An iron anchor of density 7800.00 kg/m3 appears 158 n lighter in water than in air. (a) what is the volume of the anchor? (b) how much does it weigh in air?

a) Volume of the anchor is

b) An anchor weighs 1,232.4 N in an air.

Explanation:

Weight of an anchor in water =  W

Weight of an anchor in air = w

w - W = 158 N

Difference in weight will be equal to weight of water displaced as per as Archimedes principle.

Weight of the water =

Volume of an anchor = volume of water displaced = V

Density of water =

Mass of water displaced = m

Volume of the anchor is

Mass of iron anchor = m

Density of the an iron anchor =

Volume of the anchor = V =

Weight of an anchor in an air = w

w = 1,232.4 N

An anchor weighs 1,232.4 N in an air.

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

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