To calculate the bond order and bond length of the carbon-nitrogen triple bond in cyanide ion CN^- using valence bond theory and molecular orbital theory, we need to follow these steps:1. Determine the electronic configuration of the atoms involved.2. Construct the molecular orbitals using linear combination of atomic orbitals LCAO .3. Calculate the bond order.4. Determine the bond length using experimental data or theoretical calculations.Step 1: Electronic configurationCarbon C has 6 electrons: 1s 2s 2pNitrogen N has 7 electrons: 1s 2s 2pCyanide ion CN^- has an extra electron, so there are a total of 14 electrons.Step 2: Construct molecular orbitalsFor CN^-, we will consider only the valence electrons 2s and 2p orbitals in the LCAO. The molecular orbitals formed are:- 2s and * 2s from the linear combination of 2s orbitals of C and N- 2pz , 2px , 2py , * 2pz , * 2px , and * 2py from the linear combination of 2p orbitals of C and NStep 3: Calculate bond orderNow, we fill the molecular orbitals with the 10 valence electrons 5 from C and 5 from N, plus the extra electron in CN^- . The filling order is: 2s < * 2s < 2pz < 2px = 2py < * 2pz < * 2px = * 2py The bond order can be calculated as:Bond order = number of electrons in bonding orbitals - number of electrons in antibonding orbitals / 2Bond order = 8 - 2 / 2 = 3So, the bond order of CN^- is 3, indicating a triple bond between carbon and nitrogen.Step 4: Determine bond lengthThe bond length of CN^- can be determined using experimental data or theoretical calculations. According to experimental data, the bond length of CN^- is approximately 1.16 angstroms .In summary, the bond order of the carbon-nitrogen triple bond in cyanide ion CN^- is 3, and the bond length is approximately 1.16 .