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. The volume of the balloon at maximum inflation is 55cm. Thank you for helping find the answer. Please help.
Use PV = nRT
You know P (1 atm), v(55 cm but change that to L), n (solve for this), R (0.08206 L*atm/mol*K), T (20 C but change that to kelvin).
n = number of mols.
grams CO2 = mols x molar mass CO2
T(kelvin) = celsius T + 273
To solve this problem, we will use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is: K = °C + 273.15.
Given:
Temperature (T) = 20°C = (20 + 273.15) K = 293.15 K
Pressure (P) = 1 atmosphere
Volume (V) = 55 cm³
Now, let us rearrange the ideal gas law equation to solve for n, the number of moles:
n = PV / RT
The ideal gas constant (R) is 0.0821 L.atm/(mol.K), but since we have cm³ and atmospheres, let's convert the volume to liters. There are 1000 cm³ in 1 liter, so the volume will be 55 cm³ / 1000 = 0.055 liters.
Substituting the given values into the equation, we have:
n = (1 atm) * (0.055 L) / ((0.0821 L.atm/(mol.K)) * (293.15 K))
Now, we can calculate the number of moles:
n = 0.055 / (0.0821 * 293.15)
Simplifying this equation gives us n = 0.0023 moles.
Since we know the molar mass of carbon dioxide (CO₂) is approximately 44 g/mol, we can find the mass by multiplying the number of moles by the molar mass:
mass = n * molar mass = 0.0023 moles * 44 g/mol = 0.1012 g
Therefore, the mass of carbon dioxide in each balloon at maximum inflation is approximately 0.1012 grams, and the number of moles is approximately 0.0023 moles.
To calculate the mass and number of moles of carbon dioxide in each balloon, we can use the ideal gas law, which states: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
First, let's convert the temperature to Kelvin. We know that 0 degrees Celsius is equivalent to 273.15 Kelvin. So, the temperature in Kelvin is:
T = 20 + 273.15 = 293.15 K
Next, let's convert the volume of the balloon to liters since the ideal gas constant is expressed in liters:
V = 55 cm^3 = 55 mL = 0.055 L
The pressure is given as 1 atmosphere.
Now, we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
Substituting the known values:
n = (1 atm) * (0.055 L) / (0.0821 L·atm/mol·K) * (293.15 K)
Now, we can calculate the number of moles of carbon dioxide in each balloon:
n = 1.78 x 10^-3 mol
To calculate the mass of carbon dioxide in each balloon, we need to know the molar mass of carbon dioxide. The molar mass of carbon dioxide is 44 grams/mol.
The mass can be calculated using the equation:
Mass = number of moles * molar mass
Mass = 1.78 x 10^-3 mol * 44 g/mol
Now, we can calculate the mass of carbon dioxide in each balloon:
Mass = 0.078 g
Therefore, the mass of carbon dioxide in each balloon at maximum inflation is 0.078 grams and the number of moles is 1.78 x 10^-3 moles.