The answer is B. 2.23 * 10^23 molecules.
To solve this problem, we'll use Avogadro's number, which is the number of particles (molecules or atoms) in a mole of a substance:
1 mole = 6.022 x 10^23 particles (Avogadro's number)
First, we need to find the number of moles of NO in the balloon:
11.1 g NO x (1 mol NO / 30.01 g NO) = 0.370 mol NO
Then, we can use Avogadro's number to find the number of molecules in the balloon:
0.370 mol NO x (6.022 x 10^23 molecules NO / 1 mol NO) = 2.23 x 10^23 molecules NO
Therefore, there are approximately 2.23 x 10^23 molecules of NO in the balloon.