Experiments were done on a certain pure substance X to determine some of its properties. There's a description of each experiment in the table below. In each case, decide whether the property measured was a chemical or physical property of X, if you can. If you don't have enough information to decide, choose can't decide in the third column. Property P: A small sample of X is dissolved in water. Drops of another solution, containing dissolved sodium hydroxide, are slowly added, and a pH indicator is used to determine when the sodium hydroxide has completely reacted with X. From the amount of sodium hydroxide needed, the value of P may be calculated.
Property D: A sample of X is carefully weighed and put inside a vented flask. Water is added to the flask until it just covers the sample, and the volume of sample and water is recorded. Then the sample is removed and the volume of water alone recorded. From the mass of the sample and the difference in volumes, the value of R may be calculated.
Property V: Sample of X is melted and put into a reservoir from which a very thin tube leads down. The rate at which X flows out of the tube is measured, and from this rate the value of V may be calculated.

The property P measured, was a chemical property of X; its acidity

The property D measured, was a physical property of X; its density

The property V measured, was a physical property of X; it's viscosity probably.

Explanation:

1. The property V that was measured is the acidity of X. The acidity of X is a measure of the concentration of hydrogen ions present in it. When drops of another solution, containing dissolved sodium hydroxide, are slowly added, and a pH indicator is used to determine when the sodium hydroxide has completely reacted with X, the procedure determines the concentration of X that would neutralize the base, sodium hydroxide.

2. The property of X determined in the step is the density of X, a physical property. First the volume of X was determined by the displacement method. Then the density of X is calculated from its mass and volume.

3. Since during the determination of the property V, there was no alteration done to the chemical constitution of X, the property thus determined is a physical property. Melting of the sample is a physical change and likewise its flow rate through a very thin tube.

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