Here, we want to know loading dose which is equal to the volume of distribution x target concentration in plasma.

So our loading dose = 1.81L/kg x 10mg = 18.1mg/kg

She is a 55kg person so 18.1mg/kg x 55kg = 995.5 mg which approximates to 1000mg total loading dose.

Important Pharm Equations to Remember

loading dose= [target plasma conc. (at steady state) x vol of distribution / bioavailability] x weight

bioavailability is 100% if IV dose. so bioavailability is 1 (100/100= 1 which is 100%)

now loading dose is:

10 mg/L x 1.81 L/kg X 55 kg

(cut all the common units in numerator and denominator)

you get-- 10 mg x 1.81 x 55 = 995.5 mg ~ 1000 mg total loading dose