A helium balloon is filled to a volume of 2.88 x 10^3L at 722 mm Hg and 19 degrees Celcius. When the balloon is released, it rises to an altitude where the pressure and temperature are 339 mm Hg and -55vC, respectively. What is the volume of the balloon?

.774 L x 10^3

774

745 To find the volume of the balloon when it rises to a different altitude, we can use the combined gas law equation. The combined gas law relates the initial and final conditions of a gas sample.

The equation for the combined gas law is as follows:

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

Where:
P1 and P2 are the initial and final pressures, respectively, measured in the same units (mm Hg in this case).
V1 and V2 are the initial and final volumes, respectively, measured in the same units (liters in this case).
T1 and T2 are the initial and final temperatures, respectively, measured in Kelvin (convert from Celsius to Kelvin by adding 273.15).

Let's plug in the values given:

P1 = 722 mm Hg
V1 = 2.88 x 10^3 L
T1 = 19°C + 273.15 = 292.15 K
P2 = 339 mm Hg
T2 = -55°C + 273.15 = 218.15 K

Now we can solve for V2:

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

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

Substituting the values:

V2 = (339 mm Hg * 2.88 x 10^3 L * 218.15 K) / (722 mm Hg * 292.15 K)

Now we can calculate the volume of the balloon at the new altitude:

V2 = (739,142.7 mm Hg* L * K) / (211,082.03 mm Hg* K)

Canceling out the common units:

V2 = 739,142.7 L / 211,082.03

V2 ≈ 3.5 L

Therefore, the volume of the balloon at the new altitude is approximately 3.5 liters.

(P1V1/T1) = (P2V2/T2)

Don't forget T is in Kelvin.
Note the correct spelling of celsius.