A 3-L flask contains nitrogen gas at 21°C and 0.95atm pressure.
What is the final pressure in the flask if an additional 4 g of N2 gas is added to the flask and the flask cooled to -59°C?
To solve this problem, 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
Step 1: Determine the initial number of moles of nitrogen gas in the flask.
To find the number of moles, we can use the equation:
n = mass / molar mass
Given:
Mass = 4g
Molar mass of N2 = 28 g/mol
n = 4g / 28 g/mol
n ≈ 0.14 mol
Step 2: Convert the initial temperature from Celsius to Kelvin.
To convert Celsius to Kelvin, we can use the equation:
T(K) = T(°C) + 273.15
Given:
Initial temperature (T) = 21°C
T(K) = 21°C + 273.15
T(K) ≈ 294.15 K
Step 3: Determine the initial number of moles of nitrogen gas in the flask.
Using the ideal gas law equation, we can find the initial volume:
PV = nRT
Rearranging the equation to solve for V, we have:
V = (nRT) / P
Given:
Pressure (P) = 0.95 atm
Number of moles (n) = 0.14 mol
Ideal gas constant (R) = 0.0821 L·atm/mol·K
Temperature (T) = 294.15 K
V = (0.14 mol * 0.0821 L·atm/mol·K * 294.15 K) / 0.95 atm
V ≈ 3.42 L
Step 4: Determine the final number of moles of nitrogen gas in the flask.
Since an additional 4g of N2 gas is added, the total number of moles in the flask becomes:
n_total = n_initial + n_added
n_initial ≈ 0.14 mol
n_added = mass_added / molar mass
Given:
Mass_added = 4g
Molar mass of N2 = 28 g/mol
n_added = 4g / 28 g/mol
n_added ≈ 0.14 mol
n_total = n_initial + n_added
n_total ≈ 0.14 mol + 0.14 mol
n_total ≈ 0.28 mol
Step 5: Convert the final temperature from Celsius to Kelvin.
Using the equation:
T(K) = T(°C) + 273.15
Given:
Final temperature (T) = -59°C
T(K) = -59°C + 273.15
T(K) ≈ 214.15 K
Step 6: Calculate the final pressure using the ideal gas law.
Using the equation:
PV = nRT
Rearranging the equation to solve for P, we have:
P = (nRT) / V
Given:
Volume (V) = 3.42 L
Number of moles (n) = 0.28 mol
Ideal gas constant (R) = 0.0821 L·atm/mol·K
Temperature (T) = 214.15 K
P = (0.28 mol * 0.0821 L·atm/mol·K * 214.15 K) / 3.42 L
P ≈ 1.74 atm
Therefore, the final pressure in the flask after adding 4g of N2 gas and cooling to -59°C is approximately 1.74 atm.