The detection limit for an analyte converted into the total

The detection limit for an analyte (converted into the total mass in a sample aliquot) is known to be 0.5 µg (i.e., 0.0005 mg). If atmospheric concentration of this analyte is estimated to be 0.1 mg/m³, the minimum time required for pumping the air sample at a pumping rate of 100 mL/min such that this analyte can be detected is _____ minutes.

Solution

concentration of analyte= 0.1 mg/m3 and flow rate = 100 ml/min, 1000ml =1L and 1000L= 1m3

hence 100ml= (100/10⁶) m3=10^-4 m3

flow rate =100ml/min= 10^-4 m3/min

flow rate in mg/min = 0.1 mg/m3* 10^-4 m³/min=10^-5 mg/min

detection limit = 0.0005 mg

time required = detectable limit/ flow rate in mg/min=0.0005/10^-5 min=50 min