A 2.50 L balloon is filled with helium gas at sea level, 1.00 atm and 32 degrees celsius. The balloon is released and it rises to an altitude of 30,000 ft. If the pressure at this altitude is 228 mm Hg and the temperature is -44 degrees celsius, what is the volume of the balloon?
Combined gas law:
P1V1/T1=P2V2/T2 temps in kelvins
3.74L
To find the volume of the balloon at the new altitude, we can utilize Boyle's Law. Boyle's Law states that the product of pressure and volume is constant at constant temperature.
Boyle's Law: P1 * V1 = P2 * V2
Where:
P1 = Initial pressure (Sea level) = 1.00 atm
V1 = Initial volume = 2.50 L
P2 = Final pressure (30,000 ft altitude) = 228 mm Hg (convert to atm)
V2 = Final volume (What we need to find)
To use Boyle's law equation, we need to convert the pressure at the final altitude from mm Hg to atm:
1 atm = 760 mm Hg
Therefore, P2 (in atm) = (228 mm Hg) / (760 mm Hg/atm) = 0.3 atm
Now, we can rearrange Boyle's law equation to solve for V2:
V2 = (P1 * V1) / P2
Substituting the known values into the equation:
V2 = (1.00 atm * 2.50 L) / 0.3 atm
V2 = 8.33 L
Therefore, the volume of the balloon at an altitude of 30,000 ft is approximately 8.33 L.
To solve this problem, we can use the ideal gas law equation: PV = nRT.
Step 1: Convert the given pressure, temperature, and volume into appropriate units.
Given:
Initial volume (V₁) = 2.50 L
Initial pressure (P₁) = 1.00 atm
Initial temperature (T₁) = 32 degrees Celsius
Pressure at altitude (P₂) = 228 mm Hg
Temperature at altitude (T₂) = -44 degrees Celsius
Note: We need to convert the temperature from Celsius to Kelvin and pressure from mm Hg to atm for the ideal gas law equation. To convert Celsius to Kelvin, add 273.15 to the Celsius value. To convert mm Hg to atm, divide the mm Hg value by 760.
V₁ = 2.50 L
P₁ = 1.00 atm
T₁ = 32 °C = 32 + 273.15 = 305.15 K
P₂ = 228 mm Hg / 760 = 0.3 atm
T₂ = -44 °C = -44 + 273.15 = 229.15 K
Step 2: Calculate the number of moles using the ideal gas law equation.
PV = nRT
For the initial condition:
(P₁)(V₁) = (n)(R)(T₁)
For the final condition:
(P₂)(V₂) = (n)(R)(T₂)
Since the number of moles (n) and the gas constant (R) are the same, we can set up a ratio between the initial and final states:
(P₁)(V₁) / (T₁) = (P₂)(V₂) / (T₂)
Step 3: Solve for V₂ (final volume).
(V₂) = (P₂)(V₁)(T₁) / (P₁)(T₂)
Substituting the given values:
(V₂) = (0.3 atm)(2.50 L)(305.15 K) / (1.00 atm)(229.15 K)
Step 4: Calculate V₂.
(V₂) = 0.786 L
Therefore, the volume of the balloon at an altitude of 30,000 ft is approximately 0.786 L.