Introduction:
Complete combustion of an alkane with oxygen (O2) results in the formation of carbon dioxide (CO2) and water (H2O) as the products. During this process, there is a volume contraction observed, which can be used to determine the molecular formula of the alkane.

Volume contraction during combustion:
When an alkane undergoes complete combustion with oxygen, it reacts to form carbon dioxide and water. The balanced chemical equation for the combustion of an alkane can be represented as follows:

CnH2n+2 + (3n + 1/2)O2 → nCO2 + (n + 1)H2O

In this reaction, for each mole of alkane, n moles of carbon dioxide and (n + 1) moles of water are produced. Since gases occupy more volume compared to liquids, the formation of these products leads to a decrease in volume, resulting in volume contraction.

Determination of molecular formula:
To determine the molecular formula of the alkane, we need to analyze the volume contraction observed during complete combustion. If the volume contraction is 50%, it means that the final volume is half of the initial volume.

1. Assume an initial volume of 1 liter for the alkane.
2. After complete combustion, the final volume would be 0.5 liters (50% contraction).
3. The molar ratio between the alkane and carbon dioxide is 1:1, and between the alkane and water is 1:(n + 1).
4. Since the final volume is half of the initial volume, it indicates that the number of moles of carbon dioxide and water is also half.
5. Therefore, the mole ratio between the alkane and carbon dioxide is 1:0.5, and between the alkane and water is 1:(n + 1)/2.
6. From the balanced chemical equation, we know that the mole ratio between the alkane and carbon dioxide is 1:1. This means that the alkane has the same number of carbon atoms as the carbon dioxide.
7. Similarly, the mole ratio between the alkane and water is 1:(n + 1)/2. This indicates that the alkane has half the number of hydrogen atoms compared to water.

Molecular formula of the alkane:
Based on the above analysis, the alkane has the same number of carbon atoms as carbon dioxide and half the number of hydrogen atoms compared to water. Therefore, the molecular formula of the alkane can be determined as follows:

- The number of carbon atoms = number of carbon atoms in carbon dioxide = n
- The number of hydrogen atoms = (number of hydrogen atoms in water)/2 = (n + 1)/2

Hence, the molecular formula of the alkane is CnH((n + 1)/2).

Summary:
Complete combustion of an alkane with oxygen results in volume contraction. By analyzing the volume contraction and considering the mole ratios between the alkane, carbon dioxide, and water, the molecular formula of the alkane can be determined. The alkane has the same number of carbon atoms as carbon dioxide and half the number of hydrogen atoms compared to water.