If the total mass of a vehicle is due to 56Fe, what mass of a 1.4 metric ton (tonne) automobile is due to the electrons?
To determine the mass of electrons in a vehicle, we need to first find the mass of 56Fe in the vehicle and then subtract that from the total mass.
The molar mass of iron (Fe) is approximately 55.845 g/mol. Since we are specifically interested in 56Fe, which is the most abundant isotope of iron, we can assume that the mass of 56Fe is equal to the molar mass of iron.
To find the mass of 56Fe in a 1.4 metric ton (tonne) automobile, we can use the following steps:
1. Convert the metric ton (tonne) to grams:
1 metric ton = 1000 kilograms
1 kilogram = 1000 grams
Therefore, 1 metric ton = 1000 * 1000 grams = 1,000,000 grams
2. Divide the mass of the automobile by the molar mass of 56Fe to find the number of moles of 56Fe:
Mass of 56Fe = Mass of automobile / molar mass of 56Fe
Mass of 56Fe = 1,000,000 grams / 55.845 grams/mol
3. Multiply the number of moles of 56Fe by the Avogadro's number (6.022 x 10^23) to find the number of atoms of 56Fe:
Number of atoms of 56Fe = Number of moles of 56Fe x Avogadro's number
4. Multiply the number of atoms of 56Fe by the mass of a single electron (9.10938356 x 10^-31 kg) to find the mass of electrons:
Mass of electrons = Number of atoms of 56Fe x Mass of a single electron
Now, let's calculate the mass of electrons in a 1.4 metric ton (tonne) automobile:
1. Convert the mass of automobile to grams:
1.4 metric ton = 1.4 * 1000 * 1000 grams = 1,400,000 grams
2. Calculate the mass of 56Fe in the automobile:
Mass of 56Fe = 1,400,000 grams / 55.845 grams/mol = 25,023.79 moles
3. Calculate the number of atoms of 56Fe:
Number of atoms of 56Fe = 25,023.79 moles x 6.022 x 10^23 atoms/mol = 1.505 x 10^26 atoms
4. Calculate the mass of electrons:
Mass of electrons = 1.505 x 10^26 atoms x 9.10938356 x 10^-31 kg = 1.372 x 10^-4 kg
Therefore, the mass of electrons in a 1.4 metric ton (tonne) automobile is approximately 1.372 x 10^-4 kg.
To determine the mass of electrons in a vehicle, we first need to know the total mass and the relative abundance of iron (Fe) and its number of electrons.
The atomic mass of iron (Fe) is approximately 56 amu (atomic mass units). This means that 1 mole of iron atoms weighs 56 grams.
To find the mass of electrons, we need to determine the number of moles of iron atoms present in the vehicle first.
Step 1: Convert the mass of the automobile from metric tons to grams.
1 metric ton (tonne) = 1000 kg = 1,000,000 grams
Mass of automobile = 1.4 metric tons * 1,000,000 grams/tonne = 1,400,000 grams
Step 2: Determine the molar mass of iron (Fe).
Molar mass of iron (Fe) = 56 grams/mole
Step 3: Calculate the number of moles of iron in the vehicle.
Number of moles of iron = mass of automobile / molar mass of iron
Number of moles of iron = 1,400,000 grams / 56 grams/mole
Step 4: Calculate the number of electrons in the moles of iron.
Since each iron atom has 26 electrons (with atomic number 26), we can multiply the number of moles of iron by Avogadro's number (6.02 × 10^23) to get the number of electrons.
Number of electrons = number of moles of iron * Avogadro's number
Number of electrons = (1,400,000 grams / 56 grams/mole) * (6.02 × 10^23 electrons/mole)
Finally, we can transform the number of electrons back into mass by using the mass of 1 electron, which is approximately 9.10938356 × 10^-28 grams.
Step 5: Calculate the mass of electrons.
Mass of electrons = Number of electrons * mass of 1 electron
Mass of electrons = Number of electrons * 9.10938356 × 10^-28 grams
By following the steps above, you can calculate the mass of electrons in the given vehicle.
calculate this:
moles of 56Fe in 1.4metric ton
Then the moles of electrons must be 56 times that.
Then, calculate the mass of that number of electrons.