. A typical polyethylene bag from a grocery store weighs
12.4 g. How many molecules of ethylene, C2H4, must be
polymerized to make such a bag?
To determine the number of molecules of ethylene (C2H4) required to make a polyethylene bag, we need to use the molar mass of ethylene and the molecular weight of the bag.
Let's start by calculating the molar mass of ethylene (C2H4):
C = 12.01 g/mol (atomic mass of carbon)
H = 1.01 g/mol (atomic mass of hydrogen)
Molar mass of C2H4 = (2 * C) + (4 * H) = (2 * 12.01) + (4 * 1.01) = 24.02 + 4.04 = 28.06 g/mol
Next, we need to calculate the number of moles of ethylene needed to make a polyethylene bag:
Given: Mass of polyethylene bag = 12.4 g
Molar mass of C2H4 = 28.06 g/mol
Number of moles = Mass / Molar mass = 12.4 g / 28.06 g/mol
Number of moles = 0.4414 mol
Finally, to determine the number of molecules, we can use Avogadro's number, which states that one mole of any substance contains 6.022 x 10^23 molecules:
Number of molecules of ethylene = Number of moles * Avogadro's number
Number of molecules of ethylene = 0.4414 mol * 6.022 x 10^23 molecules/mol
Number of molecules of ethylene = 2.6546 x 10^23 molecules
Therefore, approximately 2.6546 x 10^23 molecules of ethylene (C2H4) must be polymerized to make a typical polyethylene bag from a grocery store.
To determine the number of molecules of ethylene (C2H4) needed to make a polyethylene bag weighing 12.4 g, we need a few pieces of information:
1. The molar mass of ethylene (C2H4) - We need to know the total mass of one mole of C2H4. The molar mass can be found by adding up the atomic masses of all the atoms in the molecule: 2 carbon atoms (12 g/mol each) + 4 hydrogen atoms (1 g/mol each) = 28 g/mol.
2. Avogadro's number - This is a constant that represents the number of particles in one mole of a substance, which is approximately 6.022 x 10^23 molecules/mol.
Now, we can use the following steps to find the number of molecules:
Step 1: Calculate the number of moles of ethylene:
Number of moles = Mass of ethylene bag / Molar mass of ethylene
= 12.4 g / 28 g/mol
≈ 0.443 moles (rounded to three decimal places)
Step 2: Calculate the number of molecules:
Number of molecules = Number of moles * Avogadro's number
= 0.443 moles * (6.022 x 10^23 molecules/mol)
≈ 2.666 x 10^23 molecules (rounded to three significant figures)
Therefore, to make a typical polyethylene bag weighing 12.4 g, approximately 2.666 x 10^23 molecules of ethylene (C2H4) must be polymerized.