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 414 mL drifts into the airlock where the temperature is -95 ∘C and the pressure is 0.115 atm.
Oh, boy! That balloon must be feeling quite deflated at -95 °C and 0.115 atm. It's probably thinking, "I wanted to explore Mars, not turn into an ice cube!" But hey, at least it can enjoy the "cool" view from the airlock.
To determine what will happen to the balloon when it enters the airlock, we need to consider the relationship between temperature, pressure, and volume using the ideal gas law equation: PV = nRT.
Here are the steps to follow:
Step 1: Convert the given temperatures to Kelvins.
The temperature inside the space station is 24 °C. To convert it to Kelvin, add 273.15: 24 °C + 273.15 = 297.15 K.
The temperature in the airlock is -95 °C. To convert it to Kelvin: -95 °C + 273.15 = 178.15 K.
Step 2: Convert the given pressures to atmospheres (atm).
The pressure inside the space station is given as 745 mmHg. To convert to atm, divide by 760 (since 1 atm = 760 mmHg): 745 mmHg ÷ 760 mmHg/atm = 0.9797 atm.
The pressure in the airlock is given as 0.115 atm, which is already in atm units.
Step 3: Calculate the initial volume of the balloon in the airlock using the ideal gas law equation:
PV = nRT.
Since the number of moles (n) and the gas constant (R) are constant, we can write the equation as: V1/T1 = V2/T2.
V1 = (P1 * V1 * T2) / (P2 * T1), where V1 is the initial volume of the balloon in the space station (414 mL).
V1 = (0.9797 atm * 414 mL * 178.15 K) / (0.115 atm * 297.15 K)
V1 ≈ 221.27 mL.
Step 4: Compare the initial volume of the balloon in the airlock (V1) to the volume of the balloon in the airlock (414 mL).
Since V1 (221.27 mL) is less than the volume of the balloon in the airlock (414 mL), the balloon will expand when it enters the airlock.
In summary, when the balloon enters the airlock, it will experience a decrease in pressure and a decrease in temperature. According to the ideal gas law, this will cause the balloon to expand to a larger volume.
P(1) = 745mm
P(2) = 0.115atm(760mm/atm)= 87.4mm
V(1) = 414ml
V(2) = ?
T(1) = 24C = 297K
T(2) = -95C = 178K
(PV/T)1 = (PV/T)2
Substitute above data into equation and solve for V(2).