Question

Suppose you wanted to know how many grams of KCl would be left if 350 mL of a 2.0 M KCl solution were evaporated to dryness. a. What is the molar mass of KCl? b. How would heating the solution affect the mass of KCl remaining? c. How many grams of KCl would remain?

Short answer

The molar mass of KCl is 74.6 g/mol. Heating the solution evaporates the water, leaving 52.22 grams of KCl.

Step-by-step solution

Find the Molar Mass of KCl

To find the molar mass of KCl, add the atomic masses of potassium (K) and chlorine (Cl). The atomic mass of K is approximately 39.1 g/mol, and the atomic mass of Cl is approximately 35.5 g/mol. So, the molar mass of KCl is: \[ 39.1 \text{ g/mol} + 35.5 \text{ g/mol} = 74.6 \text{ g/mol} \]

Determine the Moles of KCl in Solution

Use the molarity formula to find the moles of KCl in the solution. Molarity (M) is defined as moles of solute per liter of solution. The given solution has a volume (V) of 350 mL or 0.350 L and a molarity (M) of 2.0 M. Using the formula: \[ \text{Moles} = M \times V \]the moles of KCl are: \[ \text{Moles of KCl} = 2.0 \text{ M} \times 0.350 \text{ L} = 0.7 \text{ moles} \]

Convert Moles of KCl to Grams

To find the mass of KCl in grams, use the molar mass. The relationship between moles, molar mass, and mass is given by: \[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \]Thus, the mass of KCl is: \[ \text{Mass of KCl} = 0.7 \text{ moles} \times 74.6 \text{ g/mol} = 52.22 \text{ grams} \]

Effect of Heating Solution

Heating the solution causes the water to evaporate. Only the solvent (water) vanishes, while the solute (KCl) remains. This leaves all the KCl initially in the solution as a solid residue.

Key concepts

Molar Mass Calculation

Calculating the molar mass of a compound is fundamental in stoichiometry. The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). To find the molar mass of a compound, you'll need to add up the atomic masses of each element in the compound as listed on the periodic table.
In the given exercise, we calculated the molar mass of potassium chloride (KCl). The atomic mass of potassium (K) is approximately 39.1 g/mol, and the atomic mass of chlorine (Cl) is approximately 35.5 g/mol. Hence, the molar mass of KCl is: \[ 39.1 \text{ g/mol} + 35.5 \text{ g/mol} = 74.6 \text{ g/mol} \].
Knowing the molar mass allows us to convert between the mass of a substance and the amount in moles, which is crucial for solving many chemistry problems.

Molarity and Solutions

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution and is denoted by the letter M.
The formula for molarity (\text{M}) is: \[ \text{M} = \frac{\text{moles of solute}}{\text{liters of solution}} \].
In the problem, we have a 2.0 M solution of KCl and a volume of 350 mL, which we convert to liters: \[0.350 \text{ L} \]. To determine the moles of KCl, we use the molarity formula: \[ \text{Moles of KCl} = 2.0 \text{ M} \times 0.350 \text{ L} = 0.7 \text{ moles} \].
This shows how when you know the molarity and the volume of a solution, you can easily find the number of moles of the solute present in the solution, which is critical for the next steps.

Evaporation and Solute Concentration

Evaporation affects the solvent in a solution but leaves the solute unchanged in mass. When you heat a solution, such as an aqueous KCl solution, the water molecules (solvent) evaporate. However, all the solute (KCl) remains.
Therefore, when a solution evaporates to dryness, we're left with the solute originally dissolved in the solution. In our case, heating the 350 mL of 2.0 M KCl solution will evaporate all the water but leave 0.7 moles of KCl as a solid residue.
This concept is important in practical situations to determine the quantity of leftover substances after evaporation.

Chemical Quantities

Understanding chemical quantities involves conversions between mass, moles, and solution concentrations. These conversions rely on the molar mass of substances and concepts like molarity.
To find how many grams of KCl would remain after evaporation, we need to convert the moles of KCl to grams using the molar mass calculated earlier: \[ \text{Mass of KCl} = 0.7 \text{ moles} \times 74.6 \text{ g/mol} = 52.22 \text{ grams} \].
This calculation shows that the amount of KCl left is solely dependent on the initial concentration and volume of the solution, which can be meticulously controlled and predicted using stoichiometric principles.
These processes highlight why it's crucial to understand the relationship between moles, molarity, and mass to handle chemical substances accurately.