Calculate the mass of Cr(ClO2)2 that contains 5.57 × 10
^22 chlorine atoms.

Explanation:

Your strategy here will be to

use the chemical formula of carbon dioxide to find the number of molecules of

CO

2

that would contain that many atoms of oxygen

use Avogadro's constant to convert the number of molecules to moles of carbon dioxide

use the molar mass of carbon dioxide to convert the moles to grams

So, you know that one molecule of carbon dioxide contains

one atom of carbon,

1

×

C

two atoms of oxygen,

2

×

O

This means that the given number of atoms of oxygen would correspond to

4.8

⋅

10

22

atoms O

⋅

1 molecule CO

2

2

atoms O

=

2.4

⋅

10

22

molecules CO

2

Now, one mole of any molecular substance contains exactly

6.022

⋅

10

22

molecules of that substance -- this is known as Avogadro's constant.

In your case, the sample of carbon dioxide molecules contains

2.4

⋅

10

22

molecules CO

2

⋅

1 mole CO

2

6.022

⋅

10

23

molecules CO

2

=

0.03985 moles CO

2

Finally, carbon dioxide has a molar mass of

44.01 g mol

−

1

, which means that your sample will have a mass of

0.03985

moles CO

2

⋅

44.01 g

1

mole CO

2

=

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

a

a

1.8 g

a

a

∣

∣

−−−−−−−−−

The answer is rounded to two sig figs, the number of sig figs you have for the number of atoms of oxygen present in the sample.