Question

A carbon monoxide (CO) molecule has a dipole moment of approximately \(8.0 \cdot 10^{-30} \mathrm{C} \mathrm{m}\). If the carbon and oxygen atoms are separated by \(1.2 \cdot 10^{-10} \mathrm{~m}\), find the net charge on each atom and the maximum amount of torque the molecule would experience in an electric field of \(500.0 \mathrm{~N} / \mathrm{C}\)

Short answer

Answer: The net charge on each atom of the CO molecule is approximately 6.67 * 10^{-20} C. The maximum torque experienced by the molecule in the given electric field is 4.0 * 10^{-27} Nm.

Step-by-step solution

Determine net charge on each atom

We can find the net charge on each atom by using the relationship between dipole moment, charge, and separation distance. The formula for the dipole moment is: Dipole moment (p) = q * d Where q is the net charge on each atom and d is the separation distance between the atoms. Here, we have p = 8.0 * 10^{-30} Cm and d = 1.2 * 10^{-10} m. Rearranging the formula, we can solve for q: q = p / d

Calculate the net charge on each atom

Now we can substitute the given values of p and d to find the net charge on each atom: q = (8.0 * 10^{-30} Cm) / (1.2 * 10^{-10} m) q = 6.67 * 10^{-20} C The net charge on each atom is approximately 6.67 * 10^{-20} C.

Calculate the maximum torque experienced by the molecule in an electric field

The torque (τ) experienced by a dipole in an electric field (E) can be calculated using the formula: τ = p * E * sinϴ Where ϴ is the angle between the dipole moment vector and the electric field vector. In this case, we want to find the maximum torque, which occurs when the dipole moment aligns itself perpendicular to the electric field (i.e., ϴ = 90°). Since sin(90°) = 1, we can simplify the formula for maximum torque as: τ_max = p * E

Calculate the maximum torque experienced by the molecule

Now we can substitute the given values of p and E to find the maximum torque experienced by the molecule: τ_max = (8.0 * 10^{-30} Cm) * (500.0 N/C) τ_max = 4.0 * 10^{-27} Nm The maximum torque experienced by the carbon monoxide molecule in the given electric field is 4.0 * 10^{-27} Nm.