<u>Answer:</u> The correct answer is Option d.
<u>Explanation:</u>
We are given:
Mass percentage of
= 20 %
So, mole fraction of
= 0.2
Mass percentage of
= 30 %
So, mole fraction of
= 0.3
Mass percentage of
= 35 %
So, mole fraction of
= 0.35
Mass percentage of
= 15 %
So, mole fraction of
= 0.15
We know that:
Molar mass of
= 16 g/mol
Molar mass of
= 28 g/mol
Molar mass of
= 26 g/mol
Molar mass of
= 48 g/mol
To calculate the average molecular mass of the mixture, we use the equation:
![\text{Average molecular weight of mixture}=\frac{_{i=1}^n\sum{\chi_im_i}}{n_i}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20molecular%20weight%20of%20mixture%7D%3D%5Cfrac%7B_%7Bi%3D1%7D%5En%5Csum%7B%5Cchi_im_i%7D%7D%7Bn_i%7D)
where,
= mole fractions of i-th species
= molar masses of i-th species
= number of observations
Putting values in above equation:
![\text{Average molecular weight}=\frac{(\chi_{CH_4}\times M_{CH_4})+(\chi_{C_2H_4}\times M_{C_2H_4})+(\chi_{C_2H_2}\times M_{C_2H_2})+(\chi_{C_2H_2O}\times M_{C_2H_2O})}{4}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20molecular%20weight%7D%3D%5Cfrac%7B%28%5Cchi_%7BCH_4%7D%5Ctimes%20M_%7BCH_4%7D%29%2B%28%5Cchi_%7BC_2H_4%7D%5Ctimes%20M_%7BC_2H_4%7D%29%2B%28%5Cchi_%7BC_2H_2%7D%5Ctimes%20M_%7BC_2H_2%7D%29%2B%28%5Cchi_%7BC_2H_2O%7D%5Ctimes%20M_%7BC_2H_2O%7D%29%7D%7B4%7D)
![\text{Average molecular weight of mixture}=\frac{(0.20\times 16)+(0.30\times 28)+(0.35\times 26)+(0.15\times 42)}{4}\\\\\text{Average molecular weight of mixture}=6.75](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20molecular%20weight%20of%20mixture%7D%3D%5Cfrac%7B%280.20%5Ctimes%2016%29%2B%280.30%5Ctimes%2028%29%2B%280.35%5Ctimes%2026%29%2B%280.15%5Ctimes%2042%29%7D%7B4%7D%5C%5C%5C%5C%5Ctext%7BAverage%20molecular%20weight%20of%20mixture%7D%3D6.75)
Hence, the correct answer is Option d.