A piece of dry ice (solid carbon dioxide) with a mass of 30.5g is allowed to sublime.
Assuming that all of the carbon dioxide ends up in the balloon, what will be the volume of the balloon at a temperature of 22 ∘ C and a pressure of 746mmHg?
Use PV = nRT. Calculate n as
n = grams/molar mass
To find the volume of the balloon, we need to use the Ideal Gas Law equation:
PV = nRT
Where:
P is the pressure of the gas (given as 746 mmHg)
V is the volume of the gas (unknown)
n is the number of moles of gas (we'll calculate this)
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature of the gas in Kelvin (22 °C = 295 K)
First, we need to calculate the number of moles of carbon dioxide.
Given that the molar mass of carbon dioxide is approximately 44.01 g/mol, we can use the following equation:
n = mass / molar mass
n = 30.5 g / 44.01 g/mol
n ≈ 0.693 mol
Now we have all the values required to find the volume of the gas:
PV = nRT
V = (nRT) / P
V = (0.693 mol * 0.0821 L·atm/(mol·K) * 295 K) / 746 mmHg
Notice that we need to convert the pressure from mmHg to atm:
1 atm = 760 mmHg
V = (0.693 * 0.0821 * 295) / (746/760)
V ≈ 0.079 L or 79 mL
Therefore, the volume of the balloon will be approximately 79 mL.