a wet gas collected over water has a volume of 900 mL at50 degrees Celsius and a pressure of 84.6 kPa. The partial pressure of water at this temperature is 12.3 kPa. What is the volume of the dry gas at 120 kPa?
Use (P1V1/T1) = (P2V2/T2)
P1 = 84.6 kPa for wet gas
pH2O = 12.3 kPa
P1 = 84.6 kPa - 12.3 kPa = ? kPa for dry gas.
P2 = 120 kPa
To find the volume of the dry gas at 120 kPa, we can make use of the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In this case, we know the initial conditions of the wet gas collected over water and want to find the final volume of the dry gas. Let's break down the problem step by step:
Step 1: Find the number of moles of water vapor
To do this, we can use the relationship between pressure and number of moles:
P_water * V_water = n_water * R * T
Where:
P_water = partial pressure of water
V_water = volume of water vapor
n_water = number of moles of water vapor
Substituting the given values:
12.3 kPa * V_water = n_water * R * (50 + 273.15) K
Step 2: Find the number of moles of the wet gas
The number of moles of the wet gas can be calculated using the ideal gas law equation and the given values:
P_wet_gas * V_wet_gas = n_wet_gas * R * T
Where:
P_wet_gas = pressure of the wet gas
V_wet_gas = volume of the wet gas
n_wet_gas = number of moles of the wet gas
Substituting the given values:
84.6 kPa * 900 mL = n_wet_gas * R * (50 + 273.15) K
Step 3: Find the total number of moles
Now, we can find the total number of moles of the gas mixture by adding the moles of water vapor and the moles of the wet gas:
n_total = n_wet_gas + n_water
Step 4: Find the volume of the dry gas
Using the ideal gas law, we can find the final volume of the dry gas:
V_dry_gas = (n_total * R * T) / P_dry_gas
Where:
P_dry_gas = pressure of the dry gas
Substituting the given values:
V_dry_gas = (n_total * R * T) / 120 kPa
Now, to get the final answer, let's substitute the values obtained in each step into the formula and solve for V_dry_gas.