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?
To find the total pressure in the flask after the dry ice has completely sublimed, you need to consider the gases present in the flask.
First, let's calculate the number of moles of N2 gas present in the flask using the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Given:
Pressure of N2 gas (P1) = 725 mmHg
Volume of flask (V1) = 750 mL
Temperature (T1) = 25.0 °C = 298 K (since temperature must be in Kelvin)
Converting mL to L:
V1 = 750 mL = 0.75 L
Now, rearranging the ideal gas law equation to solve for moles (n):
n = PV / RT
Substituting the given values:
n1 = (725 mmHg * 0.75 L) / (0.0821 L·atm/mol·K * 298 K)
Next, we need to consider the sublimation of dry ice (solid CO2). When solid CO2 (dry ice) sublimes, it directly converts into CO2 gas without a liquid phase. This means that the number of CO2 gas moles after sublimation will be equal to the number of moles of dry ice that was initially present.
Given that the mass of dry ice added is 1.25 g and the molar mass of CO2 is approximately 44.01 g/mol, we can calculate the moles of CO2 (n2) produced from the dry ice:
n2 = mass of dry ice / molar mass of CO2
n2 = 1.25 g / 44.01 g/mol
Now that we have the moles of both N2 gas (n1) and CO2 gas (n2), we can calculate the total moles (nt) by adding them together:
nt = n1 + n2
Finally, to find the total pressure in the flask after the dry ice has completely sublimed, we can apply the ideal gas law once again using the total moles (nt) and the known values of volume (V1) and temperature (T1):
P2 = nt * R * T1 / V1
Where:
P2 = total pressure in the flask after sublimation
R = ideal gas constant = 0.0821 L·atm/mol·K
Substituting the values:
P2 = (nt * 0.0821 L·atm/mol·K * 298 K) / 0.75 L
By calculating the expression, you can find the total pressure (P2) in the flask after the dry ice has sublimed.