If each balloon is filled with carbon dioxide gas at 20 degrees C and 1 atmosphere, calculate the mass and the number of moles of carbon dioxide in each balloon at maximum inflation. Use the ideal gas law in your calculation. Someone please let me know the answer! Thank you so much!!
To calculate the mass and number of moles of carbon dioxide in each balloon at maximum inflation, we can use the ideal gas law, which is expressed as:
PV = nRT
Where:
- P is the pressure of the gas (in this case, 1 atmosphere)
- V is the volume of the gas (unknown, as it depends on the balloon's size when fully inflated)
- n is the number of moles of the gas (what we need to find)
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature of the gas (in this case, 20 degrees Celsius or 293 Kelvin)
Since the balloons are fully inflated, we can assume that the pressure inside the balloon is equal to the external pressure (1 atmosphere).
To determine the volume of the gas, you need to measure or estimate the size of the balloon when it is fully inflated.
Once you have the volume, you can rearrange the ideal gas law equation to solve for n (the number of moles of CO2):
n = PV / RT
Substitute the known values:
- P = 1 atmosphere
- V = volume of the balloon (in liters)
- R = 0.0821 L·atm/(mol·K)
- T = 293 Kelvin
Let's say that the volume of the balloon is 5 liters. Plug in the values into the equation and calculate:
n = (1 atm) * (5 L) / (0.0821 L·atm/(mol·K) * 293 K)
Simplify the equation:
n = 0.0607 moles
Therefore, each balloon contains approximately 0.0607 moles of carbon dioxide.
To calculate the mass of carbon dioxide, we need to know the molar mass of the gas. Carbon dioxide (CO2) has a molar mass of 44.01 g/mol.
Mass = number of moles * molar mass
Mass = 0.0607 moles * 44.01 g/mol
The mass of carbon dioxide in each balloon at maximum inflation would be approximately 2.67 grams.
Keep in mind that these calculations are based on ideal gas behavior, so they may not be entirely accurate in the real world, where there might be deviations from ideal gas behavior.