Question

A 8.40-L vessel contains 3.80 moles of ideal gas at a pressure of 1.60 ✕ 106 Pa. (a) Find the temperature of the gas. K (b) Find the average kinetic energy of a gas molecule in the vessel. J (c) What additional information would you need if you were asked to find the average speed of a gas molecule?

Answer 1

Part a)

`T = 425.6 K`

Part b)

`KE_(avg) = 8.81* 10^(-21) J`

Part c)

in order to find the average speed we need to know about the the gas molar mass or we need to know which gas it is.

Step-by-step explanation:

Part a)

As per ideal gas equation we know that

`PV = nRT`

here we know that

`P = 1.60 * 10^6 Pa`

n = 3.80 moles

`V = 8.40 L = 8.40 * 10^(-3) m^3`

now from above equation we have

`T = (PV)/(nR)`

`T = ((1.60 * 10^6)(8.40 * 10^(-3)))/((8.31)(3.80))`

`T = 425.6 K`

Part b)

Average kinetic energy of the gas is given as

`KE_(avg) = (3)/(2)KT`

here we know that

`K = 1.38 * 10^(-23)`

T = 425.6 K

now we have

`KE_(avg) = (3)/(2)(1.38 * 10^(-23))(425.6)`

`KE_(avg) = 8.81* 10^(-21) J`

Part c)

in order to find the average speed we need to know about the the gas molar mass or we need to know which gas it is.