Answer:
- 131.5° C
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 = [tex]\frac{{4.20\times10^{11}}{6.022\times10^{23}}[/tex]
= 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
