Chemical Kinetics

The most commonly used catalyst for the hydrogenation of oils and fats is a nickel catalyst. Nickel catalysts are typically used in the form of finely divided nickel metal or nickel compounds, such as nickel oxide (NiO) or nickel on a support material like silica or alumina. These catalysts facilitate the addition of hydrogen gas (H₂) to the carbon-carbon double bonds present in unsaturated fatty acids, leading to the conversion of liquid vegetable oils into more solid fats or semi-solid products like margarine or shortening. Hydrogenation improves the stability and shelf life of oils and fats by reducing their susceptibility to oxidation and rancidity.

These catalysts facilitate the addition of hydrogen gas to the carbon-carbon double bonds present in unsaturated fatty acids, converting them into saturated fats. This process is utilized in the food industry to produce solid fats from liquid vegetable oils, thereby improving the texture, shelf life, and cooking properties of various food products.

To determine the effect of changing concentrations on the rate of reaction for the given rate law , we need to analyze how the rate is impacted when the concentration of is doubled and is halved.

Let's denote the initial concentrations as and . The initial rate is:

After doubling and halving , the new concentrations are and . The new rate is:

Calculating :

Now, find the factor by which the rate changes:

Thus, the rate increases by a factor of .

Therefore, the correct answer is:

To solve the problem, we use the first-order reaction kinetics formula and the concept of half-life.

1. Use the first-order reaction formula:

2. Given data:
- 25% complete in 30 minutes means 75% remains:

- We want to find time when 75% is complete, meaning 25% remains:

3. Calculate the rate constant :

4. Calculate time for 75% completion:

5. Substitute :

6. Approximate values:

7. Interpretation:
The time for 75% completion is about 145 minutes.

Final Answer:
The time required for 75% completion is approximately .