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?

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aristocles aristocles · Answer 1 · 2019-07-28T04:05:01+02:00

Answer:

Part a)

[tex]T = 425.6 K[/tex]

Part b)

[tex]KE_{avg} = 8.81\times 10^{-21} J[/tex]

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.

Explanation:

Part a)

As per ideal gas equation we know that

[tex]PV = nRT[/tex]

here we know that

[tex]P = 1.60 \times 10^6 Pa[/tex]

n = 3.80 moles

[tex]V = 8.40 L = 8.40 \times 10^{-3} m^3[/tex]

now from above equation we have

[tex]T = \frac{PV}{nR}[/tex]

[tex]T = \frac{(1.60 \times 10^6)(8.40 \times 10^{-3})}{(8.31)(3.80)}[/tex]

[tex]T = 425.6 K[/tex]

Part b)

Average kinetic energy of the gas is given as

[tex]KE_{avg} = \frac{3}{2}KT[/tex]

here we know that

[tex]K = 1.38 \times 10^{-23}[/tex]

T = 425.6 K

now we have

[tex]KE_{avg} = \frac{3}{2}(1.38 \times 10^{-23})(425.6)[/tex]

[tex]KE_{avg} = 8.81\times 10^{-21} J[/tex]

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.