Your spaceship has docked at a space station above Mars. The temperature inside the space station is a carefully controlled 24 ºC at a pressure of 745 mmHg. A balloon with a volume of 425 mL from inside the space station drifts into the airlock where the temperature is -95 ºC and the pressure is 0.115 atm. What is the final volume, in liters (L), of the balloon, if the amount of gas does not change?
Use (P1V1/T1) = (P2V2/T2)
Don't forget to use T1 and T2 in Kelvin.
Post your work if you get stuck.
To solve this problem, we can use the combined gas law equation, which relates the initial and final pressure, volume, and temperature of a gas.
The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure (in mmHg)
V1 = Initial volume (in mL)
T1 = Initial temperature (in Kelvin)
P2 = Final pressure (in atm)
V2 = Final volume (in L)
T2 = Final temperature (in Kelvin)
Now let's convert the initial and final temperatures to Kelvin.
Initial temperature (T1) = 24 ºC = 24 + 273.15 = 297.15 K
Final temperature (T2) = -95 ºC = -95 + 273.15 = 178.15 K
Initial pressure (P1) = 745 mmHg
Final pressure (P2) = 0.115 atm
Initial volume (V1) = 425 mL
Now, let's plug these values into the equation and solve for V2:
(745 mmHg * 425 mL) / (297.15 K) = (0.115 atm * V2) / (178.15 K)
Simplifying the equation:
(745 * 425) / 297.15 = (0.115 * V2) / 178.15
Solve for V2:
(745 * 425 * 178.15) / (297.15 * 0.115) = V2
V2 = 1210.47 mL
Finally, convert the final volume from mL to L:
V2 = 1210.47 mL * (1 L / 1000 mL) = 1.21047 L
Therefore, the final volume of the balloon is approximately 1.21047 L.
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature of a gas:
P1 * V1 / T1 = P2 * V2 / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume (what we want to find)
T2 = final temperature
Let's begin by converting the initial and final temperatures to Kelvin, as the gas law requires Kelvin temperature values. To convert Celsius to Kelvin, we add 273.15.
Initial temperature (T1) = 24 ºC + 273.15 = 297.15 K
Final temperature (T2) = -95 ºC + 273.15 = 178.15 K
Now we can plug the known values into the gas law equation:
P1 * V1 / T1 = P2 * V2 / T2
P1 = 745 mmHg (initial pressure)
V1 = 425 mL (initial volume) = 0.425 L (since 1 L = 1000 mL)
T1 = 297.15 K (initial temperature)
P2 = 0.115 atm (final pressure)
V2 = what we want to find (final volume)
T2 = 178.15 K (final temperature)
Now we rearrange the equation and solve for V2:
V2 = (P2 * V1 * T2) / (P1 * T1)
V2 = (0.115 atm * 0.425 L * 178.15 K) / (745 mmHg * 297.15 K)
To make the calculation simpler, we need to convert atmospheres to millimeters of mercury:
1 atm = 760 mmHg
V2 = (0.115 atm * 0.425 L * 178.15 K) / (745 mmHg * 297.15 K)
V2 = (0.115 * 0.425 * 178.15) / (745 * 297.15)
V2 ≈ 0.00854 L
Therefore, the final volume of the balloon, when it reaches the airlock, is approximately 0.00854 liters (L).