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Math  /  Numbers & Operations

QuestionUsing the Avogadro Number
A virus has a mass of 9.0×10−12mg9.0 \times 10^{-12} \mathrm{mg} and an oil tanker has a mass of 3.0×107 kg3.0 \times 10^{7} \mathrm{~kg}. Use this information to answer the questions below. Be sure your answers have the correct number of significant digits. \begin{tabular}{|l|l|} \hline What is the mass of 1 mole of viruses? & \\ Round your answer to 2 significant digits. & \\ \hline \begin{tabular}{l} How many moles of viruses have a mass equal to the mass \\ of an oil tanker? \end{tabular} & \\ Round your answer to 2 significant digits. & \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The mass of a single virus is 9.0×10−12 mg9.0 \times 10^{-12} \, \text{mg}.
2. The mass of an oil tanker is 3.0×107 kg3.0 \times 10^{7} \, \text{kg}.
3. Avogadro's number is 6.022×10236.022 \times 10^{23} particles/mole.
4. We need to convert units where necessary to ensure consistency.
5. The answers should be rounded to 2 significant digits.

STEP 2

1. Convert the mass of a virus to kilograms.
2. Calculate the mass of 1 mole of viruses.
3. Convert the mass of the oil tanker to milligrams.
4. Calculate the number of moles of viruses equivalent to the mass of the oil tanker.

STEP 3

Convert the mass of a virus from milligrams to kilograms.
9.0×10−12 mg=9.0×10−15 kg9.0 \times 10^{-12} \, \text{mg} = 9.0 \times 10^{-15} \, \text{kg}

STEP 4

Calculate the mass of 1 mole of viruses using Avogadro's number.
Mass of 1 mole of viruses=9.0×10−15 kg/virus×6.022×1023 viruses/mole\text{Mass of 1 mole of viruses} = 9.0 \times 10^{-15} \, \text{kg/virus} \times 6.022 \times 10^{23} \, \text{viruses/mole}

STEP 5

Perform the multiplication to find the mass of 1 mole of viruses.
=5.4198×109 kg/mole= 5.4198 \times 10^{9} \, \text{kg/mole}
Round to 2 significant digits:
=5.4×109 kg/mole= 5.4 \times 10^{9} \, \text{kg/mole}

STEP 6

Convert the mass of the oil tanker from kilograms to milligrams.
3.0×107 kg=3.0×1010 mg3.0 \times 10^{7} \, \text{kg} = 3.0 \times 10^{10} \, \text{mg}

STEP 7

Calculate the number of moles of viruses that have a mass equal to the mass of the oil tanker.
Number of moles=3.0×1010 mg9.0×10−12 mg/virus×6.022×1023 viruses/mole\text{Number of moles} = \frac{3.0 \times 10^{10} \, \text{mg}}{9.0 \times 10^{-12} \, \text{mg/virus} \times 6.022 \times 10^{23} \, \text{viruses/mole}}

STEP 8

Perform the division to find the number of moles.
=3.0×10105.4198×109= \frac{3.0 \times 10^{10}}{5.4198 \times 10^{9}}
=5.5×100 moles= 5.5 \times 10^{0} \, \text{moles}
Round to 2 significant digits:
=5.5 moles= 5.5 \, \text{moles}
The mass of 1 mole of viruses is:
5.4×109 kg/mole\boxed{5.4 \times 10^{9} \, \text{kg/mole}}
The number of moles of viruses that have a mass equal to the mass of the oil tanker is:
5.5 moles\boxed{5.5 \, \text{moles}}

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