please explain Orthonormalize the set with respect to the st

please explain

Orthonormalize the set with respect to the standard inner production on R4.

Reaction

4 B(s) + 3 O2 (g) ? 2 B2O3 (s)

1g boron = 1/10.81 = 0.0925 moles B

4 moles B produce 2 moles B2O3

so 0.0925 moles produce 0.0925*2/4 = 0.0462 molesB2O3

now specific heat of water = 4.186 j/g-c

mass = 723g

dT = 38-18 = 20C

q = m*C*dT = 723*4.186*20 = 60529.56 J = 60.529KJ

now this heat is given by 0.0462 moles

so molar heat of formation of B2O3 = 60.529/0.0462 = 1310.152 KJ/mole.........ANS