Problem 1
1 point
Water (H₂O) has a bond angle of approximately 104.5°. What does this tell us about the molecule's geometry?
A linear molecule would have a bond angle of 180°. What does an angle less than this indicate?
Problem 2
2 points
The dipole moment of a bond depends on both the bond length and the difference in electronegativity. For a diatomic molecule, the dipole moment μ = q × d, where q is the partial charge and d is the bond length.
If two vectors \(\vec{a} = (3, 4)\) and \(\vec{b} = (1, 0)\) represent bond dipoles in a molecule, calculate the dot product \(\vec{a} \cdot \vec{b}\).
The dot product formula: \(\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y\)
Problem 3
2 points
Explain why CO₂ is nonpolar even though each C=O bond is polar. Use the concept of vector addition in your explanation.
Think about the geometry of CO₂ (linear) and what happens when you add two vectors pointing in opposite directions.
Problem 4
1 point
Two vectors are orthogonal (perpendicular) when their dot product equals:
Recall that \(\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\theta\). What is \(\cos(90°)\)?
Problem 5
2 points
Calculate the magnitude of the vector \(\vec{v} = (3, 4, 0)\) representing a bond in 3D space. Give your answer as a whole number.
Magnitude formula: \(|\vec{v}| = \sqrt{v_x^2 + v_y^2 + v_z^2}\)
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