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Chapter 3: Problem 17

Lead is a heavy metal that remains in the bloodstream, causing mental retardation in children. It is believed that \(3 \times 10^{-7} \mathrm{~g}\) of \(\mathrm{Pb}\) in \(1.00 \mathrm{~mL}\) of blood is a health hazard. For this amount of lead (a) how many atoms of lead are there in one \(\mathrm{mL}\) of a child's blood? (b) how many moles of lead are in \(1.00 \mathrm{~L}\) of blood?

Short Answer

Expert verified
Question: In 1 mL of a child's blood, there are \(3 \times 10^{-7}\mathrm{~g}\) of lead. Calculate the following: a) The number of lead atoms in this 1 mL sample. b) The number of moles of lead in 1 L (1000 mL) of blood. Answer: a) The number of lead atoms in 1 mL of blood is \((3 \times 10^{-7} \mathrm{~g})/(207.2 \mathrm{~g/mol}) \times 6.022 \times 10^{23}\mathrm{~atoms/mol}\). b) The number of moles of lead in 1 L of blood is \(((3 \times 10^{-7}\mathrm{g/mL})(1\ 000\mathrm{~mL}))/(207.2 \mathrm{~g/mol})\).

Step by step solution

01

Convert mass of lead to moles

To convert the mass of lead to moles, we can use the equation: moles = mass of substance / molecular weight In this case, the mass of lead in 1 mL of blood is \(3 \times 10^{-7} \mathrm{~g}\), and the molecular weight of lead is 207.2 g/mol. So, moles of lead in 1 mL of blood is: moles = \((3 \times 10^{-7} \mathrm{~g})/(207.2 \mathrm{~g/mol})\)
02

Calculate the number of lead atoms

Once we have the moles of lead, we can calculate the number of lead atoms by using Avogadro's number: Number of lead atoms = moles x Avogadro's number Now, let's calculate the number of lead atoms in 1 mL of a child's blood. Number of lead atoms = \((3 \times 10^{-7} \mathrm{~g})/(207.2 \mathrm{~g/mol}) \times 6.022 \times 10^{23}\mathrm{~atoms/mol}\) #b) Finding the number of moles in 1 L of blood#
03

Calculate the mass of lead in 1 L of blood

Since there are 1000mL in 1 L, the mass of lead in 1 L is 1000 times the mass in 1mL: mass of lead in 1 L = \((3 \times 10^{-7}\mathrm{g/mL})(1\ 000\mathrm{~mL})\)
04

Convert mass of lead in 1 L to moles

Using the same method as in part (a), we can convert the mass of lead in 1 L to the number of moles using the equation: moles in 1 L = mass of lead in 1 L / molecular weight of lead moles in 1 L = \(((3 \times 10^{-7}\mathrm{g/mL})(1\ 000\mathrm{~mL}))/(207.2 \mathrm{~g/mol})\)

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