A hydroxide ion (OH−) in a glass of water has an average speed of about 600 m/s. Determine the magnitude of the electrical force between the hydroxide ion (charge −e) and a positive ion (charge +e) that is 1.0 × 10−8 m away (about the separation of 30 atoms). The ions are in water.
Fe = 23.04*10^-13
To determine the magnitude of the electrical force between the hydroxide ion (OH^-) and the positive ion (+e) in water, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electrical force (Fe) between two charged particles is given by the equation:
Fe = (k * |q1 * q2|) / r^2
Where:
Fe is the magnitude of the electrical force
k is the electrostatic constant, approximately equal to 8.99 × 10^9 Nm^2/C^2
q1 and q2 are the charges of the two particles
r is the distance between the two particles
In this case, the charge of the hydroxide ion (OH-) is -e, and the charge of the positive ion is +e. Given that the separation between the ions is 1.0 × 10^-8 m, we can calculate the magnitude of the electrical force.
Plugging in the values to the equation, we have:
Fe = (8.99 × 10^9 Nm^2/C^2 * |-e * +e|) / (1.0 × 10^-8 m)^2
The charge of an electron is approximately -1.6 × 10^-19 C, so the magnitude of the electrical force can be simplified to:
Fe = (8.99 × 10^9 Nm^2/C^2 * (1.6 × 10^-19 C)^2) / (1.0 × 10^-8 m)^2
Fe = 23.04 × 10^-13 N
Therefore, the magnitude of the electrical force between the hydroxide ion and the positive ion in water is 23.04 × 10^-13 N.
To determine the magnitude of the electrical force between the hydroxide ion and the positive ion, we can use Coulomb's Law. Coulomb's Law states that the electrical force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The equation for Coulomb's Law is as follows:
F = (k * q1 * q2) / r^2
Where:
F is the electrical force between the ions
k is the electrostatic constant (k = 8.99 × 10^9 N m^2 / C^2)
q1 and q2 are the charges of the ions (in this case, -e and +e, respectively)
r is the distance between the ions
First, we need to convert the charge of an electron (-e) and the separation distance (1.0 × 10^-8 m) into their respective values.
The charge of an electron, -e, is approximately -1.6 × 10^-19 C.
The separation distance, 1.0 × 10^-8 m, remains the same.
Now we can substitute these values into Coulomb's Law:
F = (8.99 × 10^9 N m^2 / C^2) * (-1.6 × 10^-19 C) * (+1.6 × 10^-19 C) / (1.0 × 10^-8 m)^2
Simplifying:
F = (8.99 × 10^9 N m^2 / C^2) * (-2.56 × 10^-38 C^2) / (1.0 × 10^-16 m^2)
F = -2.30144 × 10^-15 N m^2 / C^2 / m^2
F = -2.30144 × 10^-15 N
Therefore, the magnitude of the electrical force between the hydroxide ion and the positive ion is approximately 2.30144 × 10^-15 N (Newtons).