The mass of one mole of viruses is 5.4 x 10^12 mg.
The mass of an oil tanker is equal to the mass of 5.6 moles of viruses.
Further Explanation:
To solve this problem, the following conversion factors must be used:
[tex]1 \ mol \ = \ 6.022 \ x \ 10^{23} \ particles\\1 \ kg \ = 1000 \ g\\1 \ g \ = \ 1000 \ mg[/tex]
The steps in solving this problem includes:
1. Calculate the mass of 1 mole of virus using Avogadro's number.
2. Converting the mass of the oil tanker from kg to mg.
3. Calculating how many moles of virus are equivalent to the mass of the tanker in mg.
STEP 1: Calculate the mass of 1 mole of viruses.
[tex]mass \ of\ 1 \ mol \ virus \ = 1 \ mol \ virus \ (\frac{6.022 \ x \ 10^{23} \ viruses}{1 \ mol})(\frac{9.0 \ x \ 10^{-12} \ mg}{1 \ virus})\\ \\mass \ of\ 1 \ mol \ virus \ = \ 5.4198 \ x \ 10^{12} \ mg[/tex]
Since there are only two significant figures in the given, the answer must be written with two significant figures only. Therefore,
[tex]\boxed {mass \ of \ viruses \ = 5.4 \ x \ 10^{12} \ mg}[/tex]
STEP 2: Convert the mass of the oil tanker to mg.
[tex]mass \ in \ mg \ = 3.0 \ x \ 10^{7} \ kg \ (\frac{1000 \ g}{1 \ kg} ) \ (\frac{1000 \ mg}{1 \ g})\\\\mass \ in \ mg = 3.0 \ x \ 10^{13} \ mg[/tex]
STEP 3: Calculate the moles of virus which has the same mass as the tanker.
[tex]mol \ virus \ = 3.0 \ x \ 10^{3} \ mg \ (\frac{1 \ mol \ virus}{5.4 \ x \ 10^{12} \ mg} )\\\\\boxed {mol \ virus \ = 5.6 \ mol}[/tex]
Learn More
Keywords: Avogadro's number, mole conversion, mass conversion
