Your spaceship has docked at a space station above Mars. The temperature inside the space station is a carefully controlled 24 ∘C at a pressure of 745 mmHg . A balloon with a volume of 475 mL drifts into the airlock where the temperature is -89 ∘C and the pressure is 0.140 atm .
what is the volume
p1v1/t1 = p2v2/t2
Remember to convert t1 and t2 to kelvin.
Post your work if you get stuck.
To find the new volume of the balloon when it is inside the airlock, we can use the combined gas law.
The combined gas law is given by the equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where:
P1 and P2 are the initial and final pressures
V1 and V2 are the initial and final volumes
T1 and T2 are the initial and final temperatures
Given:
P1 = 745 mmHg (convert to atm: 1 atm = 760 mmHg, so P1 = 745/760 = 0.9789 atm)
V1 = 475 mL (convert to liters: 1 L = 1000 mL, so V1 = 475/1000 = 0.475 L)
T1 = 24 ∘C (convert to Kelvin: T1 = 24 + 273.15 = 297.15 K)
P2 = 0.140 atm
T2 = -89 ∘C (convert to Kelvin: T2 = -89 + 273.15 = 184.15 K)
Now we can substitute these values into the equation and solve for V2:
(0.9789 atm * 0.475 L) / (297.15 K) = (0.140 atm * V2) / (184.15 K)
0.4633 atm.L/K = 0.7627 atm.L/K * V2
V2 = (0.4633 atm.L/K) / (0.7627 atm.L/K) = 0.607 L
Therefore, the new volume of the balloon inside the airlock is 0.607 L.