the mole fraction of h2 in a mixture of h2 and ch4 is same as the mole fraction of c2h6in a mixture of c2h6 and c3h8 containing equal weight of c2h6 and c3h8 calculate mole fraction of ch4 in the mixture of h2 and Ch4
The easy way of doing this is to assume a mass(any number will do as long as you make mass C2H6 the same as mass of CH8) for mass C2H6 and C3H8 and calculate XC2H6. To do this you have mols C2H6 and mols C3H8. Then XC2H6 - mols C2H6/total mols.
That becomes XH2 (the same number it says in the problem) and 1-XH2 = XCH4.
To calculate the mole fraction of CH4 in the mixture of H2 and CH4, we first need to understand the concept of mole fraction.
Mole fraction (X) is defined as the ratio of the moles of a particular component to the total number of moles in the mixture. It is expressed as a decimal or a fraction.
In the given problem, we are given that the mole fraction of H2 in the mixture of H2 and CH4 is the same as the mole fraction of C2H6 in the mixture of C2H6 and C3H8. It is also mentioned that the mixture of C2H6 and C3H8 contains an equal weight of C2H6 and C3H8.
Let's assume that the total weight of the mixture of C2H6 and C3H8 is 1 unit (e.g., 1 gram).
Since the weight of C2H6 and C3H8 is equal, we can assign 0.5 units of weight to each of them. As we know the molecular weights of C2H6 and C3H8, we can now calculate the moles of each compound.
The molecular weight of C2H6 is 30 g/mol:
Moles of C2H6 = Weight of C2H6 / Molecular weight of C2H6
= 0.5 units / 30 g/mol
Similarly, the molecular weight of C3H8 is 44 g/mol, so the moles of C3H8 would also be:
Moles of C3H8 = Weight of C3H8 / Molecular weight of C3H8
= 0.5 units / 44 g/mol
Since we are given that the mole fraction of C2H6 in the mixture is the same as the mole fraction of H2 in the other mixture, it means the mole fractions of C2H6 and H2 would be equal.
Now, we need to calculate the moles of H2 using the given information. The molecular weight of H2 is 2 g/mol.
Given that the moles of C2H6 and H2 are equal, let's calculate the moles of H2:
Moles of H2 = Moles of C2H6
= 0.5 units / 30 g/mol
Now that we have the moles of H2, we can calculate the total moles in the mixture of H2 and CH4:
Total moles = Moles of H2 + Moles of CH4
Since we know that the mole fractions of H2 and CH4 should add up to 1, we can express the mole fraction of CH4 as:
Mole fraction of CH4 = Moles of CH4 / (Moles of H2 + Moles of CH4)
Substituting the values of moles into this equation will give us the desired mole fraction.