A 6.0 L flask contains a mixture of methane, argon and helium at 45 degrees C and 1.75 am. If the mole fractions of helium and argon are 0.25 and 0.35, respectively, how many molecules of methane are present?
9.6*10^22
total mole fraction = 1.00 (always)
XHe + XAr + XCH4 = 1.00
Solve for XCH4.
Then PCH4 = XCH4*Ptotal
Use PV = nRT to solve for n
Then remember there are 6.022E23 molecules in 1 mole.
To determine the number of molecules of methane present, we need to find the mole fraction of methane first.
The total mole fraction of the mixture can be calculated by summing the mole fractions of each component:
X_total = X_methane + X_argon + X_helium
Where:
X_total = Total mole fraction of the mixture
X_methane = Mole fraction of methane
X_argon = Mole fraction of argon
X_helium = Mole fraction of helium
Since the mole fractions of helium and argon are given, we can rearrange the equation to find the mole fraction of methane:
X_methane = X_total - X_argon - X_helium
Given that X_total = 1 (since it represents the total mole fraction of the mixture), X_argon = 0.35, and X_helium = 0.25, we can substitute these values into the equation:
X_methane = 1 - 0.35 - 0.25
X_methane = 0.4
Now, we can use the ideal gas law to calculate the number of molecules of methane:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
We need to calculate the number of moles of methane, so we rearrange the equation:
n = PV / RT
Given that the pressure is 1.75 atm, the volume is 6.0 L, and the temperature is 45 degrees C (which needs to be converted to Kelvins: 45 + 273 = 318 K), and the gas constant R is 0.0821 L·atm/mol·K, we can substitute these values into the equation to find the number of moles of methane:
n = (1.75 atm) * (6.0 L) / (0.0821 L·atm/mol·K * 318 K)
n ≈ 0.331 mol
Finally, we can calculate the number of molecules of methane:
Number of molecules = n * Avogadro's number
Given that Avogadro's number is approximately 6.022*10^23 molecules/mol, we can substitute these values into the equation:
Number of molecules = (0.331 mol) * (6.022*10^23 molecules/mol)
Number of molecules ≈ 1.99*10^23 molecules
Therefore, there are approximately 1.99*10^23 molecules of methane present in the mixture.
To find the number of molecules of methane present in the flask, we need to:
Step 1: Convert the given conditions to the number of moles of each gas. We can use the ideal gas law equation, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Given:
- Volume (V) = 6.0 L
- Temperature (T) = 45 degrees C = 45 + 273.15 = 318.15 K
- Pressure (P) = 1.75 atm
Step 2: Calculate the mole fraction of methane. Since we are given the mole fractions of helium and argon, we can calculate the mole fraction of methane by subtracting the sum of helium and argon mole fractions from 1.
Given:
- Mole fraction of helium (X_He) = 0.25
- Mole fraction of argon (X_Ar) = 0.35
Mole fraction of methane:
X_CH4 = 1 - (X_He + X_Ar)
X_CH4 = 1 - (0.25 + 0.35)
X_CH4 = 1 - 0.60
X_CH4 = 0.40
Step 3: Calculate the number of moles of methane. We can use the equation n = (P * V) / (R * T), where n is the number of moles, P is the pressure, V is the volume, R is the gas constant, and T is the temperature.
Given:
- Gas constant (R) = 0.0821 L·atm/(mol·K)
Number of moles of methane:
n_CH4 = (P * V) / (R * T)
n_CH4 = (1.75 atm * 6.0 L) / (0.0821 L·atm/(mol·K) * 318.15 K)
Step 4: Calculate the number of molecules of methane. Since 1 mole of any gas contains Avogadro's number of molecules (6.022 × 10^23), we can multiply the number of moles of methane by Avogadro's number to get the number of molecules.
Number of molecules of methane:
Number of molecules_CH4 = n_CH4 * Avogadro's number
Using the calculated value of n_CH4 from Step 3 and Avogadro's number (6.022 × 10^23), you can compute the final answer to find the number of molecules of methane present in the flask.