A magnesium ion, Mg2+, with a charge of 3.2×10?19C and an oxide ion, O2?, with a charge of ?3.2×10?19C, are separated by a distance of 0.45 nm. How much work would be required to increase the separation of the two ions to an infinite distance?
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To calculate the work required to separate the two ions to an infinite distance, we can use Coulomb's law:
F = k * (q1 * q2) / r^2
where F is the electrostatic force between the two ions, k is the Coulomb's constant (9 × 10^9 N m^2/C^2), q1 and q2 are the charges of the ions, and r is the distance between the ions.
First, let's calculate the force between the magnesium ion and the oxide ion:
F = (9 × 10^9 N m^2/C^2) * ((3.2×10^(-19) C) * (-3.2×10^(-19) C)) / (0.45 × 10^(-9) m)^2
≈ -2.3 × 10^(-8) N
The negative sign indicates an attractive force between the ions.
The work done to separate the ions to an infinite distance can be calculated as the integral of force with respect to distance:
W = ∫(F * dr)
Integrating from the initial distance (0.45 nm) to infinity, we get:
W = ∫(-2.3 × 10^(-8) N * dr)
W = -2.3 × 10^(-8) N * ∫(dr)
W = -2.3 × 10^(-8) N * ∞
W = -∞
The work required to separate the two ions to an infinite distance is infinite.
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