A nurse practitioner orders Medrol to be given 1.4 mg/kg of body weight. Medrol is an anti-inflammatory administered as an intramuscular injection. If a child weighs 71.6 lb and the available stock of Medrol is 20. mg/mL, how many milliliters does the nurse administer to the child? Express your answer to two significant figures and include the appropriate units.

The nurse give 2.3 ml Medrol to the child

Mass is one of the principal quantities, which is related to the matter in the object  

The main mass unit consists of 7 units

kg, hg, dag, g, dg, cg, mg

Conversion :

1 Lb=0,453592 kg

For 71.6 lb :

Medrol to be given 1.4 mg/kg of body weight, so amount for the child :

The available stock of Medrol is 20. mg/mL, so the volume to the child :

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years