A 5.00-L flask contains nitrogen gas at 25°C and 1.00 atm pressure. What is the final pressure in the flask if an additional 2.00 g of N2 gas is added to the flask and the flask cooled to -55°C?
To answer this question, we can use the ideal gas law equation, which is:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature
The first step is to calculate the initial number of moles of nitrogen gas in the flask.
Given:
Temperature (T1) = 25°C = 25 + 273 = 298 K
Pressure (P1) = 1.00 atm
Volume (V) = 5.00 L
Using the ideal gas law, we can find the number of moles (n) of nitrogen gas in the flask:
n1 = (P1 * V) / (R * T1)
Next, we need to calculate the final number of moles of nitrogen gas in the flask after adding 2.00 g of N2 gas.
Given:
Mass of nitrogen gas added (m) = 2.00 g
We can convert the mass to moles using the molar mass of nitrogen gas, which is 28.0134 g/mol:
n_added = m / molar mass of N2
Now, we need to calculate the final temperature (T2) after cooling the flask to -55°C:
Given:
Temperature (T2) = -55°C = -55 + 273 = 218 K
We can now calculate the final pressure (P2) in the flask using the ideal gas law:
P2 = (n1 + n_added) * (R * T2) / V
Substituting the values we calculated, we can determine the final pressure in the flask.
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 (0.0821 L·atm/mol·K)
T = temperature in Kelvin
Let's first calculate the initial number of moles of nitrogen gas in the flask.
Step 1: Convert the temperature to Kelvin.
T_initial = 25°C + 273.15 = 298.15 K
Step 2: Use the ideal gas law to calculate the initial number of moles.
P_initial = 1.00 atm
V = 5.00 L
R = 0.0821 L·atm/mol·K
n_initial = (P_initial * V) / (R * T_initial)
= (1.00 atm * 5.00 L) / (0.0821 L·atm/mol·K * 298.15 K)
≈ 0.2018 mol
Now let's calculate the final pressure after adding 2.00 g of N2 gas and cooling to -55°C.
Step 3: Convert the temperature to Kelvin.
T_final = -55°C + 273.15 = 218.15 K
Step 4: Calculate the number of moles of nitrogen gas added.
molar mass of N2 = 28.01 g/mol
m_N2_added = 2.00 g / 28.01 g/mol
≈ 0.0714 mol
Step 5: Calculate the total number of moles of nitrogen gas in the flask after adding.
n_final = n_initial + m_N2_added
≈ 0.2018 mol + 0.0714 mol
≈ 0.2732 mol
Step 6: Use the final number of moles and temperature to calculate the final pressure.
P_final = (n_final * R * T_final) / V
= (0.2732 mol * 0.0821 L·atm/mol·K * 218.15 K) / 5.00 L
≈ 0.2084 atm
Therefore, the final pressure in the flask, when an additional 2.00 g of N2 gas is added and the flask is cooled to -55°C, is approximately 0.2084 atm.
Use PV = nRT and solve for n in the flask initially. Then mols N2 added = 2 grams/molar mass N2.
Add to find total n (no of mols), and substitute into a new PV = nRT along with the new conditions and solve for the new pressure. Don't forget that T must be in kelvin.