a sample of natural gas is 85.2% methan, CH4, and 14.8% ethane, C2H6, by mass. What is the density of this mixture @ 18C and 748mmHg.
so i know that i have to use this formula
d=(PM)/(RT) but i don't know how to convert the percentages into g/mol (molecular weight)
can someone help me please?
thanks
0.852 x (16.04 g/mol) = 13.666 grams/mol.
0.148 x (30.07 g/mol) = 4.45036 grams/mol
18.11636 g/mol which rounds to 18.1 to three s.f.
Actually you are only using molar masses and multiplying them by a fraction so you still have molar mass when finished.
To find the density of the natural gas mixture, you first need to determine the molecular weight of each component based on their percentage composition.
To do this, you can start by assuming you have a 100g sample of the natural gas mixture. This means you have 85.2g of methane (CH4) and 14.8g of ethane (C2H6).
Next, you need to determine the number of moles of each component. To do this, you divide the mass of each component by its molar mass.
The molar mass of methane (CH4) is:
1 carbon (C) + 4 hydrogens (H) = 12.01 g/mol + 4(1.01 g/mol) = 16.05 g/mol
So, the number of moles of methane is:
85.2g / 16.05 g/mol = 5.3 mol
Similarly, the molar mass of ethane (C2H6) is:
2 carbons (C) + 6 hydrogens (H) = 2(12.01 g/mol) + 6(1.01 g/mol) = 30.07 g/mol
So, the number of moles of ethane is:
14.8g / 30.07 g/mol = 0.49 mol
Now that you have the number of moles of each component, you can calculate the total moles (n) in the mixture by adding the moles of methane and ethane together:
n = 5.3 mol + 0.49 mol = 5.79 mol
Next, you will need to use the ideal gas law equation to calculate the density of the mixture:
d = (PM) / (RT)
Where:
d = density (in g/L)
P = pressure (in atm)
M = molar mass of the mixture (in g/mol)
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature (in Kelvin)
In this case, the pressure is given as 748 mmHg. To convert this to atm, you need divide it by 760 mmHg (since 1 atm = 760 mmHg):
P = 748 mmHg / 760 mmHg = 0.984 atm
The temperature is given as 18°C. To convert this to Kelvin, you need to add 273.15:
T = 18°C + 273.15 = 291.15 K
Now you can substitute the values into the equation:
d = (0.984 atm) * (M) / (0.0821 L*atm/mol*K * 291.15 K)
To find M, you need to calculate the average molar mass of the mixture. This can be done by taking the sum of the products of the mole fractions of each component and their respective molar masses.
The mole fraction of methane (XCH4) is given by the moles of methane divided by the total moles:
XCH4 = 5.3 mol / 5.79 mol = 0.92
Similarly, the mole fraction of ethane (XC2H6) is given by the moles of ethane divided by the total moles:
XC2H6 = 0.49 mol / 5.79 mol = 0.08
To calculate the average molar mass, you can use the equation:
M = (XCH4 * MCH4) + (XC2H6 * MC2H6)
Substituting the values:
M = (0.92 * 16.05 g/mol) + (0.08 * 30.07 g/mol)
Now you have all the values to calculate the density of the mixture. Substitute the values of M, P, R, and T into the equation:
d = (0.984 atm) * [(0.92 * 16.05 g/mol) + (0.08 * 30.07 g/mol)] / (0.0821 L*atm/mol*K * 291.15 K)
Solve this equation to find the density of the natural gas mixture at 18°C and 748 mmHg.
0.852 x 16 = ?? for the methane part.
0.148 x 30 = ?? for the ethane part.
mass methane part + mass ethane part = effective molar mass of the mixture.
just for future references can u also put the units so i know what to cancel out and what units i will end up with?
thanks