The job that I am currently working at has just increased our hours to nine and a half per day (with a five day notice of the half hour a day increase). We do not get any breaks during the day. We basically have to grab lunch whenever we can, but we can not leave the office. If a customer comes into our office or calls us we must quit eating our lunch and tend to them. We never have been able to eat an uninterrupted lunch. Some days we don't even get to eat lunch depending on how busy we are. Is this legal? I though for every eight hours one worked you get two fifteen minute breaks and a half an hour lunch. The company does not even provide a private room for employees to go to to take a break or lunch. Can the company legally do this, or are they just hoping that their employees don't find out they are breaking labor laws?

Straight from Iowa's Workforce Development web site:

Iowa law does not require that employers give employees a lunch or rest break unless certain conditions exist (they are under the age of 16, there is a union contract or some other employment agreement that promises such breaks, they work in a specific profession, such as truck drivers or airline pilots). If an employer does elect to provide a lunch or rest breaks, and many employers do recognize that employees need such a break, an employer may require that an employee remain on the business premises during the break, regardless if the break is paid or unpaid.
Iowa Workforce Development

So, the practice of your employer is legal. Not that I would want to work there.

Federal law does not require breaks at all; it only requires that IF breaks are offered certain requirements as to pay be followed.

About half the states require employers to offer meal breaks. Only six or eight require any kind of rest break. The ONLY time anywhere in the United States that two 15 minute breaks are required by law, is for certain hotel workers in the state of Illinois, and that law has existed for less than a year. Nowhere else does such a requirement exist (a few states require 10 minutes for every four hours worked).

Despite this, a persistant belief that Federal law requires a half hour lunch and two 15 minute breaks for an 8 hour day continues. I don't know where this belief originates.

As Scott indicates, Iowa does not require any breaks at all except in the circumstances noted.