Final answer:
The nurse expects to see an indurated painless nodule on the vulva, known as a hard chancre, as a sign of primary syphilis.
Step-by-step explanation:
The sign of primary syphilis a nurse expects the client to exhibit is an indurated painless nodule on the vulva, which is also known as a hard chancre. This chancre is firm, round, and painless, appearing at the location where the syphilis bacteria entered the body. It is characteristic of the first stage of syphilis and often occurs within 10 to 90 days after the transmission of the disease. The chancre generally heals on its own within three to six weeks, but it's important to note that even after it heals, without proper treatment, the individual remains infected and the disease can progress to later, more dangerous stages.