A sample of methane gas, CH4 was collected over water at 25 degrees celcius and 720 torr. The volume of the wet gas is 2.50L. What will be the volume of the dry methane at a standard pressure?
To find the volume of the dry methane gas at standard pressure, we need to use the combined gas law and apply Dalton's Law of Partial Pressure. Here's how we can solve this step by step:
Step 1: Convert degrees Celsius to Kelvin
To convert from Celsius to Kelvin, we add 273 to the Celsius temperature. So, 25 degrees Celsius is equal to 25 + 273 = 298 Kelvin.
Step 2: Calculate the partial pressure of methane gas
According to Dalton's Law of Partial Pressure, the total pressure of the mixture is equal to the sum of the individual partial pressures of the gases present. Since methane gas is collected over water, we need to consider the vapor pressure of water at the given temperature.
At 25 degrees Celsius, the vapor pressure of water is approximately 23.8 torr. So, the partial pressure of methane gas can be calculated by subtracting the vapor pressure of water from the total pressure:
Partial pressure of methane gas = Total pressure - Vapor pressure of water
= 720 torr - 23.8 torr
= 696.2 torr
Step 3: Apply the combined gas law
The combined gas law equation is:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = Initial pressure of the gas
V1 = Initial volume of the gas
T1 = Initial temperature of the gas
P2 = Final pressure of the gas
V2 = Final volume of the gas
T2 = Final temperature of the gas
Since we are comparing the initial wet gas volume with the final dry gas volume at standard pressure (which is 1 atmosphere or 760 torr), we have:
P1 = 696.2 torr
V1 = 2.50 L
T1 = 298 K
P2 = 760 torr (standard pressure)
V2 = Unknown volume (we are required to find this)
T2 = 298 K (no change in temperature)
Rearranging the equation, we get:
V2 = (P2 * V1 * T1) / (P1 * T2)
Substituting the values, we have:
V2 = (760 torr * 2.50 L * 298 K) / (696.2 torr * 298 K)
V2 = 2.545 L (rounded to three decimal places)
Therefore, the volume of the dry methane gas at standard pressure is approximately 2.545 liters.