Question

For each of the following solutions the mass of solute is given, followed by the total volume of solution prepared. Calculate the molarity. a. \(321 \mathrm{g}\) of \(\mathrm{CaCl}_{2} ; 1.45 \mathrm{L}\) b. \(4.21 \mathrm{mg}\) of \(\mathrm{NaCl} ; 1.65 \mathrm{mL}\) c. \(6.45 \mathrm{g} \mathrm{KBr} ; 125 \mathrm{mL}\) d. \(62.5 \mathrm{g} \mathrm{NH}_{4} \mathrm{NO}_{3} ; 7.25 \mathrm{L}\)

Short answer

a. \(1.995 \mathrm{M}\) b. \(0.0436 \mathrm{M}\) c. \(0.433 \mathrm{M}\) d. \(0.1075 \mathrm{M}\)

Step-by-step solution

Find the Molar Mass of Each Solute

We can find the molar mass of each solute using the periodic table. The molar mass is the sum of the atomic masses of each element in the compound. a. CaCl₂: \(1\times \mathrm{Ca} + 2 \times \mathrm{Cl} =40.08 + 2 \times 35.45 = 110.98 \mathrm{g/mol}\) b. NaCl: \(1\times \mathrm{Na} + 1 \times \mathrm{Cl} =22.99 + 35.45 = 58.44 \mathrm{g/mol}\) c. KBr: \(1\times \mathrm{K}+ 1\times \mathrm{Br} = 39.10 + 79.90 = 119.00 \mathrm{g/mol}\) d. NH₄NO₃: \(1\times \mathrm{N} + 4\times \mathrm{H} + 1\times\mathrm{N} + 1 \times \mathrm{O} + 3\times \mathrm{O} = 14.01 + 4 \times 1.01 + 14.01 + 16.00 + 3 \times 16.00 = 80.05 \mathrm{g/mol}\)

Convert Mass of Solute to Moles

We can now convert the mass of solute to moles by dividing the mass of solute by the molar mass. a. \(321 \mathrm{g}/110.98 \mathrm{g/mol} = 2.89 \mathrm{mol}\) b. \(4.21 \mathrm{mg} = 0.00421 \mathrm{g}; 0.00421 \mathrm{g}/58.44 \mathrm{g/mol} = 7.20 \times 10^{-5} \mathrm{mol}\) c. \(6.45 \mathrm{g}/119.00 \mathrm{g/mol} = 0.0542 \mathrm{mol}\) d. \(62.5 \mathrm{g}/80.05 \mathrm{g/mol} = 0.780 \mathrm{mol}\)

Calculate Molarity

Finally, we can calculate the molarity by dividing the moles of solute by the liters of solution. a. \(2.89\mathrm{mol} / 1.45 \mathrm{L} = 1.995 \mathrm{M}\) b. \(7.20 \times 10^{-5}\mathrm{mol} / 0.00165 \mathrm{L} = 0.0436 \mathrm{M}\) c. \(0.0542\mathrm{mol} / 0.125 \mathrm{L} = 0.433 \mathrm{M}\) d. \(0.780\mathrm{mol} / 7.25 \mathrm{L} = 0.1075 \mathrm{M}\) The molarity for each solution is: a. 1.995 M b. 0.0436 M c. 0.433 M d. 0.1075 M

Key concepts

Understanding Molar Mass Calculation

Molar mass is a key concept in chemistry that refers to the mass of one mole of a given substance. It is usually expressed in grams per mole (g/mol). To calculate it, you need the atomic masses of all the elements in the compound from the periodic table.
To find the molar mass of a compound, follow these steps:

• Identify all elements in the compound and their respective atomic masses. For example, Calcium (Ca) has an atomic mass of 40.08 g/mol.
• Multiply the atomic mass of each element by the number of times it appears in the compound. In CaCl₂, Chlorine (Cl) appears twice, so its contribution to the molar mass will be doubled.
• Add up all these values together to get the molar mass of the compound.

As seen in the original exercise, the molar mass of calcium chloride (CaCl₂) is calculated by adding the mass of 1 calcium atom and 2 chlorine atoms, resulting in 110.98 g/mol. This process is crucial for converting mass into moles, which is essential for determining solution concentration.

Deciphering Solution Concentration

Solution concentration is a measure of how much solute is present in a given volume of solution. Molarity (M) is the most common unit used to express concentration and is defined as moles of solute per liter of solution (mol/L).

• To calculate molarity, first determine the number of moles of solute. This is done by dividing the mass of the solute by its molar mass.
• Convert all volumes to liters as molarity uses liters in its computation. For example, 1.65 mL should be converted to 0.00165 L.
• Finally, divide the number of moles by the volume in liters to obtain molarity.

In the textbook example, the concentration of NaCl in a 1.65 mL solution is calculated as 0.0436 M. Knowing how to compute and express concentration is crucial for understanding chemical reactions and solution preparation.

Mastering Chemical Calculations

Chemical calculations involve converting between masses, moles, and concentration for substances in a solution. These are foundational skills in chemistry required for further study and practical applications.
Let's break down these steps:

• First, use the molar mass to convert the given mass of a solute to moles. This conversion allows you to frame chemical reactions in terms of reactants and products.
• Next, calculate how concentrated your solution is by finding its molarity. Concentration plays a critical role in determining how substances react with each other.
• Finally, different chemical calculations come into play, such as dilution equations and stoichiometry. These skills help to predict outcomes and manage resource usage while experimenting or manufacturing chemicals.

In the given exercise, understanding these calculations helps determine how much of each substance you have in your solution, guiding both practical applications and academic investigations.