It is necessary to make 500 mL of a 0.375 M solution of hydrochloric acid (HCl) using distilled water and full strength hydrochloric acid (M=12.0). what volume of the full strength HCl and what volume of water are necessary to make the desired solution?

15.625 mL

Explanation:

To solve this problem, we have to make use of the dilution formula. By so doing we can obtain the volume of stock solution that should be required to prepare the specified concentration and volume of the dilute acid as shown in the given question.

The dilution formula is;

C1V1= C2V2

Where;

C1= concentration of stock solution = 12.0 M

V1= volume of stock solution = ???

C2= concentration of dilute solution = 0.375 M

V2= volume of dilute solution= 500 mL

Making V1 the subject of the formula;

V1= C2V2/C1

V1= 0.375 × 500 /12.0

V1= 15.625 mL

Therefore, 15.625 mL of stock solution is required.

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