cronbach alpha for missing data

I have an indicator which consists of questions 24, 25, 27, 29, 30, 31, and 32. I am in the middle of determining internal consistency and cronbach alpha. I am running into a bit of a problem because the questionnaire has some skip patterns where when people answer 24, 25 they don't answer 27, 29. What should I do in this case to determine the cronbach of the whole indicator and when I'm trying to determine item-total correlations. Should I try to impute the missing data? Thank you.