A helium-filled weather balloon has a volume of 842 L at 18.9°C and 758 mmHg. It is released and rises to an altitude of 6.99 km, where the pressure is 375 mmHg and the temperature is –24.1°C.
The volume of the balloon at this altitude is___ L.
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(P1V1/T1) = (P2V2/T2) will work all of these gas law problems if you remember to use Kelvin and not C for temperature.
For gas law problems that has moles (or grams that must be converted to mols) in it then PV = nRT is the one to use.
To find the volume of the balloon at the given altitude, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume (unknown)
T2 = final temperature
First, we need to convert the temperatures to Kelvin since the equation requires temperatures in Kelvin.
T1 = 18.9°C + 273.15 = 292.05 K
T2 = -24.1°C + 273.15 = 249.05 K
Now let's substitute the given values into the equation:
(758 mmHg * 842 L) / (292.05 K) = (375 mmHg * V2) / (249.05 K)
Next, we can solve for V2:
(758 mmHg * 842 L * 249.05 K) = (375 mmHg * V2 * 292.05 K)
(758 * 842 * 249.05) / (375 * 292.05) = V2
V2 = 127121.21 / 109304.375
V2 ≈ 1.162 L
Therefore, the volume of the balloon at this altitude is approximately 1.162 L.
To find the volume of the balloon at the given altitude, we need to use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature measured in Kelvin.
First, let's convert the initial and final temperatures to Kelvin by adding 273.15:
Initial temperature = 18.9°C + 273.15 = 292.05 K
Final temperature = -24.1°C + 273.15 = 249.05 K
Next, we need to calculate the initial number of moles using the ideal gas law:
(P1)(V1) = (n)(R)(T1)
Where:
P1 = Initial pressure = 758 mmHg
V1 = Initial volume = 842 L
T1 = Initial temperature = 292.05 K
R = Ideal gas constant = 0.0821 L·atm/(mol·K)
Now we need to calculate the final number of moles using the same equation, but with the final pressure, volume, and temperature:
(P2)(V2) = (n)(R)(T2)
Where:
P2 = Final pressure = 375 mmHg
V2 = Final volume (unknown)
T2 = Final temperature = 249.05 K
We can rearrange the equation to solve for V2:
V2 = (P2)(V1)(T1)/(P1)(T2)
Plugging in the values:
V2 = (375 mmHg)(842 L)(292.05 K) / (758 mmHg)(249.05 K)
Now we can calculate the value of V2:
V2 = (375 mmHg * 842 L * 292.05 K) / (758 mmHg * 249.05 K)
= (92336475 L·mmHg·K) / (1889188.9 L·mmHg)
= 48.91 L
Therefore, the volume of the balloon at the given altitude is approximately 48.91 L.