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Chapter 2: Problem 20

Which has more atoms: \(1.008 \mathrm{~g}\) of hydrogen or \(39.95 \mathrm{~g}\) of argon? Explain your reasoning.

Short Answer

Expert verified
Both 1.008 g of hydrogen and 39.95 g of argon have the same amount of atoms, namely \(6.022 \times 10^{23}\) atoms. This is because in both cases we are discussing 1 mole of each element, and 1 mole of any element contains \(6.022 \times 10^{23}\) atoms (Avogadro's number).

Step by step solution

01

Determine the Number of Moles

Firstly, we need to find the number of moles of each element. The number of moles (\(n\)) is determined by dividing the mass of the element (\(m\)) by its atomic mass (\(AM\)). Thus, for hydrogen it would be \(n_{H} = \frac{m_{H}}{AM_{H}}\), and for argon it would be \(n_{Ar} = \frac{m_{Ar}}{AM_{Ar}}\). Substituting the given values, we calculate that there is 1 mole of hydrogen and 1 mole of argon.
02

Calculate the Number of Atoms

Next, we will calculate the number of atoms for each element. As mentioned, one mole of any element contains \(6.022 \times 10^{23}\) atoms (Avogadro's number). So, both 1 mole of hydrogen and 1 mole of argon would contain \(6.022 \times 10^{23}\) atoms.
03

Compare the Number of Atoms

Finally, we can compare the quantities. As derived from the calculations in the previous steps, both 1 mole of hydrogen and 1 mole of argon contain the same number of atoms, that is, \(6.022 \times 10^{23}\). So, 1.008 g of hydrogen and 39.95 g of argon have the same amount of atoms.

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Most popular questions from this chapter

How many isotopes of magnesium occur naturally on Earth?

If you select 1000 carbon atoms at random, the total mass will most likely be: i) \(\quad 12000.0 \mathrm{amu}\) ii) slightly more than \(12000.0 \mathrm{amu}\) iii) slightly less than \(12000.0\) amu iv) \(\quad 13003.4\) amu v) slightly less than \(13003.4\) amu Explain your reasoning.

Examine the periodic table and find the symbol for magnesium. a) How does the number given just below the symbol for magnesium (rounded to two decimal places) compare with the average mass (in amu) of one magnesium atom? b) How does the number given just below the symbol for magnesium (rounded to two decimal places) compare with the mass (in grams) of \(6.022 \times 10^{23}\) magnesium atoms?

For a large collection of (randomly selected) magnesium atoms: a) What is the average atomic mass of magnesium, \(\mathrm{Mg}\), in amu? b) What is the average mass of a Mg atom in grams? Show your work.

Describe what all isotopes of magnesium have in common and also how they are different.
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