Answer:
- 178 ºC
Explanation:
The ideal gas law states that :
PV = nRT,
where P is the pressure, V is the volume, n is number of moles , R is the gas constant and T is the absolute temperature.
For the initial conditions :
P₁ V₁ = n₁ R T₁ (1)
and for the final conditions:
P₂V₂= n₂ R T₂ where n₂ = n₁/2 then P₂ V₂ = n₁/2 T₂ (2)
Assuming V₂ = V₁ and dividing (2) by Eqn (1) :
P₂ V₂ = n₁/2 R T₂ / ( n₁ R T₁) then P₂ / P₁ = 1/2 T₂ / T₁
4.10 atm / 25.7 atm = 1/2 T₂ / 298 K ⇒ T₂ = 0.16 x 298 x 2 = 95.1 K
T₂ = 95 - 273 = - 178 º C
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