Electric dipole moments of molecules are often measured in debyes (D), where 1 D = 3.34 ⋅ 10–30 C m1 𝐷 = 3.34 · 10–30 C m . For instance, the dipole moment of hydrogen chloride gas molecules is 1.05 D. Calculate the maximum torque such a molecule can experience in the presence of an electric field of magnitude 223 N/C. (You may enter your calculation using scientific notation.) N m
Question
Electric dipole moments of molecules are often measured in debyes (D), where 1 D = 3.34 ⋅ 10–30 C m1 𝐷 = 3.34 · 10–30 C m . For instance, the dipole moment of hydrogen chloride gas molecules is 1.05 D. Calculate the maximum torque such a molecule can experience in the presence of an electric field of magnitude 223 N/C. (You may enter your calculation using scientific notation.) N m
Solution
To calculate the maximum torque (τ) that a molecule can experience in the presence of an electric field, we can use the formula:
τ = pEsinθ
where: p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field.
In this case, the maximum torque occurs when the dipole moment is perpendicular to the electric field, i.e., when θ = 90°. Therefore, sinθ = 1.
Given: p = 1.05 D = 1.05 * 3.34 * 10^-30 Cm = 3.507 * 10^-30 Cm E = 223 N/C
Substituting these values into the formula, we get:
τ = (3.507 * 10^-30 Cm) * (223 N/C) * 1 = 7.82161 * 10^-28 Nm
So, the maximum torque that a hydrogen chloride gas molecule can experience in the presence of an electric field of magnitude 223 N/C is approximately 7.82 * 10^-28 Nm.
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