Answer:
-254°C will be the needed temperature
Explanation:
We use the Ideal Gases Law to solve this problem:
Ideal Gases Law → P . V = n . R . T
If we apply the formula for the two situations, we cancel the n because the number of moles stays the same and we also cancel the R, because it is the same value for both situations (Ideal Gases Constant), so now we have these formulas
P₁ . V₁ / T₁ = P₂ . V₂ / T₂
We do some conversions to have homogeneous units:
233.7 mL . 1L / 1000 mL = 0.2337 L
386.3 mL . 1L / 1000 mL = 0.3863 L
498 kPa . 1atm / 101.3 kPa = 4.91 atm
First of all, we need the pressure for the first situation:
We convert the mass to moles → 39.9 g / 32g/mol = 1.25 moles
We convert the T°C to T° K → 158°C + 273 = 431K
P . V = n . R . T → P = (n. R . T) / V We replace
P = (1.25 mol . 0.082 . 431K) / 0.2337L = 189 atm
With all data, we can replace in the main formula
(189 atm . 0.2337L) / 431 K = (4.91 atm . 0.3886L) / T₂
0.1025 atm.L / K = 1.908 atm.L / T₂
T₂ = 1.908 atm.L / 0.1025 K / atm.L = 18.6 K
We convert the value to T°C → 18.6 K - 273 = -254°C
