The specific rotation of (r) - 2-butanol is - 13.5°. what specific rotation would be observed for a 3:1 mixture of (s) : (r) 2-butanol?

If the specific rotation of (r) - 2-butanol is - 13.5° then the specific rotation of (s) - 2-butanol is simply the opposite in sign 13.5°. In a 3:1 mixture of (s) : (r) 2-butanol, 75% is (s) while 25% is r, so the specific rotation of the mixture is:

mixture rotation = 0.75 * (13.5°) + 0.25 * ( - 13.5°)

mixture rotation = 6.75°