Question

Calculate the molarity of each of the following solutions: (a) \(6.57 \mathrm{~g}\) of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) in \(1.50 \times 10^{2} \mathrm{~mL}\) of solution, (b) \(10.4 \mathrm{~g}\) of calcium chloride \(\left(\mathrm{CaCl}_{2}\right)\) in \(2.20 \times 10^{2} \mathrm{~mL}\) of solution, \((\mathrm{c}) 7.82 \mathrm{~g}\) of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) in \(85.2 \mathrm{~mL}\) of benzene solution.

Short answer

(a) 1.37 M, (b) 0.426 M, (c) 0.716 M.

Step-by-step solution

Understanding Molarity

Molarity is the concentration of a solution expressed as the number of moles of solute per liter of solution. It is calculated using the formula:\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \] where \( M \) is the molarity.

Calculating Moles of Methanol

First, calculate the moles of methanol \( (\mathrm{CH}_3\mathrm{OH}) \) in part (a). The molar mass of methanol is approximately \( 32.04 \, \text{g/mol} \). Use the formula:\[ \text{moles of } \mathrm{CH}_3\mathrm{OH} = \frac{6.57 \, \text{g}}{32.04 \, \text{g/mol}} \] This gives approximately \( 0.205\text{ moles}. \)

Converting Solution Volume for Methanol

Convert the solution volume from milliliters to liters for methanol. Given that the solution volume is \( 1.50 \times 10^2 \, \text{mL} \), convert this to liters by dividing by 1000, resulting in \( 0.150 \, \text{L}. \)

Calculating Molarity of Methanol Solution

Now calculate the molarity using the moles of methanol and the volume in liters:\[ M = \frac{0.205 \, \text{moles}}{0.150 \, \text{L}} = 1.37 \, \text{M} \] Thus, the molarity of the methanol solution is \( 1.37 \, \text{M}. \)

Calculating Moles of Calcium Chloride

For part (b), calculate the moles of calcium chloride \( (\mathrm{CaCl}_2) \). The molar mass of \( \mathrm{CaCl}_2 \) is approximately \( 110.98 \, \text{g/mol} \). Use the formula:\[ \text{moles of } \mathrm{CaCl}_2 = \frac{10.4 \, \text{g}}{110.98 \, \text{g/mol}} \] This gives approximately \( 0.0937\text{ moles}. \)

Converting Solution Volume for Calcium Chloride

Convert the solution volume from milliliters to liters for calcium chloride. The solution volume is \( 2.20 \times 10^2 \, \text{mL} \), equivalent to \( 0.220 \, \text{L}. \)

Calculating Molarity of Calcium Chloride Solution

Calculate the molarity of the calcium chloride solution:\[ M = \frac{0.0937 \, \text{moles}}{0.220 \, \text{L}} = 0.426 \, \text{M} \] Therefore, the molarity of the calcium chloride solution is \( 0.426 \, \text{M}. \)

Calculating Moles of Naphthalene

For part (c), calculate the moles of naphthalene \( (\mathrm{C}_{10}\mathrm{H}_8) \). The molar mass of naphthalene is approximately \( 128.17 \, \text{g/mol} \). Use the formula:\[ \text{moles of } \mathrm{C}_{10}\mathrm{H}_8 = \frac{7.82 \, \text{g}}{128.17 \, \text{g/mol}} \] This yields approximately \( 0.0610 \, \text{moles}. \)

Converting Solution Volume for Naphthalene

Convert the solution volume from milliliters to liters for naphthalene. The solution volume is \( 85.2 \, \text{mL} \), which is \( 0.0852 \, \text{L}. \)

Calculating Molarity of Naphthalene Solution

Finally, calculate the molarity of the naphthalene solution:\[ M = \frac{0.0610 \, \text{moles}}{0.0852 \, \text{L}} = 0.716 \, \text{M} \] Thus, the molarity of the naphthalene solution is \( 0.716 \, \text{M}. \)

Key concepts

Concentration

Concentration is a term used in chemistry to describe the amount of a substance (solute) present in a certain quantity of solution or solvent. It tells us how 'crowded' the substance is within the solution. One common way to express concentration is through **molarity**. Molarity is particularly useful because it relates to the mole concept, which is a fundamental measurement in chemistry. Keeping track of concentration is crucial in chemical reactions as it affects their rate and equilibrium position.

• **Units**: Molarity (M) is expressed in moles of solute per liter of solution.
• **Effect of Concentration**: Changes in concentration can lead to different reaction paths or speeds, so precise control is often necessary in experimental settings.

Understanding concentration helps chemists to predict how substances interact and react in varying scenarios.

Solution Chemistry

Solution chemistry deals with how substances dissolve and interact on a molecular level. Solutions are homogeneous mixtures of two or more substances.

• **Solute**: The substance that is dissolved.
• **Solvent**: The substance, often a liquid, in which the solute is dissolved.
• **Factors Influencing Solubility**: Temperature, pressure, and the nature of the solute and solvent.

Solutions can exist in various states of matter - gas, liquid, or solid. The process of dissolution involves the breaking of intermolecular forces within the solute and solvent and the formation of new interactions between them. This varies based on the chemical nature of the involved substances, affecting the ease with which the solute dissolves.

Moles Calculation

Calculating moles is an essential step in finding molarity. The mole is a basic unit in chemistry that represents a specific number (Avogadro's number) of particles, typically atoms or molecules. One mole corresponds to approximately \(6.022 \times 10^{23}\) entities. This makes it a very practical way to count particles in chemistry.
To calculate the number of moles, use the formula:

\[ ext{moles} = \frac{ ext{mass of substance (g)}}{ ext{molar mass (g/mol)}} \]
Here, the molar mass is the mass of one mole of a substance and it’s usually found on the periodic table. For example, to convert 6.57 g of methanol ( \(\mathrm{CH_3OH}\) ) to moles, you need to know its molar mass, which is approximately 32.04 g/mol. By plugging these values into the formula, you find the moles of methanol.

Volume Conversion

Volume conversion is fundamental when dealing with solutions in chemistry, particularly when calculating molarity. Since molarity involves liters, it's often necessary to convert other units of volume such as milliliters to liters.

• **Conversion Formula**: 1 liter (L) = 1000 milliliters (mL)
• **Conversion Strategy**: Divide the number of milliliters by 1000 to convert to liters.

For instance, if you have a solution volume of \(150 \, ext{mL}\), it converts to \(0.150 \, ext{L}\) by dividing by 1000. This conversion is vital in calculating molarity because it ensures the volume of the solution is in the correct units needed for the equation \( M = \frac{ ext{moles of solute}}{ ext{liters of solution}} \). Proper volume conversion ensures accuracy in concentration calculations.