An Unbranched Alkane Has A Molar Mass Of 114 G/mol 114 \, \text{g/mol} 114 G/mol . This Alkane Contains: C = 12 , H = 1 {C=12, \, H=1} C = 12 , H = 1 A) 6 Methylene Groups, 2 Methyl Groups B) 2 Methylene Groups, 6 Methyl Groups C) 4 Methylene Groups, 4 Methyl Groups D) 2

An Unbranched Alkane: Understanding Its Molecular Composition

In the world of organic chemistry, understanding the molecular composition of alkanes is crucial for grasping their properties and behavior. Alkanes are a series of hydrocarbons that consist of only carbon and hydrogen atoms. They are typically saturated, meaning they do not contain any multiple bonds between carbon atoms. In this article, we will delve into the molecular composition of an unbranched alkane with a molar mass of $114 \, \text{g/mol}$ and explore the possible combinations of methylene and methyl groups that make up its structure.

The Molar Mass of Alkanes

The molar mass of an alkane is a critical piece of information that can be used to determine its molecular composition. The molar mass of an alkane is calculated by summing the atomic masses of its constituent atoms. In the case of the alkane in question, the molar mass is $114 \, \text{g/mol}$. This value can be used to determine the number of carbon and hydrogen atoms present in the molecule.

Atomic Masses of Carbon and Hydrogen

The atomic masses of carbon and hydrogen are $12 \, \text{g/mol}$ and $1 \, \text{g/mol}$, respectively. These values are used to calculate the molar mass of the alkane.

Calculating the Number of Carbon and Hydrogen Atoms

To calculate the number of carbon and hydrogen atoms present in the alkane, we can use the following formula:

$$\text{Number of atoms} = \frac{\text{Molar mass}}{\text{Atomic mass}}$$

Using this formula, we can calculate the number of carbon and hydrogen atoms present in the alkane:

$$\text{Number of carbon atoms} = \frac{114 \, \text{g/mol}}{12 \, \text{g/mol}} = 9.5$$

$$\text{Number of hydrogen atoms} = \frac{114 \, \text{g/mol}}{1 \, \text{g/mol}} = 114$$

Since the number of carbon atoms must be an integer, we can round down to 9 carbon atoms. This means that the alkane has 9 carbon atoms and 114 hydrogen atoms.

Methylene and Methyl Groups

Methylene groups are a type of functional group that consists of a carbon atom bonded to two hydrogen atoms. Methyl groups, on the other hand, are a type of functional group that consists of a carbon atom bonded to three hydrogen atoms. In an unbranched alkane, the carbon atoms are arranged in a straight chain, with each carbon atom bonded to two hydrogen atoms and one other carbon atom.

Possible Combinations of Methylene and Methyl Groups

Given the number of carbon and hydrogen atoms present in the alkane, we can explore the possible combinations of methylene and methyl groups that make up its structure. Let's consider the following options:

a) 6 methylene groups, 2 methyl groups

In this option, the alkane would have 6 methylene groups and 2 methyl groups. The 6 methylene groups would contribute 12 carbon atoms and 12 hydrogen atoms, while the 2 methyl groups would contribute 2 carbon atoms and 6 hydrogen atoms. This would give a total of 14 carbon atoms and 18 hydrogen atoms, which is not consistent with the calculated values.

b) 2 methylene groups, 6 methyl groups

In this option, the alkane would have 2 methylene groups and 6 methyl groups. The 2 methylene groups would contribute 4 carbon atoms and 4 hydrogen atoms, while the 6 methyl groups would contribute 6 carbon atoms and 18 hydrogen atoms. This would give a total of 10 carbon atoms and 22 hydrogen atoms, which is not consistent with the calculated values.

c) 4 methylene groups, 4 methyl groups

In this option, the alkane would have 4 methylene groups and 4 methyl groups. The 4 methylene groups would contribute 8 carbon atoms and 8 hydrogen atoms, while the 4 methyl groups would contribute 4 carbon atoms and 12 hydrogen atoms. This would give a total of 12 carbon atoms and 20 hydrogen atoms, which is not consistent with the calculated values.

d) 2 methylene groups, 7 methyl groups

In this option, the alkane would have 2 methylene groups and 7 methyl groups. The 2 methylene groups would contribute 4 carbon atoms and 4 hydrogen atoms, while the 7 methyl groups would contribute 7 carbon atoms and 21 hydrogen atoms. This would give a total of 11 carbon atoms and 25 hydrogen atoms, which is not consistent with the calculated values.

