To solve this problem, we can use the combined gas law, which relates the initial and final conditions of a gas sample.
The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where: P1 = Initial pressure (1 ATM) V1 = Initial volume (6.2 L) T1 = Initial temperature (25 degrees Celsius + 273.15) = 298.15 K P2 = Final pressure (1 ATM) V2 = Final volume (unknown) T2 = Final temperature (100 degrees Celsius + 273.15) = 373.15 K
Plugging in the known values:
(1 ATM * 6.2 L) / (298.15 K) = (1 ATM * V2) / (373.15 K)
Simplifying the equation:
6.2 / 298.15 = V2 / 373.15
To solve for V2, we can cross-multiply and divide:
V2 = (6.2 / 298.15) * 373.15
Calculating this:
V2 ≈ 7.77 L
Therefore, at 100 degrees Celsius and 1 ATM pressure, the helium gas will occupy approximately 7.77 liters.