The temperature of a gas having 2 . 0 × 10 ^ 25 molecules per cubic...

From ideal gas equation, $PV = nRT$

$⇒ PV = \dfrac{N}{{N}_{A}}RT$, where $N =$ total number of molecules

$⇒ P = \dfrac{N}{V}\left(\dfrac{R}{{N}_{A}}\right)T ⇒ P = \dfrac{N}{V}kT$

$⇒ 1 . 38 \times \left(1 . 01 \times {10}^{5}\right) = \left(2 \times {10}^{25}\right) \times \left(1 . 38 \times {10}^{- 23}\right) \times T$

$⇒ 1 . 01 \times {10}^{5} = 2 \times {10}^{2} \times T$

$T = \dfrac{1 . 01 \times {10}^{3}}{2} \approx 500K$