To answer this question, you must understand how to convert grams of a molecule into the number of molecules. To do this, you have to utilize the concepts of moles and molar mass.
A mole is just a unit of measurement. Avogadro's number is equal to 6.022*10^236.022⋅1023 molecules/mole. This number is the number of molecules of a specific compound in which when you multiply the compound by it, it converts atomic mass into grams.
For example, one mole of hydrogen gas (H_2H2) or 6.022*10^236.022⋅1023 molecules of H_2H2 weighs 2.016 grams because one molecule of H_2H2 has an atomic weight of 2.016.
So the overall solution for this problem is to use molar mass of CH_4CH4 (methane) to convert grams of methane into moles of methane. Then, use Avogadro's number to convert moles of methane into molecules of methane.
One mole of methane equals 16.04 grams because a molecule of methane has an atomic weight of 16.04. The conversion factor will be 16.04 grams/mole.
48g CH_4*(1 mol CH_4)/(16.04 g CH_4)* (6.022*10^23 mcls CH_4)/(1 mol CH_4) 48gCH4⋅1molCH416.04gCH4⋅6.022⋅1023mclsCH41molCH4
When you multiple and divide everything out, you get 1.8021 *10^241.8021⋅1024 molecules of CH_4CH4
Notice this is a modified T-chart so the grams CH_4CH4 cancels out when you do the first conversion, and the moles CH_4CH4 cancels out when you do the second conversion. This leaves you with the unit molecules of CH_4CH4 which corresponds to what the question asks.
