A balloon has a volume of 2.5 L and contains 0.100 moles of Helium. Another balloon has
a volume of 5.0 L. They are at the same temperature and pressure. How many moles of
gas does the second balloon contain?

n₂ = 0.2 mol

Explanation:

Given data:

Volume of 1st balloon = 2.5 L

Moles of He in 1st balloon = 0.100 mol

Volume of second balloon = 5.0 L

Moles in second balloon = ?

Solution:

According to the Avogadro law,

Number of moles of gas is directly proportional to the volume of gas at constant temperature and pressure.

Mathematical expression:

V₁/n₁  =  V₂/n₂

V₁ = Volume of 1st balloon

n₁  =  Moles of He in 1st balloon

V₂ = Volume of second balloon

n₂ = Moles in second balloon

Now we will put the values.

2.5 L / 0.100 mol = 5 L /n₂

n₂ = 5 L× 0.100 mol  /2.5 L

n₂ = 0.5 mol /2.5

n₂ = 0.2 mol

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

b) nuclear ive learned that in a pedtrodic table