A solution was prepared by dissolving 42.0 g of KCl in 225 g of water. Part A Calculate the mass percent of KCl in the solution. Part B Calculate the mole fraction of the ionic species KCl in the solution. Express the concentration numerically as a mole fraction in decimal form. Part C Calculate the molarity of KCl in the solution if the total volume of the solution is 239 mL.
The Correct Answer and Explanation is:
Part A: Mass Percent of KCl
Mass percent is defined as the mass of solute divided by the total mass of the solution, multiplied by 100%.
- Mass of KCl = 42.0 g
- Mass of water = 225 g
- Mass of solution = 42.0 g + 225 g = 267.0 g
Mass % of KCl=(42.0 g267.0 g)×100=15.7%\text{Mass \% of KCl} = \left( \frac{42.0\ \text{g}}{267.0\ \text{g}} \right) \times 100 = 15.7\%Mass % of KCl=(267.0 g42.0 g)×100=15.7%
Part B: Mole Fraction of KCl
To find the mole fraction, we convert grams to moles and divide the moles of KCl by the total moles of all species.
- Molar mass of KCl = 39.10 (K) + 35.45 (Cl) = 74.55 g/mol
- Moles of KCl = 42.0 g74.55 g/mol\frac{42.0\ \text{g}}{74.55\ \text{g/mol}}74.55 g/mol42.0 g = 0.5634 mol
- Molar mass of H₂O = 18.02 g/mol
- Moles of H₂O = 225 g18.02 g/mol\frac{225\ \text{g}}{18.02\ \text{g/mol}}18.02 g/mol225 g = 12.49 mol
Mole fraction of KCl=0.56340.5634+12.49=0.0433\text{Mole fraction of KCl} = \frac{0.5634}{0.5634 + 12.49} = 0.0433Mole fraction of KCl=0.5634+12.490.5634=0.0433
Part C: Molarity of KCl
Molarity (M) is defined as the moles of solute per liter of solution.
- Volume of solution = 239 mL = 0.239 L
- Moles of KCl = 0.5634 mol
Molarity=0.5634 mol0.239 L=2.36 M\text{Molarity} = \frac{0.5634\ \text{mol}}{0.239\ \text{L}} = 2.36\ \text{M}Molarity=0.239 L0.5634 mol=2.36 M
Explanation (300 words)
When working with solutions in chemistry, it is important to express concentration in various ways depending on the context. In this problem, we examine a solution of potassium chloride (KCl) dissolved in water and calculate three commonly used concentration units: mass percent, mole fraction, and molarity.
Mass percent gives the proportion of the solute by mass in the total solution. It is useful for quick estimations and practical mixing in the lab. To find this, we divide the mass of KCl (42.0 g) by the total mass of the solution (267.0 g) and multiply by 100. This yields a mass percent of 15.7%, meaning about 16% of the total solution’s mass is KCl.
Mole fraction is a dimensionless quantity that expresses the ratio of moles of one component to the total number of moles in the solution. This is particularly useful in thermodynamic calculations, such as those involving vapor pressure or colligative properties. First, we calculate the moles of KCl and water using their respective molar masses. The mole fraction of KCl turns out to be 0.0433, indicating that KCl represents just over 4% of the particles in the solution.
Molarity (mol/L) is one of the most common ways to express concentration, especially for reactions in aqueous solutions. Knowing the total volume of the solution (239 mL), we divide the number of moles of KCl by the volume in liters. This gives a molarity of 2.36 M, showing the solution is moderately concentrated.
Each of these measures gives insight into different properties of the solution and is selected depending on the experimental needs.
