What is the mass, in grams, of 7.40×1020 molecules of caffeine, C8H10N4O2
Well, caffeine may keep you awake, but I can see that this question is putting me to sleep! Let's calculate that mass, shall we?
To calculate the mass, we need to know the molar mass of caffeine, which is approximately 194.19 grams per mole. Since the question gives us the number of molecules, we need to convert that to moles first.
So, let's do some math. We have 7.40×10^20 molecules of caffeine. To convert that to moles, we divide by Avogadro's number, which is 6.022×10^23 molecules per mole.
(7.40×10^20 molecules)/(6.022×10^23 molecules/mole) ≈ 1.23×10^-3 moles
Now that we have moles, we can calculate the mass. We multiply the number of moles by the molar mass of caffeine:
(1.23×10^-3 moles) × (194.19 grams/mole) ≈ 0.24 grams
So, the mass of 7.40×10^20 molecules of caffeine is approximately 0.24 grams. That's a tiny fraction of the caffeine content in a cup of coffee! So, if you're looking for a jolt, you might need a bit more caffeine than that.
To find the mass of 7.40×10^20 molecules of caffeine, C8H10N4O2, you will need to know the molar mass of caffeine.
To calculate the molar mass of caffeine (C8H10N4O2), you need to add up the atomic masses of all the atoms in one molecule of caffeine.
- Carbon (C) has an atomic mass of 12.01 g/mol.
- Hydrogen (H) has an atomic mass of 1.01 g/mol.
- Nitrogen (N) has an atomic mass of 14.01 g/mol.
- Oxygen (O) has an atomic mass of 16.00 g/mol.
The molecular formula for caffeine (C8H10N4O2) indicates that there are 8 carbon atoms, 10 hydrogen atoms, 4 nitrogen atoms, and 2 oxygen atoms in one molecule.
Now, let's calculate the molar mass of caffeine:
(8 carbon atoms × 12.01 g/mol) + (10 hydrogen atoms × 1.01 g/mol) + (4 nitrogen atoms × 14.01 g/mol) + (2 oxygen atoms × 16.00 g/mol)
= (96.08 g/mol) + (10.10 g/mol) + (56.04 g/mol) + (32.00 g/mol)
= 194.22 g/mol
So, the molar mass of caffeine is 194.22 g/mol.
Now, to find the mass of 7.40×10^20 molecules of caffeine, you can use the following conversion factor:
1 mole of caffeine = 194.22 grams
To convert from molecules to grams, we need to use Avogadro's number, which states that 1 mole of any substance contains 6.022×10^23 particles (molecules in this case).
So, the calculation is as follows:
7.40×10^20 molecules × (1 mol / 6.022×10^23 molecules) × (194.22 g / 1 mol)
= (7.40×10^20 × 194.22) / (6.022×10^23)
= 23.783 g
Therefore, the mass of 7.40×10^20 molecules of caffeine is approximately 23.783 grams.
To find the mass of 7.40×10^20 molecules of caffeine (C8H10N4O2), we need to calculate the molar mass of caffeine and then convert it to grams.
First, let's determine the molar mass of caffeine (C8H10N4O2) by adding up the atomic masses of all the atoms in one molecule of caffeine.
The atomic masses can be found on the periodic table. Here are the atomic masses of the elements involved in caffeine:
C = 12.01 g/mol
H = 1.01 g/mol
N = 14.01 g/mol
O = 16.00 g/mol
Now, we can calculate the molar mass of caffeine by multiplying the atomic masses by the number of atoms in one molecule of caffeine:
(8 * 12.01 g/mol) + (10 * 1.01 g/mol) + (4 * 14.01 g/mol) + (2 * 16.00 g/mol)
= 96.08 g/mol + 10.10 g/mol + 56.04 g/mol + 32.00 g/mol
= 194.22 g/mol
The molar mass of caffeine is 194.22 g/mol.
Next, we can use Avogadro's number, which is 6.022 × 10^23, to convert the number of caffeine molecules to moles. Divide the given number of molecules by Avogadro's number:
(7.40×10^20 molecules) / (6.022 × 10^23 molecules/mol)
≈ 0.0123 moles of caffeine
Finally, we can calculate the mass in grams by multiplying the number of moles by the molar mass of caffeine:
0.0123 moles * 194.22 g/mol
≈ 2.39 grams
Therefore, the mass of 7.40×10^20 molecules of caffeine is approximately 2.39 grams.
what's the molar mass? That's the mass of one mole.
How many moles do you have?
7.40x10^20 / 6.02x10^23 = ?
Now multiply that by the molar mass.