A gas mixture being used to simulate the atmosphere of another planet consists of 342 mg
of methane, 169 mg of argon, and 234 mg of
nitrogen. The partial pressure of nitrogen at
311 K is 10 kPa. Calculate the total pressure
of the mixture.
Answer in units of kPa
and calculate the volume in units of L
How many mols of N2 do you have ?
Well, 1 mol has mass of 2*14 = 28 grams
You have 0.234 grams so 0.234 grams * 1 mol/28 grams = 0.00836 mols of N2
P V = nRT
for the N2
10 kPascals * V = 0.00836 * R * 311
calculate V
then the partial pressures of the others are proportional to the number of mols of each
add those partial pressures to get total pressure.
To calculate the total pressure of the gas mixture, we need to understand the concept of partial pressure and use the ideal gas law. The ideal gas law equation is given by:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(K·mol)), and T is the temperature in Kelvin.
First, we need to calculate the number of moles of each gas component in the mixture. To do this, we use the formula:
n = (mass of substance) / (molar mass of substance)
The molar mass of methane (CH4) is 16.04 g/mol, for argon (Ar) is 39.95 g/mol, and for nitrogen (N2) is 28.02 g/mol. To convert milligrams to grams, we divide the given masses by 1000:
mass of methane = 342 mg = 342/1000 g
mass of argon = 169 mg = 169/1000 g
mass of nitrogen = 234 mg = 234/1000 g
Using the formula, we can now calculate the number of moles for each gas:
moles of methane = (342/1000) / (16.04) mol
moles of argon = (169/1000) / (39.95) mol
moles of nitrogen = (234/1000) / (28.02) mol
Next, we need to calculate the total moles of gas in the mixture by summing up the moles of each gas component:
total moles of gas = moles of methane + moles of argon + moles of nitrogen
Now, let's calculate the total pressure using the ideal gas law equation. Since we are given the temperature (311 K), we can rearrange the equation as follows:
P = (nRT) / V
We can solve for the total pressure by substituting the values of the total moles of gas, the ideal gas constant, and the temperature:
total pressure = (total moles of gas) * (R) * (temperature) / (volume)
Finally, we need to convert the pressure from atm to kPa by multiplying the total pressure by 101.325:
total pressure in kPa = (total pressure in atm) * (101.325)
To calculate the volume in L, we need to rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
Substituting the values of the total moles of gas, the ideal gas constant, the temperature, and the total pressure:
volume in L = (total moles of gas) * (R) * (temperature) / (total pressure in atm)
Now let's plug in the numbers to calculate the total pressure and volume:
1. Calculate the number of moles for each gas component:
moles of methane = (342/1000) / (16.04) = 0.021 mol
moles of argon = (169/1000) / (39.95) = 0.00423 mol
moles of nitrogen = (234/1000) / (28.02) = 0.00833 mol
2. Calculate the total moles of gas:
total moles of gas = 0.021 + 0.00423 + 0.00833 = 0.0336 mol
3. Calculate the total pressure:
total pressure = (0.0336) * (0.0821) * (311) / (V)
4. Convert the pressure from atm to kPa:
total pressure in kPa = (total pressure) * (101.325)
5. Calculate the volume:
volume in L = (0.0336) * (0.0821) * (311) / (total pressure in atm)