Consider an electric system of two aluminium spheres of 54 g each, separated by a distance 75 cm. Calculate the number of electrons each sphere contains. The atomic mass of aluminum is 26.982 g/mol and its atomic number is 13
To calculate the number of electrons each sphere contains, we need to find the number of moles of aluminum in each sphere and then multiply by Avogadro's number.
1. Calculate the molar mass of aluminum:
The atomic mass of aluminum is given as 26.982 g/mol.
2. Calculate the number of moles of aluminum in each sphere:
Mass of each sphere = 54 g
Number of moles = Mass / Molar mass
Number of moles = 54 g / 26.982 g/mol
3. Calculate the number of electrons in each sphere:
Number of electrons = Number of moles x Avogadro's number
Now let's perform the calculations:
1. Molar mass of aluminum: 26.982 g/mol
2. Number of moles in each sphere:
Number of moles = 54 g / 26.982 g/mol
Number of moles = 2.000 mol (rounded to 3 significant figures)
3. Number of electrons in each sphere:
Number of electrons = 2.000 mol x 6.022 x 10^23 electrons/mol
Number of electrons = 1.204 x 10^24 electrons
Therefore, each aluminum sphere contains approximately 1.204 x 10^24 electrons.
Consider an electric system of two aluminium spheres of 54 g each, separated by a distance 75 cm. Calculate the number of electrons each sphere contains. The atomic mass of aluminum is 26.982 g/mol and its atomic number is 13
9.04 cross times 10 to the power of 23 space end exponentelectrons
None of the above
2.11 cross times 10 to the power of 26 electrons
1.57 cross times 10 to the power of 25 electrons
1.57 cross times 10 to the power of 24 electrons
To calculate the number of electrons each sphere contains, we need to use the charge of an electron and the charge of each aluminum sphere.
1. Calculate the charge of the spheres:
Each sphere is neutral, so the total charge is zero. Since the spheres are separated in an electric system, they must have equal and opposite charges to maintain neutrality. Therefore, the charge on each sphere is equal to half of the charge of the system.
2. Calculate the charge of the system:
The charge of the system depends on the potential difference between the spheres and the capacitance between them. However, since only the distance between the spheres is provided and no other information about the system's configuration or voltage is given, we cannot determine the exact charge of the system.
Therefore, it is not possible to calculate the number of electrons each sphere contains with the given information.
To calculate the number of electrons in each aluminum sphere, we can use the atomic mass and the atomic number of aluminum.
Step 1: Calculate the molar mass of aluminum
The molar mass of aluminum is given as 26.982 g/mol.
Step 2: Convert the mass of each sphere to moles
The mass of each sphere is given as 54 g. We divide this by the molar mass of aluminum to convert it to moles.
Moles of aluminum = mass of each sphere / molar mass of aluminum
Moles of aluminum = 54 g / 26.982 g/mol
Step 3: Calculate the number of atoms in each sphere
To calculate the number of atoms, we use Avogadro's number, which states that there are 6.022 × 10^23 atoms in one mole of a substance.
Number of atoms = Moles of aluminum x Avogadro's number
Number of atoms = (54 g / 26.982 g/mol) x (6.022 × 10^23 atoms/mol)
Step 4: Calculate the number of electrons
In an electrically neutral aluminum atom, the number of electrons is equal to the number of protons, which is the same as the atomic number.
Number of electrons = Number of atoms x Atomic number
Number of electrons = [(54 g / 26.982 g/mol) x (6.022 × 10^23 atoms/mol)] x 13
Performing the calculations:
Moles of aluminum = 54 g / 26.982 g/mol
Moles of aluminum = 2.000 moles
Number of atoms = 2.000 mol x (6.022 × 10^23 atoms/mol)
Number of atoms = 1.2044 × 10^24 atoms
Number of electrons = (1.2044 × 10^24 atoms) x 13
Number of electrons = 1.56572 × 10^25 electrons
Therefore, each aluminum sphere contains approximately 1.57 × 10^25 electrons.
To calculate the number of electrons in each aluminum sphere, we need to determine the number of moles of aluminum in 54 grams.
First, let's calculate the molar mass of aluminum.
The molar mass of aluminum is 26.982 g/mol, as given.
Next, we can calculate the number of moles of aluminum using the formula:
Number of moles = Mass / Molar mass
Number of moles = 54 g / 26.982 g/mol
Number of moles ≈ 2.001 mol
Now, since we know that each mole of aluminum contains 6.022 x 10^23 atoms (Avogadro's number), we can find the total number of atoms in the 54 grams of aluminum using the formula:
Number of atoms = Number of moles x Avogadro's number
Number of atoms = 2.001 mol x 6.022 x 10^23 atoms/mol
Number of atoms ≈ 1.205 x 10^24 atoms
Since each aluminum atom has 13 electrons (as indicated by its atomic number), the total number of electrons in the aluminum spheres can be calculated as:
Number of electrons = Number of atoms x Number of electrons per atom
Number of electrons ≈ 1.205 x 10^24 atoms x 13 electrons/atom
Number of electrons ≈ 1.566 x 10^25 electrons
Therefore, each aluminum sphere contains approximately 1.566 x 10^25 electrons.