Danial N. answered 01/05/21
Experienced MCAT Tutor/Medical Student| 97th percentile MCAT scores
This is testing if you understand Avogadro's number, molecular weight, and the concept molar mass.
165x10^6 tons is the same as writing 1.65 x 10^8 tons (always use scientific notation)
Now we do a unit conversion:
1.65 x 10^8 tons x 1000 kg/ton = 1.65 x 10^11 kg (the unit "tons" cancels out)
We need to convert the number of kilograms into the number of moles. 1 mole is defined as being equal to 6.022×10^23 particles/atoms/molecules (this is analogous to how a "dozen" means 12)
To convert kg into moles we need the molecular weight of the substance, in this case H2SO4. To calculate the MW of H2SO4 we must take the atomic weight of each constituent (from the periodic table) of the compound and add them together.
Molecular weight H2SO4 =
Hydrogen (amu = 1.01)
Sulfur (amu = 32.06)
Oxygen (amu = 15.9994)
but remember we have 2 Hydrogens, 1 sulfur, and 4 oxygens so we must multiply each amu by the amount of each atom present in the compound:
Hydrogen (amu = 1.01) x 2 = 2.02
Sulfur (amu = 32.06) x1 = 32.06
Oxygen (amu = 15.9994) x 4 = 63.976
2.02 + 32.06 + 63.976 = 98.052 so we'll just round that to 98 g/mol. It's important to note here that Molecular Weight and Molar Mass are confusing terms. Molecular weight refers the mass of a molecule of a particular substance. Molar mass refers to mass of a mole of a particular substance. However, their numerical value ends up being the same. The units for MM or MW are grams per mole or g/mol.
Now we have 98 g/mol of H2SO4. Remember we have 1.65 x 10^11 kg of H2SO4. In order to determine the number of molecules are in 1.65 x 10^11 kg of H2SO4 we need to figure out how many moles of H2SO4 there are in that many kilograms. We need to make our units the same so let's convert kilograms of H2SO4 into grams. (1000 grams in a kilogram)
1.65x10^11 kg x 1000 grams/kilogram = 1.65 x 10^14 grams H2SO4.
Now we can finally answer the question how many molecules of H2SO4 are released.
The formula for the conversion between Molar Mass, moles, and mass is as follows:
n = m ÷ M
moles = mass ÷ molar mass
m = n × M
mass = moles × molar mass
where n is moles, m is mass and M is molar mass
Let's plug in and solve for moles:
n = 1.65 x 10^14 grams/H2SO4 ÷ 9.8 x 10^1 g/mol = 1.6836734693878 × 1012 moles
Last step: multiply the number of moles by avogadro's number to determine number of molecules:
1.6836734693878 × 10^12 moles x 6.022 x 10^23 = 1.0139081632653 × 1036