Question

a) In the deep space between galaxies, the density of atoms is as low as 10⁶ atoms/m³, and the temperature is a frigid 2.7 K. What is the pressure (in Pa)?

(b) What volume (in m³) is occupied by 6 mol of gas?

(c) If this volume is a cube, what is the length of its sides in kilometers?

Answer 1

(a) PV = nRT

P = nRT / V

here R = 1.38e-23 J/K

P = 10⁶ * 1.38e-23 * 2.7

P = 3.726e-17 Pa

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(b) Again

PV = nRT

V = nRT / P

V = 6 * 8.314 * 2.7 / 3.726e-17

V = 3.614e18 m³

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(c) we now volume of cube is

V = L³

so,

L = V^1/3

L = 1534.7 Km