Which answer choices are true statements about the properties of an enclosed gas?
select all that apply.
if the temperature of a gas remains constant, then increasing its volume will decrease its pressure.
if the volume of a gas remains constant, then increasing its temperature will increase its pressure.
if the pressure of a gas remains constant, then increasing its temperature will increase its volume.
if the temperature of a gas remains constant, then increasing its volume will increase its pressure

option 1:

True

option 2:

True

option 3:

True

option 4:

False

Explanation:

we know from ideal gas equation that

or

..............(1)

option 1:

True

Explanation

From equation 1 it is clear that if temperature remains constant than on increasing the volume of gas, pressure of gas will get decreases.

Option-2

True:

Explanation

From equation 1 it is clear that if volume of gas remains constant then on increasing the temperature, pressure of gas will increases.

Option-3

True

Explanation:

From equation 1 it is clear that if pressure of gas remains constant then on increasing the temperature volume of gas will increases.

Option-4

False

Explanation:

From equation 1 it is clear that if temperature of gas remains constant then on increasing the volume of gas, pressure of gas will decreases.

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 answers would be

the first one and the second one