To tackle the problem of chloroform contamination in drinking water, we need to break it down into two parts: converting the concentration from parts per million (ppm) to percent by mass, and then calculating the molality of chloroform in the water sample. Let’s go through each step carefully.
Converting ppm to Percent by Mass
Parts per million (ppm) is a way of expressing very dilute concentrations of substances. In this case, 15 ppm means there are 15 grams of chloroform in 1,000,000 grams of water. To convert this to percent by mass, we can use the following relationship:
- 1 percent by mass = 10,000 ppm
Now, we can convert 15 ppm to percent by mass:
Calculation:
Percent by mass = (ppm / 10,000) = (15 ppm / 10,000) = 0.0015
To express this as a percentage, we multiply by 100:
0.0015 × 100 = 0.15%
Result:
The concentration of chloroform in the water sample is 0.15% by mass.
Calculating Molality of Chloroform
Next, we need to determine the molality of chloroform in the water sample. Molality (m) is defined as the number of moles of solute per kilogram of solvent. Here, chloroform is the solute, and water is the solvent.
First, we need to find the number of moles of chloroform in the sample. To do this, we need the molar mass of chloroform (CHCl3):
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.01 g/mol
- Chlorine (Cl): 35.45 g/mol × 3 = 106.35 g/mol
Molar mass of CHCl3:
12.01 + 1.01 + 106.35 = 119.37 g/mol
Now, we can calculate the number of moles of chloroform in 15 grams:
Calculation:
Moles of CHCl3 = mass (g) / molar mass (g/mol) = 15 g / 119.37 g/mol ≈ 0.125 moles
Next, we need to find the mass of the solvent (water) in kilograms. Since we have 1,000,000 grams of water (the total mass of the solution), we can calculate the mass of water as follows:
Mass of water = 1,000,000 g - 15 g = 999,985 g
Convert this to kilograms:
999,985 g = 999.985 kg
Now we can calculate the molality:
Calculation:
Molality (m) = moles of solute / mass of solvent (kg) = 0.125 moles / 0.999985 kg ≈ 0.125 m
Final Answer:
The molality of chloroform in the water sample is approximately 0.125 mol/kg.
In summary, we found that the concentration of chloroform in the water is 0.15% by mass, and the molality is about 0.125 mol/kg. This process illustrates how to convert between different concentration units and calculate molality, which is essential in understanding the behavior of solutions in chemistry.
