When the pressure changes from 1417 psi to psi the volume changes from 0.145 l to 0.878 l and the temperature changes from 287 k to 196k

When the pressure changes from 1417 psi to  160.186 psi the volume changes from 0.145 L to 0.878 l and the temperature changes from 287 k to 196 k

Explanation:

According to general gas equation:

P₁V₁/T₁ = P₂V₂/T₂

Given data:

Initial volume = 0.145 L

Initial pressure = 1417 psi (1417/14.696 =96.42 atm)

Initial temperature = 287 K

Final temperature = 196 K

Final volume = 0.878 L

Final pressure = ?

Formula:

P₁V₁/T₁ = P₂V₂/T₂

P₁ = Initial pressure

V₁ = Initial volume

T₁ = Initial temperature

P₂ = Final pressure

V₂ = Final volume

T₂  = Final temperature

Solution:

P₂ = P₁V₁ T₂/ T₁ V₂  

P₂ = 96.42 atm × 0.145 L × 196 K / 287 K × 0.878 L

P₂  =  2740.26 atm .L.  K  / 251.99 k. L

P₂  = 10.9 atm

atm to psi:

10.9 × 14.696 = 160.186 psi

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