A 1.25g sample of dry ice is added to a 750ml flask containing nitrogen gas at a temperature of 25.0 C and a pressure of 725mmHg. The dry ice is allowed to sublime (convert from solid to gas) and the mixture is allowed to return to 25.0C. What is the total pressure in the flask?
figure the pressure due to the dry ice alone, then add it to the original pressure.
dryicepressure= moleCO2*R*T/V
molesCO2=1.25/40
molar mass of CO2 is 44.01 g/mol
To find the total pressure in the flask, we need to consider the pressure due to the nitrogen gas and the pressure due to the carbon dioxide gas produced by the sublimation of dry ice.
First, let's calculate the number of moles of nitrogen gas in the flask using the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
Given:
Pnitrogen = 725 mmHg = 725/760 atm (converting mmHg to atm)
V = 750 mL = 0.75 L
T = 25 + 273.15 K = 298.15 K
Using the ideal gas law, we can solve for n:
(725/760) atm * 0.75 L = n * 0.0821 L·atm/(mol·K) * 298.15 K
Solving for n:
n = (725/760) * 0.75 L / (0.0821 L·atm/(mol·K) * 298.15 K)
n = 0.0299 moles
Now, let's calculate the number of moles of carbon dioxide gas produced by the sublimation of dry ice. Dry ice is solid carbon dioxide, and it directly converts from a solid to a gas without passing through the liquid phase.
Given:
Mass of dry ice = 1.25 g
Molar mass of carbon dioxide = 44.01 g/mol
Using the formula n = mass / molar mass, we can calculate the amount of carbon dioxide gas produced:
n = 1.25 g / 44.01 g/mol
n = 0.0284 moles
The total number of moles in the flask can be obtained by adding the moles of nitrogen gas and the moles of carbon dioxide gas:
Total moles = Moles of nitrogen gas + Moles of carbon dioxide gas
Total moles = 0.0299 moles + 0.0284 moles
Total moles = 0.0583 moles
Now, we can calculate the total pressure using the ideal gas law:
P total = n total * R * T / V
Where:
P total = total pressure
n total = total number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
V = volume (in L)
Using the given values and the calculated total number of moles, we can solve for P total:
P total = 0.0583 moles * 0.0821 L·atm/(mol·K) * 298.15 K / 0.75 L
P total = 1.49 atm