Your space ship has docked at a space station above Mars. The temperature inside the space station is 24oC at a pressure of 745mmHg. A balloon with a volume of 425mL drifts into the airlock where the temperature is -95oC and the pressure is 0.115 atm. What is the new volume of this balloon (assume it’s very elastic)?
Use (P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
To find the new volume of the balloon, we can use the combined gas law, which states that:
(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, and T1 and T2 are the initial and final temperatures.
Given:
P1 = 745 mmHg
V1 = 425 mL
T1 = 24oC = 24 + 273 = 297 K
P2 = 0.115 atm
T2 = -95oC = -95 + 273 = 178 K
Plugging in these values into the combined gas law:
(745 mmHg * 425 mL)/297 K = (0.115 atm * V2)/178 K
Now, we need to convert mmHg to atm and mL to liters for consistent units.
1 mmHg = 0.00131578947 atm
1 mL = 0.001 L
(0.982358974 atm * 0.425 L)/297 K = (0.115 atm * V2)/178 K
Simplifying the equation:
0.414828845 atm/L = 0.646067416 atm/L * V2
Dividing both sides of the equation by 0.646067416 atm/L:
V2 = (0.414828845 atm/L)/(0.646067416 atm/L)
V2 = 0.641793 L
Therefore, the new volume of the balloon is 0.641 liters.