A piece of dry ice (solid carbon dioxide) with a mass of 25.5 g is allowed to sublime (convert from solid to gas) into a large balloon.
Assuming that all of the carbon dioxide ends up in the balloon, what will be the volume of the balloon at a temperature of 18 degrees Celsius and a pressure of 745mmHg?
Use PV = nRT
n = moles CO2 = grams/molar mass. Don't forget T is in Kelvin.
To find the volume of the balloon, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's calculate the number of moles of carbon dioxide. We can use the molar mass of carbon dioxide (CO2) to convert the mass of dry ice to moles.
1. Find the molar mass of CO2:
The molar mass of carbon dioxide (CO2) is calculated by adding the atomic masses of its components, one carbon atom (C) and two oxygen atoms (O):
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of CO2 = (12.01 g/mol) + 2(16.00 g/mol) = 44.01 g/mol
2. Calculate the number of moles:
The number of moles (n) can be calculated using the formula:
n = mass / molar mass
Given that the mass is 25.5 g and the molar mass is 44.01 g/mol:
n = 25.5 g / 44.01 g/mol ≈ 0.579 mol
Now, let's proceed with the Ideal Gas Law equation and solve for the volume (V):
P = 745 mmHg
T = 18 °C = 18 + 273.15 K = 291.15 K (we convert to Kelvin)
R is the ideal gas constant, which is typically listed as:
R = 0.0821 L·atm/(mol·K)
Using these values, we can rearrange the equation to solve for V:
V = nRT / P
3. Plug in the values:
n = 0.579 mol
R = 0.0821 L·atm/(mol·K)
T = 291.15 K
P = 745 mmHg
V = (0.579 mol) * (0.0821 L·atm/(mol·K)) * (291.15 K) / (745 mmHg)
4. Convert mmHg to atm:
1 atm = 760 mmHg
P = 745 mmHg / 760 mmHg/atm ≈ 0.980 atm
V = (0.579 mol) * (0.0821 L·atm/(mol·K)) * (291.15 K) / (0.980 atm)
Calculating this expression will give you the volume of the balloon in liters.