A sugar crystal contains approximately 1.7×10^17 sucrose (C12H22O11) molecules
What is its mass in mg?
Well, let's do some math... or should I say "sweet arithmetic"!
The molar mass, or molecular weight, of sucrose (C12H22O11) is approximately 342.3 grams per mole.
To find the mass of 1.7×10^17 sucrose molecules, we need to calculate the number of moles first.
1 mole of any substance contains 6.022 × 10^23 molecules (that's Avogadro's number).
So, the number of moles in 1.7 × 10^17 molecules of sucrose is:
(1.7 × 10^17 molecules) / (6.022 × 10^23 molecules per mole) ≈ 2.825 × 10^-7 moles
Now, we can calculate the mass using the formula:
mass (in grams) = moles × molar mass
mass = 2.825 × 10^-7 moles × 342.3 grams/mole
After all the calculations, we finally get... *drumroll*...
A sugar crystal with approximately 1.7×10^17 sucrose molecules would have a mass of about 9.67 × 10^-5 grams, or in milligrams, that's approximately 0.0967 mg!
So, the answer is: "This sugar crystal weighs about as much as the laughter of a tiny clown!"
To calculate the mass of a sugar crystal in milligrams (mg), we need to know the molar mass of sucrose (C12H22O11) and then use Avogadro's number to convert the number of molecules to grams. Finally, we convert grams to milligrams.
The molar mass of sucrose (C12H22O11) can be calculated by adding up the atomic masses of each element in the compound.
Molar mass of C12H22O11 = (12.01 g/mol × 12) + (1.01 g/mol × 22) + (16.00 g/mol × 11)
= 144.12 g/mol + 22.22 g/mol + 176.00 g/mol
= 342.34 g/mol
Now, we can calculate the mass of 1 mole of sucrose.
Mass of 1 mole of sucrose = 342.34 g/mol
Next, we can use Avogadro's number to convert the number of molecules to grams.
1 mole of any substance contains 6.022 × 10^23 molecules (Avogadro's number)
Mass of 6.022 × 10^23 molecules of sucrose = 342.34 g
Therefore, to find the mass of 1.7×10^17 molecules of sucrose, we can set up a proportion.
(1.7×10^17 molecules) / (6.022 × 10^23 molecules) = x mg / 342.34 g
Simplifying the equation:
x = (1.7×10^17 molecules × 342.34 g) / (6.022 × 10^23 molecules)
≈ 9.6 × 10^(-7) g
Finally, we convert grams to milligrams by multiplying by 1000:
Weight of the sugar crystal ≈ 9.6 × 10^(-7) g × 1000
≈ 9.6 × 10^(-4) mg
Therefore, the mass of the sugar crystal is approximately 9.6 × 10^(-4) mg.
To find the mass of the sugar crystal in milligrams (mg), we need to know the molar mass of sucrose (C12H22O11) and the number of molecules in the crystal.
The molar mass of sucrose is calculated by adding up the atomic masses of its constituent elements.
Carbon (C) has an atomic mass of approximately 12.01 g/mol.
Hydrogen (H) has an atomic mass of approximately 1.01 g/mol.
Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
Therefore, the molar mass of sucrose is calculated as follows:
(12.01 g/mol × 12) + (1.01 g/mol × 22) + (16.00 g/mol × 11) = 342.30 g/mol.
Now, to find the mass of 1 sucrose molecule, we divide the molar mass by Avogadro's number (6.022 × 10^23), which gives us:
342.30 g/mol / 6.022 × 10^23 molecules/mol ≈ 5.67 × 10^-22 g/molecule.
Finally, to find the mass of the sugar crystal containing approximately 1.7 × 10^17 sucrose molecules, we multiply the mass of 1 sucrose molecule by the number of molecules:
(5.67 × 10^-22 g/molecule) × (1.7 × 10^17 molecules) ≈ 9.64 × 10^-5 g.
To convert this mass to milligrams (mg), we need to multiply the mass by 1000:
9.64 × 10^-5 g × 1000 mg/g = 9.64 × 10^-2 mg.
Therefore, the mass of the sugar crystal is approximately 9.64 × 10^-2 milligrams (mg).
moles sucrose = 1.7 x 10^17/6.022 x 10^23.
grams = mols x molar mass
Convert to mg.