Question

Viscosity cocfficient \((\eta)\) of the liquids \(\mathrm{CII}_{3}\left(\mathrm{CII}_{2}\right)_{3}\) \(\mathrm{CII}_{3} ; \mathrm{CII}_{3}\left(\mathrm{CII}_{2}\right)_{4} \mathrm{CII}_{3}\) and \(\mathrm{CII}_{3}\left(\mathrm{CII}_{2}\right)_{5} \mathrm{CII}_{3}\) at \(30^{\circ} \mathrm{C}\) is \(2.11,2.89\) and \(3.68\) millipoise, respectively. The order of \(\eta\) of the liquids (1) \(a>b>c \) (2) \(a>b=c\) (3) \(\mathrm{a}<\mathrm{b}<\mathrm{c}\) (4) all are the same

Short answer

The order is (3) \(\mathrm{a} < \mathrm{b} < \mathrm{c}\).

Step-by-step solution

Understand Viscosity Coefficients

Viscosity is the measure of a fluid's resistance to deform under shear stress. Higher values indicate more resistance (thicker fluid). The given viscosities are 2.11, 2.89, and 3.68 millipoise.

Identify the Compounds

Examine the chemical formulas: 1. \(\text{CII}_{3}\text{(CII}_{2})_{3}\text{CII}_{3}\) 2. \(\text{CII}_{3}\text{(CII}_{2})_{4}\text{CII}_{3}\) 3. \(\text{CII}_{3}\text{(CII}_{2})_{5}\text{CII}_{3}\) These correspond to increasing chain lengths.

Match Viscosities to Compounds

List the viscosities with their respective compounds: 1. \(\text{CII}_{3}\text{(CII}_{2})_{3}\text{CII}_{3}\) with 2.11 millipoise 2. \(\text{CII}_{3}\text{(CII}_{2})_{4}\text{CII}_{3}\) with 2.89 millipoise 3. \(\text{CII}_{3}\text{(CII}_{2})_{5}\text{CII}_{3}\) with 3.68 millipoise

Compare Viscosities

Compare the values: 2.11, 2.89, and 3.68 millipoise. We can see that 2.11 < 2.89 < 3.68.

Conclusion

The order of viscosity coefficients \(\eta\) of the liquids is in ascending order. Thus, (3) \(\text{a} < \text{b} < \text{c}\) is correct.

Key concepts

Viscosity Coefficients

Viscosity coefficients are a measure of a fluid's resistance to flow or deform under shear stress. When we talk about viscosity, we are essentially discussing how 'thick' or 'thin' a liquid is. The higher the viscosity coefficient, the greater the resistance to flow. For instance, honey has a high viscosity coefficient compared to water, which means honey flows much slower than water. Let's look at the given liquids:

• The first liquid with a chemical formula of \(\text{CII}_{3}\text{(CII}_{2})_{3}\text{CII}_{3}\) has a viscosity coefficient of 2.11 millipoise.
• The second one, \(\text{CII}_{3}\text{(CII}_{2})_{4}\text{CII}_{3}\), has a viscosity of 2.89 millipoise.
• The third liquid, \(\text{CII}_{3}\text{(CII}_{2})_{5}\text{CII}_{3}\), shows a viscosity of 3.68 millipoise.

As the chain length increases, so does the viscosity coefficient, indicating these liquids become thicker and more resistant to flow.

Chemical Formulas

Chemical formulas represent the elemental composition and structure of a compound. In our exercise, we have three chemical compounds, all variations of a similar structure: \(\text{CII}_{3}\text{(CII}_{2})_{n}\text{CII}_{3}\), where \( n \) varies. Here's a breakdown:

• For \(\text{CII}_{3}\text{(CII}_{2})_{3}\text{CII}_{3}\), the subscript \((CII_{2})_{3}\) indicates three repeating units in the chain.
• \(\text{CII}_{3}\text{(CII}_{2})_{4}\text{CII}_{3}\) has four repeating units.
• \(\text{CII}_{3}\text{(CII}_{2})_{5}\text{CII}_{3}\) contains five units.

This progression shows an increase in the molecular chain length, which directly impacts the viscosity of the liquids. Longer chains mean more internal friction, leading to higher resistance to flow, thus increasing the viscosity coefficient.

Fluid Resistance

Fluid resistance is an essential concept in understanding how different liquids flow. It refers to the resistance a liquid offers to objects moving through it or to its own motion. Fluid resistance is strongly linked to viscosity. Higher viscosity means higher fluid resistance because the liquid is 'thicker' and harder to move through.

• In the context of our exercise, the fluid with \(\text{CII}_{3}\text{(CII}_{2})_{5}\text{CII}_{3}\), having a viscosity of 3.68 millipoise, offers the highest resistance.
• The liquid with \(\text{CII}_{3}\text{(CII}_{2})_{4}\text{CII}_{3}\) and viscosity of 2.89 millipoise has moderate resistance.
• Finally, the compound \(\text{CII}_{3}\text{(CII}_{2})_{3}\text{CII}_{3}\), with a viscosity of 2.11 millipoise, displays the least resistance.

Comparing these values helps us understand the concept better: higher viscosity entails greater fluid resistance, meaning the liquid moves more slowly and is harder to stir or pour.