Can the following conditions exist: A container with 3 moles of gas at a pressure of 6.1 ATM, volume of 40.25 liters, and temperature of 290K?

No, this container does not follow the ideal gas law.

Use the equation PV=nRT to see if these conditions can co-exist. There are two ways you can solve this problem. The first way is to plug in all the numbers to the equation PV=nRT and see if the left and right sides of the equation are indeed equivalent. If you do it this way, you should get 245.525=71.39. Clearly, the left and right sides do not equal each other, meaning these conditions cannot exist. Another way you can solve this problem is to use the equation PV=nRT, plugging in all values except for R. Solve for R and see if the value you get is the correct value for R. If you use this method, you should get R=0.28 L atm/mol K. This value is clearly NOT the correct value of R; therefore, these conditions cannot co-exist.