Calculating Absolute Pressure of Air in a Balloon
How do we calculate the absolute pressure of air in a balloon?
Answer:
The absolute pressure of the air in a balloon can be calculated using the combined ideal gas equation. In this case, we are given that a balloon is filled with 0.250 moles of air at 35°C and has a volume of 6.23 liters. To find the absolute pressure of the air in the balloon, we can follow these steps:
- Assume that the air inside the balloon behaves as an ideal gas at the given temperature.
- Use the combined ideal gas equation, which is PV = nRT, where P is the absolute pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin.
- Substitute the given values into the equation and solve for P to find the absolute pressure.
Calculating Absolute Pressure
To calculate the absolute pressure of the air in the balloon, we need to use the combined ideal gas equation:
PV = nRT
Where:
P = Absolute pressure of the air inside the balloon
V = Volume of air inside the balloon (6.23 L = 6.23 * 10⁻³ m³)
n = Moles of gas (0.250 mol)
R = Universal gas constant (8.314 J / mol·K)
T = Temperature in Kelvin
Given that the temperature is 35°C, we need to convert it to Kelvin:
T = 35 + 273.15 = 308.15 K
Plugging in the values into the equation, we get:
P = (0.250 * 8.314 * 308.15) / (6.23 * 10⁻³)
P ≈ 102.807 * 10³ Pa
Therefore, the absolute pressure of the air in the balloon is approximately 102.807 kPa.