Problem 157 - A Complete Resource Book in Chemistry for JEE Main

Question

Hydrogenation of vegetable ghee at \(27^{\circ} \mathrm{C}\) reduces the pressure of \(\mathrm{H}_{2}\) from \(3 \mathrm{~atm}\) to \(2.18 \mathrm{~atm}\) in 40 minutes. The rate of reaction in terms of molarity per second is \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-t}\right)\) (a) \(1.357 \times 10^{-6}\) (b) \(1.537 \times 10^{-5}\) (c) \(1.375 \times 10^{-5}\) (d) \(6.250 \times 10^{-4}\)

Step-by-Step Solution

Answer

The rate of reaction is \( 1.375 \times 10^{-5} \), option (c).

Step 1: Identify Given Data

We are given that the initial pressure \( P_1 \) is \( 3 \, \text{atm} \), the final pressure \( P_2 \) is \( 2.18 \, \text{atm} \), and the time taken is 40 minutes.

Step 2: Convert Time to Seconds

Since the rate of reaction needs to be expressed in per second, convert 40 minutes to seconds by multiplying by 60: \( 40 \times 60 = 2400 \, \text{seconds} \).

Step 3: Calculate Change in Pressure

The change in pressure, \( \Delta P \), is given by \( P_1 - P_2 = 3 - 2.18 = 0.82 \, \text{atm} \).

Step 4: Use Ideal Gas Law to Find Molarity

Using the Ideal Gas Law, \( PV = nRT \), re-arranging gives \( n = \frac{PV}{RT} \). Hence, change in moles \( \Delta n = \frac{\Delta P \times V}{R \times T} \).

Step 5: Find Rate of Reaction

The rate of reaction, \( r \), is the change in moles per volume and per unit time. Therefore, we calculate:\[ r = \frac{\Delta P}{R \times T} \times \frac{1}{\text{time}} \]Substitute \( \Delta P = 0.82 \), \( R = 0.082 \), \( T = 27^{\circ} \text{C} + 273 = 300 \text{K} \), and time \( = 2400 \text{ seconds} \):\[ r = \frac{0.82}{0.082 \times 300} \times \frac{1}{2400} \approx 1.375 \times 10^{-5} \]

Step 6: Select the Correct Option

The calculated rate of reaction is \( 1.375 \times 10^{-5} \), which matches with option (c).

Key Concepts

Hydrogenation

Hydrogenation is a chemical reaction widely known for its ability to transform unsaturated fat into saturated fat. This process involves adding hydrogen to the fat molecule's double or triple bonds using a catalyst. A common example of this process is the hydrogenation of vegetable oils to produce margarine or shortenings, which results in a solid form of fat. This reaction requires specific conditions such as controlled temperature, pressure, and the presence of a catalyst, often nickel. During industrial hydrogenation, the pressure of hydrogen is a key factor that influences the speed and efficiency of the reaction. The process can be partial, resulting in substances with various degrees of saturation, or complete, totally saturating the fat molecule.
This significant industrial process influences the texture, shelf-life, and thermal stability of food products, making it an essential part of food manufacturing.

Ideal Gas Law

The Ideal Gas Law is an essential principle in chemistry and physics, represented by the equation \( PV = nRT \). This equation connects the pressure \(P\), volume \(V\), and temperature \(T\) of an ideal gas with the amount of gas measured in moles \(n\), where \(R\) is the ideal gas constant.

• The constant \(R\) varies depending on the units used but is typically given as \(0.082 \, \text{L} \, \text{atm} \, \text{mol}^{-1} \, \text{K}^{-1}\).
• Temperature \(T\) is measured in Kelvin (T\text{C} + 273 = \text{K}) to maintain consistency with the law.
• The equation assumes that gases behave ideally, meaning they conform to the laws of kinetic molecular theory and have no interactions between particles.

The ideal gas law is incredibly useful for calculating unknown values in a system when the others are known. In reactions involving gases, like hydrogenation, it helps calculate the change in the number of moles based on pressure changes, allowing for accurate reaction rate calculations.

Pressure Change

Understanding pressure change is crucial in many chemical reactions, especially those involving gases. Pressure is usually defined as the force exerted by gas particles colliding with the walls of a container. When chemical reactions occur in a closed system, such as the hydrogenation process in a pressurized container, changes in pressure indicate a change in the amount of gas present.
In hydrogenation, the pressure change from \(3 \, \text{atm}\) to \(2.18 \, \text{atm}\) signifies the consumption of hydrogen gas. Monitoring such changes can reveal insights about the reaction's progress and its rate.

• Pressure changes help in determining the effectivity of hydrogenation and the consumption rate of hydrogen.
• They aid in calculating the number of moles of gas consumed using the ideal gas law.
• Thus, pressure change data can be crucial for optimizing industrial processes, ensuring reactions are carried out at adequate rates for cost efficiency.

In summary, understanding pressure changes can offer significant insights into the behavior and efficiency of chemical reactions involving gases.