Question

A sample of 3.68 mol of krypton is confined at low pressure in a volume at a temperature of 67 °C. Describe quantitatively the effects of each of the following changes on the pressure, the average kinetic energy per molecule in the gas, and the root-mean-square speed.

(a) The temperature is decreased to -43 °C.
(b) The volume is quadrupled.
(c) The amount of krypton is decreased to 2.28 mol.

Give each answer as a decimal factor of the form: new value = factor old value.   A factor of 1 means no change.

Change	P	KEavg	urms
(a)
(b)
(c)

Answer 1

Answer 2

To analyze the effects of each change on the pressure (P), average kinetic energy per molecule (KE_avg), and root-mean-square speed (u_rms) of the krypton gas, we can use the ideal gas law and kinetic theory of gases equations. The ideal gas law is given by:

PV = nRT

Where: P = Pressure of the gas V = Volume of the gas n = Amount of gas (in moles) R = Ideal gas constant T = Temperature (in Kelvin)

The average kinetic energy per molecule (KE_avg) of an ideal gas is given by:

KE_avg = (3/2)kT

Where: k = Boltzmann constant T = Temperature (in Kelvin)

The root-mean-square speed (u_rms) of the gas molecules is given by:

u_rms = √(3RT/M)

Where: R = Ideal gas constant T = Temperature (in Kelvin) M = Molar mass of the gas (in kg/mol)

Given: n = 3.68 mol T_initial = 67 °C = 67 + 273.15 = 340.15 K V_initial = Volume (initial) M = Molar mass of krypton = 83.798 g/mol = 0.083798 kg/mol R = Ideal gas constant = 8.314 J/(mol K) k = Boltzmann constant = 1.380649 × 10^-23 J/K

Let's calculate the effects of each change:

(a) The temperature is decreased to -43 °C = -43 + 273.15 = 230.15 K.

Change P KE_avg urms (a) New Value = factor * Old Value

Pressure (P): New Value = factor * Old Value KE_avg: New Value = factor * Old Value u_rms: New Value = factor * Old Value

(b) The volume is quadrupled.

Change P KE_avg urms (b) New Value = factor * Old Value

Pressure (P): New Value = factor * Old Value KE_avg: New Value = factor * Old Value u_rms: New Value = factor * Old Value

(c) The amount of krypton is decreased to 2.28 mol.

Change P KE_avg urms (c) New Value = factor * Old Value

Pressure (P): New Value = factor * Old Value KE_avg: New Value = factor * Old Value u_rms: New Value = factor * Old Value

Please note that the actual numerical values for the new pressure, average kinetic energy, and root-mean-square speed will depend on the specific initial conditions (initial volume, pressure, and temperature) and the changes made in each scenario. The factor is calculated by dividing the new value by the old value.