a balloon is filled with 500 mL of helium at a temperature of 27 degrees celsius and 755 mmHg as the balloon rises in the atmosphere the pressure and temperature drop what volume will it have when it reaches an altitude where the temperature is -33 degrees celcius and the pressure is 0.65 atm
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To find the volume of the balloon when it reaches the new conditions, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
To solve for the volume (V), we need to keep all other variables constant and only change the pressure and temperature.
Step 1: Convert the initial pressure and temperature to their appropriate units:
Initial pressure: 755 mmHg
Convert it to atm by dividing by 760 mmHg/atm:
Initial pressure = 755/760 atm
Initial temperature: 27 degrees Celsius
Convert it to Kelvin by adding 273.15:
Initial temperature = 27 + 273.15 K
Step 2: Convert the final pressure and temperature to their appropriate units:
Final pressure: 0.65 atm
Final temperature: -33 degrees Celsius
Convert it to Kelvin by adding 273.15:
Final temperature = -33 + 273.15 K
Step 3: Calculate the initial volume using the initial conditions:
Initial volume (Vi) = 500 mL
Step 4: Apply the ideal gas law equation to find the final volume (Vf):
(Pi)(Vi) / (Ti) = (Pf)(Vf) / (Tf)
Where:
Pi = initial pressure
Vi = initial volume
Ti = initial temperature
Pf = final pressure
Vf = final volume (what we are trying to find)
Tf = final temperature
Therefore, rearrange the equation to solve for Vf:
Vf = (Pi)(Vi)(Tf) / (Pf)(Ti)
Step 5: Substitute the known values into the equation:
Vf = (755/760 atm)(500 mL)(-33+273.15 K) / (0.65 atm)(27+273.15 K)
Step 6: Perform the calculations:
Vf = (0.9934)(500 mL)(240.15) / (0.65)(300.15)
Vf = 355,985 mL / 195.0975
Vf ≈ 1825 mL (rounded to the nearest whole number)
Therefore, the volume of the balloon when it reaches the new conditions is approximately 1825 mL.
To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure, volume, and temperature will be equal to the ratio of the final pressure, volume, and temperature.
The combined gas law equation is expressed as follows:
(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 (unknown)
T2 = Final temperature (in Kelvin)
First, let's convert the given values to the appropriate units:
Initial Pressure (P1) = 755 mmHg
Initial Volume (V1) = 500 mL
Initial Temperature (T1) = 27 °C + 273.15 K = 300.15 K
Final Pressure (P2) = 0.65 atm
Final Temperature (T2) = -33 °C + 273.15 K = 240.15 K
Now, we can solve for the final volume (V2):
(P1 * V1) / T1 = (P2 * V2) / T2
(755 mmHg * 500 mL) / 300.15 K = (0.65 atm * V2) / 240.15 K
377,500 mmHg * mL / 300.15 K = 0.65 atm * V2 / 240.15 K
1256.45 = 0.65 * V2
V2 = 1256.45 / 0.65
V2 ≈ 1932.23 mL
Therefore, when the balloon reaches an altitude where the temperature is -33 degrees Celsius and the pressure is 0.65 atm, it will have a volume of approximately 1932.23 mL.