Question

The density of gas atoms at a certain location in the space above our planet is about 4.20 x 10^11/m^-3, and the pressure is 8.20 x 10^-10 N/m^2. What is the temperature there in °C?

Answer 1

- 131.5° C

Step-by-step explanation:

Given:

Density of gas atoms = 4.20 x 10¹¹ m⁻³

Pressure, P = 8.20 x 10⁻¹⁰ N/m²

Now taking the 1 m³ of volume,

we have total number of atoms = Density × Volume

= 4.20 x 10¹¹ m⁻³ × 1 m³

= 4.20 x 10¹¹ atoms

Also,

1 mol contains 6.022 × 10²³ atoms

therefore,

the number of moles given gas =

= 6.97 × 10⁻¹³ moles

Now,

From the ideal gas law

PV = nRT

here,

R is the ideal gas constant = 8.314 J / mol. K

T is the temperature in Kelvin

thus,

8.20 x 10⁻¹⁰ × 1 = 6.97 × 10⁻¹³ × 8.314 × T

or

T = 141.5 K

or

T = 141.5 - 273 = - 131.5° C