A sample of methane gas, CH4, was collected over water at 25.0ºC and 800 torr. The volume of the wet gas is 4.36 L. What will be the volume of the dry methane at standard pressure?
Voldry methane=_______L
(P1V1/T1) = (P2V2/T2)
P1 = 800 torr - vapor pressure water @ 25C.
P2 = Standard P
V1 = 4.36L
V2 = Solve for this.
T1 = 298 K
T2 = 273K
To find the volume of the dry methane at standard pressure, we need to use the concept of the ideal gas law.
The ideal gas law equation is: PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
First, we need to calculate the number of moles of methane in the collected sample.
To do this, we can use the formula:
n = PV / RT
Since the sample is collected over water, the pressure we have is the total pressure, which is the sum of the pressure of the methane gas and the vapor pressure of water.
Next, we need to calculate the vapor pressure of water at 25.0ºC. We can refer to a vapor pressure chart or use the Antoine equation:
log10(Pvp) = A - (B / (T + C))
Where:
Pvp = vapor pressure of water
A = 8.07131
B = 1730.63
C = 233.426
T = temperature in °C
By substituting T = 25.0ºC into the equation, we can calculate the vapor pressure of water.
Once we have the vapor pressure of water, we can calculate the pressure of the methane gas by subtracting the vapor pressure of water from the total pressure.
Now we can substitute the values of the pressure, volume, number of moles, and temperature into the ideal gas law equation to find the value of R.
Once we have the value of R, we can rearrange the ideal gas law equation to solve for the volume of the dry methane at standard pressure.
Vdry methane = (n * R * T) / Pstd
Where:
Pstd = standard pressure
Standard pressure is typically defined as 1 atmosphere or 760 mmHg.
Now, plug in the values for n, R, T, and Pstd into the equation and calculate the volume of the dry methane at standard pressure.
To calculate the volume of the dry methane at standard pressure, we need to use the gas laws. Specifically, we can use the ideal gas law:
PV = nRT
Where:
P is the pressure (in this case, standard pressure which is 1 atm)
V is the volume
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature (in kelvin)
First, let's convert the given temperature from Celsius to Kelvin:
T = 25.0ºC + 273.15 = 298.15 K
Next, we need to calculate the number of moles of methane in the given sample using the ideal gas law:
PV = nRT
(800 torr) * (4.36 L) = n * (0.0821 L·atm/mol·K) * (298.15 K)
n = (800 torr * 4.36 L) / (0.0821 L·atm/mol·K * 298.15 K)
n ≈ 0.181 mol
Now that we have the number of moles, we can use the ideal gas law to find the volume of the dry methane at standard pressure:
PV = nRT
(1 atm) * (V) = (0.181 mol) * (0.0821 L·atm/mol·K) * (298.15 K)
V = (0.181 mol * 0.0821 L·atm/mol·K * 298.15 K) / (1 atm)
V ≈ 4.43 L
Therefore, the volume of the dry methane at standard pressure will be approximately 4.43 L.