Your space ship has docked at a space station above Mars. The temperature inside the space station is a carefully controlled 24oC at a pressure of 689 mm Hg. A balloon with a volume of 426 ml drifts into the airlock where the temperature is -88oC and the pressure is 0.160 atm. What is the new volume (L) of the balloon?

(p1V1/T1)= (P2V2/T2)

.083 L

To find the new volume of the balloon, we can use the combined gas law equation:

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

Where:
P1 and P2 are the initial and final pressures respectively,
V1 and V2 are the initial and final volumes respectively,
T1 and T2 are the initial and final temperatures respectively.

Let's convert the given temperatures from Celsius to Kelvin:
T1 = 24°C + 273.15 = 297.15 K (temperature inside the space station)
T2 = -88°C + 273.15 = 185.15 K (temperature inside the airlock)

Given:
P1 = 689 mm Hg
V1 = 426 ml
P2 = 0.160 atm

Now, we can plug in the values into the equation and solve for V2:

(689 mm Hg * 426 ml) / (297.15 K) = (0.160 atm * V2) / (185.15 K)

To convert mm Hg to atm, divide by 760:
(689/760 atm * 426 ml) / (297.15 K) = (0.160 atm * V2) / (185.15 K)

Simplifying the equation:
(0.907 atm * 426 ml) / (297.15 K) = (0.160 atm * V2) / (185.15 K)

Now, cross multiply and solve for V2:
(0.907 atm * 426 ml * 185.15 K) = (0.160 atm * V2 * 297.15 K)

V2 = (0.907 atm * 426 ml * 185.15 K) / (0.160 atm * 297.15 K)

V2 ≈ 560.68 ml

Therefore, the new volume (in L) of the balloon is approximately 0.56068 L.