(a) What is the total negative charge, in coulombs, of all the electrons in a small 1.00 g sphere of carbon? One mole of C is 12.0 g, and each atom contains 6 protons and 6 electrons. (b) Suppose you could take out all the electrons and hold them in one hand, while the other hand you hold what is left of the original sphere. If you hold your hands 1.50 m apart at arms length, what force will each of them feel? Will it be attractive or repulsive?
The number of atoms has to be
mass/massperatom
massper atom= 12/avag number.
(a) To calculate the total negative charge of all the electrons in the carbon sphere, we need to determine the number of moles of carbon in the given mass and then multiply it by Avogadro's number. From the information provided, we know that 1 mole of carbon is 12.0 g.
The number of moles of carbon in a 1.00 g sphere can be calculated as:
Number of moles = Mass of carbon / Molar mass of carbon
Number of moles = 1.00 g / 12.0 g/mol
Now, we know that each carbon atom contains 6 protons and 6 electrons. Since electrons have a negative charge, the total negative charge will be equal to the number of electrons multiplied by the elementary charge (e), which is approximately 1.60 x 10^-19 C.
Total negative charge = Number of moles of carbon × Avogadro's number × Number of electrons per carbon atom × Elementary charge
Plugging in the values, we have:
Total negative charge = (1.00 g / 12.0 g/mol) × (6.02 × 10^23 mol^-1) × (6 electrons/atom) × (1.60 × 10^-19 C/electron)
After performing the calculation, we can find the total negative charge in coulombs.
(b) To determine the force between the electrons in one hand and the carbon sphere in the other hand, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The equation is given by:
Force = (k * |q1 * q2|) / r^2
Where:
- k is the electrostatic constant, approximately equal to 8.99 × 10^9 N m^2/C^2
- q1 and q2 are the charges of the objects (in this case, the charge of electrons and the charge of the carbon sphere)
- r is the distance between the objects
Since the electrons and the carbon sphere have opposite charges, the force will be attractive.
To calculate the force, we need to determine the magnitude of the charge of a single electron and the charge of the carbon sphere. The charge of a single electron is equal to the elementary charge, which is approximately 1.60 × 10^-19 C.
The charge of the carbon sphere can be calculated using the formula:
Charge of the carbon sphere = Total negative charge of electrons
Once we have the charges, we can calculate the force using Coulomb's Law.
Force = (k * |charge of the electron| * |charge of the carbon sphere|) / (distance^2)
Plugging in the values, we have:
Force = (8.99 × 10^9 N m^2/C^2) * (1.60 × 10^-19 C) * (charge of the carbon sphere) / (1.50 m)^2
After performing the calculation, we can find the force between the hands, which will be attractive since the electron charge is negative and the carbon sphere charge is positive.