To calculate the bond length between two carbon atoms in a molecule of ethane, we can use the formula for the potential energy of a diatomic molecule:V r = 1/2 * k * r - r0 ^2where V r is the potential energy, k is the force constant, r is the bond length, and r0 is the equilibrium bond length.We can also relate the bond energy to the potential energy:Bond energy = V r0 Given the bond energy 347 kJ/mol and the force constant 667 N/m , we can solve for the equilibrium bond length r0 .First, we need to convert the bond energy from kJ/mol to J/mol:347 kJ/mol * 1000 J/1 kJ = 347000 J/molNow, we can set the bond energy equal to the potential energy:347000 J/mol = 1/2 * 667 N/m * r0 ^2Next, we can solve for r0:r0^2 = 347000 J/mol / 1/2 * 667 N/m r0^2 = 347000 J/mol / 333.5 N/m r0^2 = 1040.48 m^2/molNow, take the square root of both sides to find r0:r0 = 1040.48 m^2/molr0 32.26 m/molSince the bond length is usually expressed in ngströms , we can convert the bond length from meters to ngströms:r0 32.26 m/mol * 1 /0.1 nm * 1 nm/1e-9 m r0 322.6 /molThus, the bond length between two carbon atoms in a molecule of ethane is approximately 322.6 /mol.