Consider three 1.0 L flasks at 25° C and 96.66 kPa containing the gases CH4 (flask A), CO2 (flask B), and C2H6 (flask C). In which flask is there 0.039 moles of gas?
flask A
flask C
flask B
none
all
To determine which flask contains 0.039 moles of gas, we need to calculate the number of moles of gas in each flask.
The ideal gas law, PV = nRT, relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas. Rearranging the equation, we have n = PV / RT, where R is the ideal gas constant.
Given that the pressure (P) is 96.66 kPa, the volume (V) is 1.0 L, and the temperature (T) is 25°C (298.15 K), we can calculate the number of moles of gas in each flask using the formula n = PV / RT.
For flask A (CH4):
n = (96.66 kPa) * (1.0 L) / ((0.0831 L*atm/K*mol) * (298.15 K))
For flask B (CO2):
n = (96.66 kPa) * (1.0 L) / ((0.0831 L*atm/K*mol) * (298.15 K))
For flask C (C2H6):
n = (96.66 kPa) * (1.0 L) / ((0.0831 L*atm/K*mol) * (298.15 K))
Evaluating these calculations will give us the number of moles of gas in each flask. Comparing the results to 0.039 moles of gas will determine which flask contains that quantity.
To determine which flask contains 0.039 moles of gas, we need to compare the number of moles of gas in each flask. The number of moles of gas can be calculated using the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Given:
Pressure (P) = 96.66 kPa
Volume (V) = 1.0 L
Temperature (T) = 25°C = 298.15 K
We can rearrange the ideal gas law equation to solve for the number of moles of gas (n):
n = PV / RT
First, let's convert the pressure from kilopascals to atmospheres (since the ideal gas constant units are based on atm):
1 atm = 101.325 kPa
So, 96.66 kPa = 96.66 / 101.325 = 0.953 atm
For each flask, we can calculate the number of moles of gas using the ideal gas law equation:
Flask A (CH4):
n(A) = (0.953 atm)(1.0 L) / (0.0821 L·atm/mol·K)(298.15 K) ≈ 0.0388 moles
Flask B (CO2):
n(B) = (0.953 atm)(1.0 L) / (0.0821 L·atm/mol·K)(298.15 K) ≈ 0.0388 moles
Flask C (C2H6):
n(C) = (0.953 atm)(1.0 L) / (0.0821 L·atm/mol·K)(298.15 K) ≈ 0.0388 moles
From the calculations, we can see that all three flasks contain approximately 0.0388 moles of gas. Therefore, none of the flasks contain exactly 0.039 moles of gas.