Question

In: Chemistry

If 20.00 mol of helium gas is at 17.0 ∘C and a gauge pressure of 0.320...

If 20.00 mol of helium gas is at 17.0 ∘C and a gauge pressure of 0.320 atm .

Calculate the temperature in celcius if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm. Original volume is 0.3608m3

Expert Solution

Moles of Helium gas = 20.00 mol

Initial conditions of Helium gas:

Given that helium gas is at 17 ^oC and a gauge pressure of 0.320 atm , original volume is 0.3608 m³

Pressure P1 = 0.320 atm

Volume V1 = 0.3608 m³

Temperature T1 = 17 ^oC = 17 + 273 K = 290 K

Final conditions of Helium gas:

Given that Helium gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

Pressure P2 = 1.00 atm

Volume V2 = V1 /2 = 0.1804 m³

Temperature T2 = ?

We know that

P1V1/T1 = P2V2/T2

T2 = (P2V2) (T1/P1V1)

= ( 1.00 atm x 0.1804 m³) ( 290K / 0.320 atm x 0.3608m³)

= 453.125 K

= 180.125 ^oC

T2 = 180.125 ^oC

Therefore, final temperature of the Helium gas = 180.125 ^oC

queen_honey_blossom answered 2 days ago

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