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Chapter 8: Problem 47

From \(2 \mathrm{mg}\) calcium, \(1.2 \times 10^{19}\) atoms are removed. The number of g-atoms of calcium left is \((\mathrm{Ca}=40)\) (a) \(5 \times 10^{-3}\) (b) \(2 \times 10^{-3}\) (c) \(3 \times 10^{-3}\) (d) \(5 \times 10^{-6}\)

Short Answer

Expert verified
Answer: 3 × 10^{-5} g-atoms

Step by step solution

01

Convert mass of calcium to moles

First, we need to convert the given amount of calcium (2 mg) to moles, using the molar mass of calcium (40 g/mol). To do this, we'll first convert 2 mg to grams: 2 mg = 0.002 g Now, to find the moles of calcium: Moles = (mass of calcium) / (molar mass of Ca) Moles = (0.002 g) / (40 g/mol) Moles = 5 × 10^{-5} mol
02

Calculate the number of moles of removed atoms

Now, let's find out how many moles of atoms were removed. It is given that 1.2 × 10^{19} atoms were removed. We use Avogadro's number (6.022 × 10^{23} atoms/mol) to convert the number of atoms to moles: Moles of removed atoms = (number of atoms) / (Avogadro's number) Moles of removed atoms = (1.2 × 10^{19}) / (6.022 × 10^{23}) Moles of removed atoms = 2 × 10^{-5} mol
03

Find the number of moles left

Now we subtract the moles of removed atoms from the initial moles of calcium: Moles left = initial moles - moles removed Moles left = (5 × 10^{-5}) - (2 × 10^{-5}) Moles left = 3 × 10^{-5} mol
04

Convert moles left to gram-atoms

Now that we have the number of moles left, we can convert it to gram-atoms. One mole corresponds to one gram-atom, so: Number of g-atoms left = moles of calcium left Number of g-atoms left = 3 × 10^{-5} g-atoms The answer is (c) 3 × 10^{-3} g-atoms.

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