Which of statements are True? (i) Octane number increases with chain length.
(ii) Cycloalkanes have higher Octane number than straight chain alkanes.
(iii) Alkenes and aromatic hydrocarbon have higher Octane number than straight chain alkanes.
(iv) Branched chain alkanes have lower octane number than straight chain alkanes.
Understanding Octane Number and Hydrocarbons
The octane number is a measure of a fuel's resistance to knocking or pinging during combustion in an internal combustion engine. Higher octane numbers indicate greater resistance to knocking. Different types of hydrocarbons have varying octane numbers based on their molecular structure.
Analyzing the Statements on Octane Number
Let's examine each statement provided regarding the octane number of different hydrocarbons:
- Statement (i): Octane number increases with chain length.
This statement is generally false for straight-chain alkanes. As the chain length of straight-chain alkanes increases, their tendency to autoignite (knock) increases, resulting in a lower octane number. For example, n-heptane (a straight-chain alkane with 7 carbon atoms) is assigned an octane number of 0, while isooctane (a branched-chain alkane with 8 carbon atoms) is assigned an octane number of 100.
- Statement (ii): Cycloalkanes have higher Octane number than straight chain alkanes.
This statement is generally true. Cycloalkanes are more stable and less prone to knocking compared to straight-chain alkanes with the same number of carbon atoms. For instance, cyclohexane typically has a higher octane rating than n-hexane.
- Statement (iii): Alkenes and aromatic hydrocarbon have higher Octane number than straight chain alkanes.
This statement is generally true. Unsaturated hydrocarbons like alkenes and aromatic hydrocarbons are more resistant to autoignition and thus have higher octane numbers than straight-chain alkanes of comparable molecular weight. For example, benzene (an aromatic hydrocarbon) and ethene (an alkene) have significantly higher octane numbers than n-hexane or n-heptane.
- Statement (iv): Branched chain alkanes have lower octane number than straight chain alkanes.
This statement is false. Branched-chain alkanes are less prone to knocking than straight-chain alkanes with the same number of carbon atoms. Branching increases the octane number. Isooctane (2,2,4-trimethylpentane), a highly branched alkane, is the reference standard with an octane number of 100, while n-heptane (a straight-chain alkane) has an octane number of 0.
Conclusion on True Statements
Based on the analysis:
- Statement (i) is False.
- Statement (ii) is True.
- Statement (iii) is True.
- Statement (iv) is False.
Therefore, the true statements are (ii) and (iii).
Revision Table: Octane Number Trends
| Hydrocarbon Type | Octane Number Trend | Resistance to Knocking |
|---|---|---|
| Straight-chain Alkanes | Lower (decreases with chain length) | Lower |
| Branched-chain Alkanes | Higher (increases with branching) | Higher |
| Cycloalkanes | Higher than straight-chain alkanes | Higher |
| Alkenes / Alkynes | Higher than alkanes | Higher |
| Aromatic Hydrocarbons | Highest among common fuel components | Highest |
Additional Information: Factors Affecting Octane Number
Several factors influence the octane number of a fuel:
- Molecular Structure: As discussed, branching and the presence of rings or double/triple bonds increase octane number.
- Additives: Substances like ethanol or MTBE (methyl tert-butyl ether) are added to gasoline to boost its octane rating.
- Engine Design: Higher compression ratio engines require fuels with higher octane numbers to prevent knocking.
Knocking occurs when the fuel-air mixture autoignites prematurely under pressure before the spark plug fires. This uncontrolled combustion can damage the engine.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
