Calculate the mass of camphor (C10H16O) that contains a million carbon atoms.
Round it to 2 significant digits.
Well, calculating the mass of camphor might be a bit tricky, but lucky for you, I wasn't voted "Least Likely to Solve Chemistry Problems" in school. So, let's break it down!
The molecular weight of camphor is given by C10H16O. So, let's calculate the atomic masses of carbon (C), hydrogen (H), and oxygen (O). Carbon has an atomic mass of approximately 12.011 grams per mole, hydrogen has an atomic mass of about 1.008 grams per mole, and oxygen has an atomic mass of around 15.999 grams per mole.
Now, let's find the molar mass of camphor. Since camphor has 10 carbon atoms, we'll multiply the atomic mass of carbon (12.011 g/mol) by 10. Then, we'll multiply the atomic mass of hydrogen (1.008 g/mol) by 16 (since there are 16 hydrogen atoms in camphor) and the atomic mass of oxygen (15.999 g/mol) by 1.
(12.011 g/mol × 10) + (1.008 g/mol × 16) + (15.999 g/mol × 1) = 120.11 g/mol + 16.128 g/mol + 15.999 g/mol ≈ 152.238 g/mol
Now that we know the molar mass of camphor is approximately 152.238 grams per mole, we can calculate the mass of camphor containing a million carbon atoms.
Mass = (1,000,000 carbon atoms / 10 carbon atoms) × 152.238 g/mol = 15,223.8 g ≈ 15,000 g
So, the mass of camphor that contains a million carbon atoms is approximately 15,000 grams when rounded to 2 significant digits. Remember, though, that accurate calculations are essential in chemistry!
To calculate the mass of camphor (C10H16O) that contains a million carbon atoms, we need to determine the molar mass of camphor and convert it into the mass containing a million carbon atoms.
1. Calculate the molar mass of camphor:
The molar mass of carbon (C) is approximately 12.01 g/mol, hydrogen (H) is approximately 1.01 g/mol, and oxygen (O) is approximately 16.00 g/mol.
Molar mass of camphor (C10H16O) = (10 * 12.01 g/mol) + (16 * 1.01 g/mol) + (1 * 16.00 g/mol) = 152.15 g/mol.
2. Determine the mass of one carbon atom:
To find the mass of one carbon atom, we divide the molar mass of carbon by Avogadro's number, which is 6.022 x 10^23 atoms/mol.
Mass of one carbon atom = 12.01 g/mol / (6.022 x 10^23 atoms/mol) = 1.99 x 10^-23 g/atom.
3. Calculate the mass of camphor with a million carbon atoms:
Mass of camphor with a million carbon atoms = (1.99 x 10^-23 g/atom) * (1 x 10^6 atoms) = 1.99 x 10^-17 g.
Rounded to 2 significant digits, the mass of camphor that contains a million carbon atoms is approximately 2.0 x 10^-17 g.
To calculate the mass of camphor (C10H16O) that contains a million carbon atoms, we need to consider the molar mass of camphor and the number of carbon atoms present in it.
1. Find the molar mass of camphor (C10H16O):
The molar mass of carbon (C) = 12.01 g/mol
The molar mass of hydrogen (H) = 1.008 g/mol
The molar mass of oxygen (O) = 16.00 g/mol
Now, calculate the molar mass of camphor:
Molar mass of camphor = (10 * molar mass of carbon) + (16 * molar mass of hydrogen) + (1 * molar mass of oxygen)
Molar mass of camphor = (10 * 12.01 g/mol) + (16 * 1.008 g/mol) + (1 * 16.00 g/mol)
Molar mass of camphor = 120.1 g/mol + 16.13 g/mol + 16.00 g/mol
Molar mass of camphor = 152.23 g/mol
2. Find the number of moles of carbon atoms that contain a million carbon atoms:
Since camphor has 10 carbon atoms, one mole of camphor contains 10 moles of carbon atoms.
Number of moles of carbon atoms = (1,000,000 carbon atoms) / (10 carbon atoms/mole)
Number of moles of carbon atoms = 100,000 moles
3. Calculate the mass of camphor that contains a million carbon atoms:
To find the mass of camphor, we can use the formula:
Mass = Number of moles * Molar mass
Mass of camphor = (100,000 moles) * (152.23 g/mol)
Mass of camphor = 15,223,000 g
Rounding the mass to two significant digits, we get 1.5 x 10^7 g as the mass of camphor that contains a million carbon atoms.