A gas mixture being used to simulate the atmosphere
of another planet consists of 322 mg
of methane, 146 mg of argon, and 251 mg of
nitrogen. The partial pressure of nitrogen at
319 K is 10 kPa. Calculate the total pressure
of the mixture.
Answer in units of kPa.
Calculate the volume.
Answer in units of L.
N comprises 251/(322+146+251) = 34.9% of the mixture, so ...
PV=kT so use that to get V.
To calculate the total pressure of the gas mixture, you need to sum up the partial pressures of each gas component.
First, let's convert the masses of each gas component from milligrams (mg) to grams (g) since the unit for pressure is typically in kilopascals (kPa) and the unit for volume is typically in liters (L).
Methane:
322 mg = 0.322 g
Argon:
146 mg = 0.146 g
Nitrogen:
251 mg = 0.251 g
Next, we need to calculate the partial pressure of each gas component. The partial pressure is given by the ideal gas law:
Partial Pressure = (n × R × T) / V
Where:
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/(K·mol))
T is the temperature in Kelvin (K)
V is the volume in liters (L)
Given that the partial pressure of nitrogen (N2) is 10 kPa, and the temperature is 319 K, we can use the formula to find the volume (V).
Partial Pressure of Nitrogen (PN2) = 10 kPa
Using the ideal gas law formula:
PN2 = (n × R × T) / V
Rearrange the equation to solve for volume (V):
V = (n × R × T) / PN2
Now, let's calculate the number of moles of nitrogen (n) using the mass and molar mass of nitrogen (28.02 g/mol):
n = mass / molecular mass
n = 0.251 g / 28.02 g/mol
Solve for n:
n ≈ 0.008963 mol
Substitute the values in the equation for volume (V):
V = (0.008963 mol × 0.0821 L·atm/(K·mol) × 319 K) / (10 kPa)
Simplify the equation and convert the pressure to kPa:
V = (0.008963 × 0.0821 × 319) / (10)
V ≈ 0.2312 L
Therefore, the volume of the mixture is approximately 0.2312 liters.
To calculate the total pressure of the mixture, we need to sum up the partial pressures of each gas component:
Total Pressure = Partial Pressure of Methane + Partial Pressure of Argon + Partial Pressure of Nitrogen
Since the partial pressures of methane and argon are not given, we'll assume they are negligible compared to the partial pressure of nitrogen. This allows us to approximate the total pressure as just the partial pressure of nitrogen.
Therefore, the total pressure of the gas mixture is approximately 10 kPa.