A sample of air occupies 4.40 L when the pressure is 2.60 atm. (a) What volume does the sample occupy at 6.20 atm at the same temperature?

L

(b) What pressure is required in order to compress it to 0.0290 L at the same temperature?

atm

Explanation:

Given that,

Initial volume, V₁ = 4.40 L

Initial pressure, P₁ = 2.6 atm

(a) Final pressure, P₂ = 6.2 atm

As per the relation,

(b) Again using the above relation,

Hence, this is the required ssolution.

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

answer : a model is often used to explain and make things easier to understand when any scientific topic needs to be demonstrated and explained.

as in this case where a scientist wants to use a model to present the results of his detailed scientific investigation. he should do it as it will him to make the audience understand the concept in a much better way. also, it can be changed according to new scientific understandings.