Bob puts several pieces of dry ice inside an empty water bottle and covers the spout with a balloon. After 5 minutes the balloon is inflated. Elaborate on what process is occurring.
A) The expanding gas is exerting pressure and doing work on the walls of the balloon causing it to inflate.
B) Quick moving molecules of the developing balloon use the gas to create work and put energy into the system.
C) The slow moving particles of the gas are transferring entropy to the expanding balloon causing it to weaken.
D) Energy is converted to enthalpy as the compression dry ice particles occurs and the gas collides with other gas particles.

A) The expanding gas is exerting pressure and doing work on the walls of the balloon causing it to inflate.

Explanation:

As the gas is gradually expanding showing an increase in the volume that exerts pressure on the walls of the balloon causing it to inflate.

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