If each balloon is filled with carbon dioxide at 20 deg. C and 1 atmosphere, calculate the mass and the number of moles of carbon dioxide in each balloon at maximum inflation.
exactly what is the volume of maximum inflation.
55cm
Use PV = nRT to find mols.
Then g = molx x molar mass
To calculate the mass and number of moles of carbon dioxide in each balloon at maximum inflation, we need to use the Ideal Gas Law equation:
PV = nRT,
where:
P is the pressure of the gas (in this case, 1 atmosphere),
V is the volume of the gas (which we can assume is the maximum volume when the balloon is fully inflated),
n is the number of moles of gas,
R is the ideal gas constant (0.08206 L·atm/mol·K),
T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15.
So, 20°C + 273.15 = 293.15 K.
Next, since the balloon is at 1 atmosphere, we can assume that the pressure inside the balloon is the same. Therefore, we don't need to include the pressure in our calculations.
We also need to know the volume of the balloon when it is fully inflated. Let's assume the volume is 2 liters (you can adjust this value if you have a different one).
Now, we can rearrange the Ideal Gas Law equation to solve for the number of moles (n):
n = PV / RT.
Using the values we have:
P = 1 atm,
V = 2 L,
R = 0.08206 L·atm/mol·K,
T = 293.15 K.
Substituting these values into the equation:
n = (1 atm * 2 L) / (0.08206 L·atm/mol·K * 293.15 K).
n = 0.0256 moles.
To calculate the mass, we need to use the equation:
mass = n * molar mass.
The molar mass of carbon dioxide (CO2) is:
C (12.01 g/mol) + O (16.00 g/mol) + O (16.00 g/mol) = 44.01 g/mol.
Substituting the values:
mass = 0.0256 moles * 44.01 g/mol.
mass = 1.125 g.
Therefore, each balloon, when fully inflated, would contain approximately 0.0256 moles of carbon dioxide and have a mass of 1.125 grams.