH.

Key Concepts

Mole Concept

Understanding the mole concept is fundamental to chemistry and is essential for calculating the quantity of substance involved in chemical reactions. A mole is a unit that measures the amount of a substance based on the number of particles it contains, specifically Avogadro's number, which is approximately 6.022 x 10²³ particles. It's similar to using a 'dozen' to count eggs, but for atoms, molecules, or ions in chemistry.

For instance, when we say there are 0.175 moles of ZnCl₂, we are actually referring to 0.175 times Avogadro's number of ZnCl₂ formula units. To relate moles to something measurable, we often convert moles to mass using the molar mass of a compound, or in the case of solutions, we work out the concentration of the solute present in a given volume of solvent, leading us to molarity calculations.

Solution Concentration

Solution concentration represents the amount of solute dissolved in a specific amount of solvent, and it is critical for quantifying the strength of a solution. Molarity (M) is a common unit of concentration in chemistry, defined as moles of solute per liter of solution. To calculate molarity, you need to know the amount of solute in moles and the volume of the solution in liters.

For example, when calculating the molarity of a ZnCl₂ solution with 0.175 moles of ZnCl₂ in 150 mL of solution, you'd convert the volume to liters (0.150 L) and then use the molarity formula:
M = \( \frac{0.175 \, \mathrm{mol}}{0.150 \, \mathrm{L}} = 1.17 \, \mathrm{M} \). Understanding molarity is key when preparing solutions in a lab setting or conducting reactions that require precise concentrations.

Stoichiometry

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is based on the conservation of mass and the stoichiometric coefficients found in balanced chemical equations. This concept allows chemists to predict the amount of substances consumed and created in a reaction.

When we are given the amount of one substance, such as the 0.325 moles of NaOH in a stoichiometric calculation, stoichiometry helps us determine how much of another substance is needed or produced. For example, using the molarity formula, we find out how many milliliters of a 6.00 M NaOH solution are necessary to provide the stated amount of NaOH. By mastering stoichiometry, students can solve complex problems in chemistry that involve multiple reactants and products, reactant excess and limiting reagents, as well as yield and purity of the substances involved.