Convert 4.50 e23 atoms of CO to grams.

10.4664 grams of CO

Explanation:

Remark

There's a couple of things you must look out for in this question.

1. The use of the term atoms. There are 2 atoms in each mol of CO

2. You need to divide by 2 to find the number of molecules which will lead to moles.

Step one

Divide the number of atoms by 2

4.50 e^23 / 2 atoms = 2.25 * 10^23 molecules.

Step Two

Find the number of moles of CO

1 mol of anything is 6.02 * 10^23 molecules in this case

x  = 2.25 * 10^23 molecules

1/x = 6.02 * 10^23/2.25 * 10 ^23            Cross multiply

1 * 2.25 * 10^23 = 6.02*10^23 * x           Divide by 6.02 * 10^23

2.25 * 10 ^ 23 / 6.02 * 10^23 = x

x = .3738 moles of CO

Step Three

Find the gram molecular mass of CO

C = 12

O = 16

1 mole = 12 + 16  = 28 grams.

Step Four

Find the number of gram in 0.3738 mols

1 mol = 28 grams

0.3738 mol = x                Cross multiply

x = 28 * 0.3738

x = 10.4664 grams

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

the answer is 0.8m.

by: nicholas