Check all the true statements concerning two identical containers, one with helium gas in it and one with xenon gas. Choose one or more:

a. When the temperature of either sample of gas increases, the root-mean-square speed increases.
b. If both gases are at the same temperature, they have the same average kinetic energy.
c. When the temperature of either sample of gas increases, the number of particles with average kinetic energy increases.
d. If both of the containers are at the same temperature, they will have the same root-mean-square speed.

The RMS velocity is said to be directly proportional to the square root of temperature and then inversely proportional to the square root of molar mass.

When there is an increase is temperature, the average speed and kinetic energy of the gas molecules also increase.

When comparing two gases at the same temperature, note that the molecules of the gas with the smaller molecular weight often have the higher RMS speed.

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The answers to the question are as follows

a. True

b. True

c. True

d. false

Explanation:

The requiredrelation is

Where R = The gas constant

T =  the temperature in kelvin

m = molecular mass

= root mean square speed

From the above relation on the kinetic energy of a gas we have the following true statements

a. When the temperature of either of the sample of gas increases, the root-mean-square speed increases.

This statement is true as the root means square velocity is directly proportional to the square root of the temperature a. is true

b. If both gases are at the same temperature, they have the same average kinetic energy.

From the equation for the average kinetic energy we see that the kinetic energy is directly proportional to its Kelvin temperature and  hence b. is true

c. When the temperature of either sample of gas increases, the number of particles with average kinetic energy increases.

This statement is true as shown in the kinetic energy equation

d. If both of the containers are at the same temperature, they will have the same root-mean-square speed.

This statement is false as xenon and helium have different, molecular masses

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

they are both synthetic elements

explanation:

d