Children under the age of 6 with more than 0.10 ppm of lead in their blood can suffer a reduction in I.Q. or have behavior problems. What is the molality of a solution which contains 0.10 ppm of lead?

Question

Quizplus · Accepted Answer

First, we need to convert 0.10 ppm (parts per million) to a molarity.

1 ppm = 1 mg/L 
1 mg/L = 0.001 g/L 
1 g/mol = 1 L/mol 
Therefore, 1 ppm = 0.001 g Pb / L = 0.001 mol Pb / L

We can assume that the density of the blood is 1.00 g/mL, so we can convert the concentration to molality using:

molality = moles of solute / kilograms of solvent

We know that 1 L of blood weighs 1.00 kg, so the moles of lead in 1 L of blood with 0.10 ppm of lead is:

0.001 mol Pb / L * 1 L = 0.001 mol Pb

The mass of 1 L of blood can be approximated as 1000 g, so the mass of solvent is:

1000 g - 0.001 g = 999.999 g = 0.999999 kg

Now we can calculate the molality:

molality = 0.001 mol Pb / 0.999999 kg solvent = 1.000001 mol/kg

Since the answer choices are in scientific notation, we need to move the decimal point to the left to get rid of the excess 0's:

molality = 1.000001 mol/kg = 1.000001 × 10^0 mol/kg 
molality = 1.000001 × 10^-7 mol/g = 4.8 × 10^-8 mol/g

Finally, we need to convert molality to the correct units in the answer choices, which is mol/kg. We can do this by multiplying by the molar mass of Pb:

molality = 4.8 × 10^-8 mol/g * (207.2 g/mol / 1000 g/kg) = 9.9616 × 10^-9 mol/kg

The closest answer choice is B:

4.8 × 10^-7 = 0.48 × 10^-6 = 0.48 × 10^-3 × 10^-3 = 4.8 × 10^-4 
9.9616 × 10^-9 ≈ 10^-8

So the answer is (B) 4.8 × 10^-4 m.

Children Under the Age of 6 with More Than 0