In conclusion, the correct answer is not among the options listed. However, we can use the information provided to determine the correct combination of methylene and methyl groups that make up the structure of the alkane. The alkane has 9 carbon atoms and 114 hydrogen atoms. To determine the correct combination of methylene and methyl groups, we can use the following formula:

$$\text{Number of methylene groups} = \frac{\text{Number of carbon atoms}}{2}$$

$$\text{Number of methyl groups} = \text{Number of carbon atoms} - \text{Number of methylene groups}$$

Using this formula, we can calculate the number of methylene and methyl groups present in the alkane:

$$\text{Number of methylene groups} = \frac{9}{2} = 4.5$$

Since the number of methylene groups must be an integer, we can round down to 4 methylene groups. This means that the alkane has 4 methylene groups and 5 methyl groups.

The correct answer is c) 4 methylene groups, 5 methyl groups.
Q&A: Understanding the Molecular Composition of Alkanes

In our previous article, we explored the molecular composition of an unbranched alkane with a molar mass of $114 \, \text{g/mol}$. We determined that the alkane has 9 carbon atoms and 114 hydrogen atoms, and we used this information to calculate the number of methylene and methyl groups present in its structure. In this article, we will answer some frequently asked questions about the molecular composition of alkanes.

Q: What is the difference between a methylene group and a methyl group?

A: A methylene group is a type of functional group that consists of a carbon atom bonded to two hydrogen atoms. A methyl group, on the other hand, is a type of functional group that consists of a carbon atom bonded to three hydrogen atoms.

Q: How do I determine the number of methylene and methyl groups in an alkane?

A: To determine the number of methylene and methyl groups in an alkane, you can use the following formula:

$$\text{Number of methylene groups} = \frac{\text{Number of carbon atoms}}{2}$$

$$\text{Number of methyl groups} = \text{Number of carbon atoms} - \text{Number of methylene groups}$$

Q: What is the significance of the molar mass of an alkane?

A: The molar mass of an alkane is a critical piece of information that can be used to determine its molecular composition. The molar mass is calculated by summing the atomic masses of its constituent atoms.

Q: How do I calculate the molar mass of an alkane?

A: To calculate the molar mass of an alkane, you can use the following formula:

$$\text{Molar mass} = \text{Number of carbon atoms} \times \text{Atomic mass of carbon} + \text{Number of hydrogen atoms} \times \text{Atomic mass of hydrogen}$$

Q: What is the difference between a branched and an unbranched alkane?

A: A branched alkane is an alkane that has a carbon atom bonded to more than two other carbon atoms. An unbranched alkane, on the other hand, is an alkane that has a carbon atom bonded to only two other carbon atoms.

Q: How do I determine the number of carbon and hydrogen atoms in an alkane?

A: To determine the number of carbon and hydrogen atoms in an alkane, you can use the following formula:

$$\text{Number of carbon atoms} = \frac{\text{Molar mass}}{\text{Atomic mass of carbon}}$$

$$\text{Number of hydrogen atoms} = \frac{\text{Molar mass}}{\text{Atomic mass of hydrogen}}$$

Q: What is the significance of the molecular composition of an alkane?

A: The molecular composition of an alkane is critical for understanding its properties and behavior. The molecular composition can be used to determine the number of methylene and methyl groups present in the alkane, which can affect its physical and chemical properties.

In conclusion, understanding the molecular composition of alkanes is crucial for grasping their properties and behavior. By using the formulas and techniques outlined in this article, you can determine the number of methylene and methyl groups present in an alkane and understand its molecular composition.