Question

Calculate the molarity of each of the following solutions. (a) \(122 \mathrm{~g}\) of acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\), in \(1.00 \mathrm{~L}\) of solution (b) \(185 \mathrm{~g}\) of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), in \(1.00 \mathrm{~L}\) of solution (c) \(70.0 \mathrm{~g}\) of hydrogen chloride, \(\mathrm{HCl}\), in \(0.600 \mathrm{~L}\) of solution (d) \(45.0 \mathrm{~g}\) of potassium hydroxide, \(\mathrm{KOH}\), in \(250.0 \mathrm{~mL}\) of solution

Short answer

The molarity of each solution is: \n(a) 2.03 M, \n(b) 0.54 M, \n(c) 3.20 M, \n(d) 3.20 M

Step-by-step solution

Convert the weights into moles

Moles are calculated using the equation moles = mass/molar mass. Molar mass is the sum of the atomic masses for the atoms in the compound. For example, for acetic acid (\(CH_3CO_2H\)), the molar mass is 12.01 g/mol (for each of the 2 carbon atoms) + 1.01 g/mol (for each of the 4 hydrogen atoms) + 16.00 g/mol (for each of the 2 oxygen atoms), totaling 60.05 g/mol. We thus have: \n \((a) 122 g / 60.05 g/mol = 2.03 mol\), \((b) 185 g / 342.30 g/mol = 0.54 mol\), \((c) 70.0 g / 36.46 g/mol = 1.92 mol\), \((d) 45.0 g / 56.11 g/mol = 0.80 mol\)

Convert liters into correct unit and calculate Molarity

To find molarity, we divide the number of moles by the volume of the solution in liters. It's important to convert milliliters (mL) to liters (L) by dividing by 1000. Thus we have \n \((a) Molarity = 2.03 mol / 1.00 L = 2.03 M\), \((b) Molarity = 0.54 mol / 1.00 L = 0.54 M\), \((c) Molarity = 1.92 mol / 0.600 L = 3.20 M\), \((d) Molarity = 0.80 mol / 0.250 L = 3.20 M\)

Key concepts

Mole-to-Mass Conversion

Understanding the mole-to-mass conversion is crucial for many chemistry calculations. The mole is a standard unit in chemistry that quantifies the amount of a substance. One mole is equal to Avogadro's number (\(6.022 \times 10^{23}\) entities), whether atoms, molecules, ions, or electrons.

When dealing with mole-to-mass conversion, it's essential to use the molar mass of the compound as a conversion factor. The molar mass is typically expressed in grams per mole (g/mol) and can be found by adding the atomic masses of each element in the compound, considering the number of atoms of each present. Once you have the molar mass, you can convert grams to moles by dividing the given mass by the molar mass of the substance.

Molar Mass Determination

Determining the molar mass of a compound involves summing the masses of all the atoms in a molecule. The periodic table provides the atomic mass of each element, usually in atomic mass units (amu). To find the molar mass, these values need to be multiplied by the number of each type of atom in the molecule, then all added together.

For instance, in the molarity calculation problem, acetic acid (\(CH_3CO_2H\)) has a molar mass computed by adding twice the atomic mass of carbon, four times the atomic mass of hydrogen, and twice the atomic mass of oxygen. Knowing the precise molar mass is vital for converting between moles and mass, and subsequently for many other chemistry calculations.

Solution Concentration

Solution concentration is a measure of the amount of solute dissolved in a solvent. Among the ways to express concentration, molarity is commonly used and is defined as the number of moles of solute per liter of solution. To calculate molarity, divide the number of moles of the solute by the volume of the solution in liters. It's expressed in moles per liter (M), and it's important to remember to convert the volume into liters if it's given in another unit, like milliliters.

Understanding solution concentration is critical for tasks such as diluting solutions, precipitating reactions, and stoichiometric calculations. Clear grasping of this concept allows learners to approach complex problems with greater confidence.

Chemistry Problem Solving

Chemistry problem solving often involves a systematic approach to break down complex concepts into manageable steps. Key to this is understanding the relationship between different units and concepts, such as moles, mass, molar mass, volume, and concentration.

Practical problem-solving strategies include writing down known values, identifying the units required for the answer, and determining which conversions and formulas are necessary to get from one to the other. For instance, when calculating molarity, the problem-solving process involves determining the molar mass to convert mass to moles, ensuring volume is in the correct unit, and then applying the formula for molarity.

By mastering these fundamental processes, students gain the proficiency to tackle an array of chemistry problems, building a strong foundation for more advanced topics.