Can a flame test and emission spectrum test be used to identify a mixture with two or three elements?
3 answers
Sometimes yes, sometimes no. It all depends upon which elements are to be identified. For example, a mixture of Na and K. The Na yellow flames is so bright that it masks the lavender/purple of the K; however, if you see the Na test, a blue cobalt glass (just a square of glass with that color) can be placed between the eye and the flame. The cobalt glass completely blocks out the yellow and the experienced observed can see the weaker K color. Few schools teach this now but when I took qual many many years ago, the book I used actually had a whole chapter on various colors of mixtures and how different colored glasses could be used to distinguish between elements. With a bunsen flame, however, usually a mixture of two is about as good as you can do.
What about an emission spectrum test? Would the lines of both elements be visible in the spectrum?
My response above gave only the flame test possibilities. If you mean by "emission spectrum test" the use of a spectroscope or spectrograph instrument, then there are no problems. One can detect and identify as many as about 60 elements with such an instrument and they can be mixed and matched at random. The spectrograph is better for this; the spectroscope is limited in practice because some of the elements burn off very quickly at the very beginning of the test and don't stick around long for the eye to scan the entire spectrum. Emission spectroscopy was quite the thing 50 years ago (I worked with it daily) but it has been replaced with other instruments. In many cases these other instruments are more advanced technologically but less useful for quick results. However, it takes more training to really know what you're doing with an emission spectrograph.