The molar volume of an ideal gas is ~22.4 liters per mole (we’ll consider O2 to be an ideal gas for these purposes, and 22.4 is an approximation that varies with temperature, it’s 22.414 at 0C). Convert from 22.4 liters to milliliters ( = 22400 ml per mol). So if you have 1 milliliter of an ideal gas, there is 1 ml / 22400 ml per mol = 0.00004464 mol of that gas, which is 44.64 µmol of the gas. Thus, if you have a volume of a gas in ml, you can calculate the µmols of that gas simply by multiplying by 44.64.
For example, if an oxygen consumption rate is quoted in µl O2 / mg tissue / hour, convert to µmol O2 / g / hr as follows:
1 µl O2 = 0.001 ml O2
0.001 ml O2 x 44.64µmol/ml = 0.04464 µmol O2.
0.04464 µmol O2/ mg / hr x 1000 mg/g = 44.64 µmol O2 / g / hr.