Explanation:
The phrase "so that" is used to express purpose or reason. In this case, the purpose for sending the children out to play was so that he might have some time alone.

Why the other options are incorrect:

A. because – This introduces a reason, but it doesn't fit as well in expressing purpose like "so that" does.

C. yet – "Yet" is used to indicate contrast or something happening in addition, which doesn't fit here.

D. since – "Since" can indicate time or cause, but it doesn’t express the purpose of being alone as clearly as "so that."

E. while – "While" indicates simultaneous action, but it's not as clear in expressing the purpose of being alone.