physical chemistry - How could I find the solubility of hydrocarbons such as iso- and n-Butane in liquid Methane?

I am trying to figure out the dissolution capacity of iso and normal butane in methane at very low temperatures (110K). This would allow me to make compositions that prevent freeze out of these hydrocarbons at these very low temperatures. For example I would like to prepare a 5% mix of iso-butane in methane and make some measurements at 110K. However, if the solubility of methane is only 3%, I will have a 2% bias in my final measurement.

Any ideas would be much appreciated.

Thanks.