A mixture of methane and helium is placed in a 2.0 l flask at 27 degrees the partial pressure of methane is 0.72 ATM and the partial pressure of helium is 0.22 ATM . What is the mole fraction of ch4?

mole fractions are proportional to temp:

find total moles:
n=PV/RT where P=.94ATM


n1/n=.72/.94

To find the mole fraction of CH4, we need to calculate the total pressure of the mixture and then use the partial pressures of each component.

Given:
Partial pressure of CH4 (PCH4) = 0.72 ATM
Partial pressure of helium (PHelium) = 0.22 ATM
Total volume of the flask (V) = 2.0 L

First, calculate the total pressure (PTotal) using the ideal gas law:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (27 degrees Celsius = 300 K)

Let's calculate the number of moles of CH4 first:

nCH4 = (PCH4 * V) / (R * T)
= (0.72 * 2.0) / (0.0821 * 300)
= 0.0247 moles of CH4

Next, calculate the number of moles of helium:

nHelium = (PHelium * V) / (R * T)
= (0.22 * 2.0) / (0.0821 * 300)
= 0.0072 moles of helium

Now, find the total number of moles in the mixture:

nTotal = nCH4 + nHelium
= 0.0247 + 0.0072
= 0.0319 moles of gas (CH4 + helium)

Finally, calculate the mole fraction of CH4:

Mole fraction of CH4 = nCH4 / nTotal
= 0.0247 / 0.0319
≈ 0.774 or 77.4% (rounded to three decimal places)

Therefore, the mole fraction of CH4 in the mixture is approximately 0.774 or 77.4%.

To find the mole fraction of CH4 (methane) in the mixture, we need to first calculate the total pressure of the mixture and then use the partial pressures to determine the mole fraction.

1. Start by calculating the total pressure of the mixture. The total pressure (Ptotal) is the sum of the partial pressures of the individual gases:

Ptotal = Pch4 + Phelium

Given that the partial pressure of methane (Pch4) is 0.72 ATM and the partial pressure of helium (Phelium) is 0.22 ATM, we can substitute these values into the equation:

Ptotal = 0.72 ATM + 0.22 ATM
Ptotal = 0.94 ATM

So, the total pressure of the mixture is 0.94 ATM.

2. Now we can calculate the mole fraction of methane (Xch4) using the formula:

Xch4 = Pch4 / Ptotal

Substituting the partial pressure of methane and the total pressure into the equation:

Xch4 = 0.72 ATM / 0.94 ATM
Xch4 ≈ 0.766

The mole fraction of CH4 in the mixture is approximately 0.766.