A weather balloon is filled with helium that occupies a volume of 4.33 104 L at 0.995 atm and 32.0°C. After it is released, it rises to a location where the pressure is 0.720 atm and the temperature is -10.2°C. What is the volume of the balloon at that new location?
(P1V1/T1) = (P2V2/T2)
Remember T must be in Kelvin.
so is it .995 times 4.33 divided by 32 +273 =.720 V2 / -10.2 + 273
To solve this problem, we can use the combined gas law equation:
(P₁V₁) / (T₁) = (P₂V₂) / (T₂)
Where:
- P₁ and P₂ are the initial and final pressures, respectively
- V₁ and V₂ are the initial and final volumes, respectively
- T₁ and T₂ are the initial and final temperatures, respectively
We are given the following information:
- P₁ = 0.995 atm
- V₁ = 4.33 x 10^4 L
- T₁ = 32.0°C = 305.15 K
- P₂ = 0.720 atm
- T₂ = -10.2°C = 262.95 K
Let's plug in the values into the equation:
(0.995 atm)(4.33 x 10^4 L) / (305.15 K) = (0.720 atm)(V₂) / (262.95 K)
Now we can solve for V₂:
V₂ = [(0.995 atm)(4.33 x 10^4 L)(262.95 K)] / [(0.720 atm)(305.15 K)]
V₂ ≈ 5.89 x 10^4 L
Therefore, the volume of the balloon at the new location is approximately 5.89 x 10^4 L.
To find the volume of the balloon at the new location, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature of the gas in Kelvin.
First, let's convert the temperatures from Celsius to Kelvin:
T1 = 32.0°C + 273.15 = 305.15 K (initial temperature)
T2 = -10.2°C + 273.15 = 262.95 K (final temperature)
Now, we can rearrange the ideal gas law equation to solve for the final volume (V2):
V2 = (P2 * V1 * T1) / (P1 * T2)
Where:
P1 is the initial pressure of the gas,
V1 is the initial volume of the gas,
T1 is the initial temperature of the gas,
P2 is the final pressure of the gas,
T2 is the final temperature of the gas.
Given:
P1 = 0.995 atm (initial pressure)
V1 = 4.33 * 10^4 L (initial volume)
T1 = 305.15 K (initial temperature)
P2 = 0.720 atm (final pressure)
T2 = 262.95 K (final temperature)
Now, we can substitute the values into the equation and calculate the final volume:
V2 = (0.720 atm * 4.33 * 10^4 L * 305.15 K) / (0.995 atm * 262.95 K)
Calculating the values:
V2 = (1.3004 * 10^7 L * K) / (0.26130875 atm * K)
Simplifying further:
V2 = 4.9747 * 10^7 L / atm
Therefore, the volume of the balloon at the new location is approximately 4.9747 * 10^7 L.