You are doing research on planet X. The temperature inside the space station is a carefully controlled 27 ∘C and the pressure is 761 mmHg . Suppose that a balloon, which has a volume of 855 mL inside the space station, is placed into the airlock, and floats out to planet X.

If planet X has an atmospheric pressure of 0.14 atm and the volume of the balloon changes to 3.21 L , what is the temperature, in degrees Celsius, on planet X (n does not change)?

Express your answer using three significant figures.

-115°C is the temperature on planet X.

Explanation:

Pressure inside the space station =

1 atm = 760 mmHg

Temperature inside the space station =

Volume of the air filled in the balloon =

1 mL = 0.001 L

Atmospheric pressure on planet X =

Temperature on the planet X =

Volume of the air filled in the balloon on planet X =

Using combined gas equation :

-115°C is the temperature on planet X.

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