Math Snap

STEP 1

1. The mass of a single virus is $9.0 \times 10^{-12} \, \text{mg}$.
2. The mass of an oil tanker is $3.0 \times 10^{7} \, \text{kg}$.
3. Avogadro's number is $6.022 \times 10^{23}$ 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.
$$9.0 \times 10^{-12} \, \text{mg} = 9.0 \times 10^{-15} \, \text{kg}$$

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

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