Four identical 1.0-L flasks contain the gases He, Cl2, CH4, and NH3, each at 0°C and 1 atm pressure. Which gas sample has the greatest number of molecules?
To determine which gas sample has the greatest number of molecules, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
Since all four gases are at the same conditions (0°C and 1 atm pressure), the equation simplifies to:
V = nRT/P
So, we can compare the number of moles for each gas and determine which gas has the greatest number of molecules.
First, let's convert the temperature from Celsius to Kelvin:
0°C = 273.15 K
Now, we can calculate the number of moles for each gas using the equation:
n = PV / RT
For Helium (He):
P = 1 atm
V = 1.0 L (given)
R = 0.0821 L·atm/mol·K
T = 273.15 K (converted from 0°C)
n(He) = (1 atm * 1.0 L) / (0.0821 L·atm/mol·K * 273.15 K) ≈ 0.0449 mol
For Chlorine (Cl2):
P = 1 atm
V = 1.0 L (given)
R = 0.0821 L·atm/mol·K
T = 273.15 K (converted from 0°C)
n(Cl2) = (1 atm * 1.0 L) / (0.0821 L·atm/mol·K * 273.15 K) ≈ 0.0449 mol
For Methane (CH4):
P = 1 atm
V = 1.0 L (given)
R = 0.0821 L·atm/mol·K
T = 273.15 K (converted from 0°C)
n(CH4) = (1 atm * 1.0 L) / (0.0821 L·atm/mol·K * 273.15 K) ≈ 0.0449 mol
For Ammonia (NH3):
P = 1 atm
V = 1.0 L (given)
R = 0.0821 L·atm/mol·K
T = 273.15 K (converted from 0°C)
n(NH3) = (1 atm * 1.0 L) / (0.0821 L·atm/mol·K * 273.15 K) ≈ 0.0449 mol
As we can see, all four gases have approximately the same number of moles, which means they have an equal number of molecules. Therefore, none of the gases has a greater number of molecules than the others.
To determine which gas sample has the greatest number of molecules, we need to use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Since all four flasks contain gases at the same temperature (0°C or 273 K) and pressure (1 atm), the only variable that will affect the number of gas molecules is the number of moles (n).
To compare the number of molecules in each sample, we can use the equation n = PV/RT. Since the volume (V) and temperature (T) are the same for all samples, we can simplify the equation to n = P/R.
The value of R is a constant, so the number of moles (n) is directly proportional to the pressure (P).
Therefore, the gas sample with the greatest number of molecules is the one with the highest pressure. In this case, 1 atm pressure is the same for all the gases. So, all four gas samples have the same number of molecules.
na
PV = nRT. Solve for n
n = PV/RT
You know P, V, R, and T, and all or them are the same; therefore, n must be ......