Question

Bond length of A - A bond is 124 pm and bond length of B - B bond is 174 pm. The bond length (in pm) of A - B molecule if percent of ionic character of A - B bond is 19.5% is ________.

Answer 1

148.9

Answer 2

The problem asks us to calculate the bond length of an A-B molecule, given the bond lengths of A-A and B-B, and the percentage of ionic character of the A-B bond.

1. Calculate the covalent radii of A and B: The covalent radius of an atom is half of its bond length in a homonuclear diatomic molecule. Covalent radius of A, $r_A = \frac{\text{Bond length of A-A}}{2} = \frac{124 \text{ pm}}{2} = 62 \text{ pm}$ Covalent radius of B, $r_B = \frac{\text{Bond length of B-B}}{2} = \frac{174 \text{ pm}}{2} = 87 \text{ pm}$

2. Calculate the theoretical bond length of a purely covalent A-B bond: For a purely covalent A-B bond, the bond length would be the sum of the covalent radii. $d_{\text{covalent}}(A-B) = r_A + r_B = 62 \text{ pm} + 87 \text{ pm} = 149 \text{ pm}$

3. Determine the electronegativity difference ($\Delta X$) using the percentage ionic character: The percentage ionic character ($P$) is related to the electronegativity difference ($\Delta X = |X_A - X_B|$) by Pauling's formula: $P = (1 - e^{-0.25(\Delta X)^2}) \times 100\%$ Given $P = 19.5\% = 0.195$ (as a fraction). $0.195 = 1 - e^{-0.25(\Delta X)^2}$ $e^{-0.25(\Delta X)^2} = 1 - 0.195 = 0.805$ Take the natural logarithm of both sides: $-0.25(\Delta X)^2 = \ln(0.805)$ $-0.25(\Delta X)^2 \approx -0.2169$ $(\Delta X)^2 = \frac{-0.2169}{-0.25} = 0.8676$ $\Delta X = \sqrt{0.8676} \approx 0.9314$

4. Calculate the actual bond length of A-B using the Schomaker-Stevenson equation: The Schomaker-Stevenson equation accounts for the shortening of bond length due to electronegativity difference (ionic character): $d_{A-B} = r_A + r_B - 0.09 |\Delta X|$ Substitute the values: $d_{A-B} = 149 \text{ pm} - 0.09 \times 0.9314$ $d_{A-B} = 149 \text{ pm} - 0.083826 \text{ pm}$ $d_{A-B} = 148.916174 \text{ pm}$

Rounding to a reasonable number of significant figures (e.g., one decimal place as inputs are integers), the bond length is approximately 148.9 pm.