Answer:
The mass of 35.6 moles of methane gas is 0.5696 kg.
Step-by-step explanation:
To solve the problem we need to start calculating the mass of 1 mole of methane (CH₄).
1st) Find the Molecular weight (Molar mass) of methane
Methane has 1 carbon atom and 4 hydrogen atoms, so we need to look for the atomic weight of these elemnts in the periodic table, and multiply them by the number of atoms in the molecule:
Carbon atomic weight + (4.Hydrogen atomic weight) = Methane molar mass
12 g/mol + (4.1 g/mol) = 16 g/mol
Up to here, we found the molar mass of methane, that means that 1 mol of methane weights 16 g.
2nd) Find the weight of 35.6 moles of methane
We can solve this by using the "Rule of three" thinking that if 1 mole of methane weighs 16 g, the 35.6 moles will weight "x" grams. The Rule of three is:
1 mol of methane ------------ 16 g
35.6 moles of methane ------------ x = (35.6 moles . 16 g)/ 1mol = 569.6 g
So, 35.6 moles of methane weight 569.6 g.
3rd) Convert the grams into kilograms
The relation between gram and kilogram is that 1000 g are equal to 1kg, so let's use this relation in a Rule of three:
1000 g ---------- 1 kg
569.6 g ---------- x = (569.6 g . 1 kg)/1000 g = 0.5696 kg
Finally, the mass of 35.6 moles of methane gas is 0.5696 kg.
Another option:
You can convert the 16g into kg first and you will reach the same final result.