A sample of helium gas has a volume of 325L at 25C and at 5atm. At what temperature the gas can be compressed at 50atm to a volume of 125L?

(P1V1/T1) = (P2V2/T2)

Don't forget T must be in Kelvin.

To solve this problem, we can use the combined gas law, which states that the ratio of pressures multiplied by the ratio of volumes is equal to the ratio of temperatures. The formula for the combined gas law is:

(P1 * V1) / T1 = (P2 * V2) / T2

where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature respectively.

Let's substitute the given values into the formula:

(P1 * V1) / T1 = (P2 * V2) / T2

Plugging in the values we have:

(5 atm * 325 L) / (25°C + 273.15) = (50 atm * 125 L) / T2

Now, we can solve for T2 by cross-multiplying and isolating T2:

(5 atm * 325 L) * T2 = (50 atm * 125 L) * (25°C + 273.15)

Divide both sides by (5 atm * 325 L):

T2 = ((50 atm * 125 L) * (25°C + 273.15)) / (5 atm * 325 L)

Simplify:

T2 = (6250 atm*L*°C) / (1625 atm*L)

Cancel out atm, L, and perform the multiplication:

T2 = 3.8461538461538463 * (25°C + 273.15)

T2 ≈ 1068.65°C

Therefore, the gas can be compressed at 50 atm to a volume of 125 L at approximately 1068.65°C.