100 cm3 of alkane X with the general formula CxHy requires 650 cm3 of oxygen for complete combustion. Deduce the structural formulae for the isomers of X.
To deduce the structural formulas of the isomers of alkane X with the general formula CxHy, we need to analyze the given information about the combustion reaction. Combustion of an alkane produces carbon dioxide (CO2) and water (H2O) as products.
From the balanced chemical equation for the complete combustion of an alkane:
CxHy + (x + y/4)O2 → xCO2 + (y/2)H2O
We can equate the number of carbon atoms and hydrogen atoms on both sides of the equation:
Number of carbon atoms:
CxHy = xCO2
Number of hydrogen atoms:
2(x + y/4) = y/2
Now, let's solve these equations to find the possible isomers.
1. Number of carbon atoms:
Since we are given that the general formula of alkane X is CxHy, the number of carbon atoms in X is equal to the coefficient of CO2, which is x.
2. Number of hydrogen atoms:
Using the second equation, we can simplify to find:
2x + y/2 = y/2
2x = 0
This means that y must be zero, indicating that there are no hydrogen atoms in alkane X. Therefore, X consists of only carbon atoms.
Based on this information, let's analyze the possible structures of alkane X:
- Alkane X consists of x carbon atoms and no hydrogen atoms, so it must be an acyclic (non-cyclic) alkane. Therefore, the structure of alkane X will be a carbon chain with x carbon atoms, with no branching or rings.
For example, if x = 4, the structural formula of alkane X with 4 carbon atoms would be:
CH3 - CH2 - CH2 - CH3
Where each dash represents a single covalent bond between carbon atoms.
By varying the value of x, you can deduce the structural formulas for the isomers of alkane X with the given general formula CxHy.
To deduce the structural formulas for the isomers of alkane X, we need to utilize the information given regarding its combustion and the balanced chemical equation for the complete combustion of alkanes.
First, let's examine the balanced chemical equation for the combustion of a generic alkane with the formula CxHy:
CxHy + (x + y/4)O2 -> xCO2 + (y/2)H2O
In this equation, CxHy represents the alkane, and the coefficients x and y represent the number of carbon and hydrogen atoms in the alkane, respectively.
From the given information, we know that 100 cm3 of alkane X requires 650 cm3 of oxygen for complete combustion. This means that the ratio of alkane X to oxygen is 100:650 or 1:6.5.
Based on this ratio, we can deduce that the simplest formula for alkane X is C1H1, which is methane (CH4). Let's verify this by plugging the values into the balanced chemical equation for combustion:
CH4 + 2O2 -> CO2 + 2H2O
Now, to determine the possible isomers of alkane X, we can manipulate the number of carbon and hydrogen atoms while preserving the ratio of 1:6.5.
Based on this ratio, here are the possible isomers of alkane X:
1) C1H6. This is not possible since it violates the concept of an alkane (saturated hydrocarbon) having the maximum number of hydrogen atoms per carbon atom.
2) C2H13. This is also not possible since it violates the concept of valency; carbon cannot have a valency greater than 4.
So, the only isomer that fulfills the condition is C1H4, which is methane (CH4). Therefore, the structural formula for alkane X is CH4.