Question

Trans fats, or partially hydrogenated cooking oils, result from efforts of food manufacturers to increase the shelf life of many different forms of cooking oils. The free-flowing oils are treated with hydrogen, a catalyst, and high heat to change the structure of the oil, raising the melting point. The now solid oil is much more stable toward spoilage. A serious drawback to this process has been the realization that the trans form of the fat poses serious health risks when compared with the naturally occurring cis forms of the oils. The part of the hydrogenation process that results in the formation of trans fats can be summarized as follows: $$ \text { cis fat }(a q)+\mathrm{H}_{2}(a q) \rightleftharpoons \operatorname{trans} \operatorname{fat}(a q) $$ A typical value of \(K\) for this type of reaction is about \(5.0 .\) If we start with \(0.10 \mathrm{~mol} / \mathrm{L}\) each of cis fat and \(\mathrm{H}_{2}\), calculate the equilibrium concentrations.

Short answer

The equilibrium concentrations of cis fat, H₂, and trans fat are 0.05 mol/L, 0.05 mol/L, and 0.05 mol/L, respectively.

Step-by-step solution

Write initial concentrations

We are given the initial concentrations of cis fat and H₂, which are both 0.10 mol/L. Since there's no mention of the initial concentration of trans fat, we'll assume it is zero. Cis fat = 0.10 mol/L H₂ = 0.10 mol/L Trans fat = 0.00 mol/L

Set up the ICE table

Now, we need to set up our ICE (Initial, Change, Equilibrium) table to track the changes in concentrations during the reaction. We'll represent the change in concentration with a variable x. | | Cis fat | H₂ | Trans fat | |---------|--------------|----------|----------------| | Initial | 0.10 mol/L | 0.10 mol/L| 0.00 mol/L | | Change | -x | -x | +x | | Equilibrium | 0.10-x mol/L | 0.10-x mol/L | x mol/L |

Determine the K expression

The equilibrium constant expression for this reaction is given by: \(K = \frac{[Trans\ fat]}{[Cis\ fat] [H_2]}\) We are told that K = 5.0. We now need to plug in the equilibrium expressions from the ICE table into the K expression. \(5.0 = \frac{x}{(0.10 - x)(0.10 - x)}\)

Solve for x and find the equilibrium concentrations

Now, we will solve for x. Since K is not too large, we can assume x is much smaller than 0.10 mol/L. Therefore, 0.10 - x ≈ 0.10. \(5.0 = \frac{x}{(0.10)(0.10)}\) Multiplying both sides by 0.01, we get: \(x = 0.05\) Now that we have the value of x, we can find the equilibrium concentrations of cis fat, H₂, and trans fat: Cis fat = 0.10 - 0.05 = 0.05 mol/L H₂ = 0.10 - 0.05 = 0.05 mol/L Trans fat = 0.05 mol/L So, the equilibrium concentrations of cis fat, H₂, and trans fat are 0.05 mol/L, 0.05 mol/L, and 0.05 mol/L, respectively.

Key concepts

Trans Fats

Trans fats, often found in various processed foods, have become a topic of major health concern. They originate from the industrial process of converting unsaturated fats, such as vegetable oils, into semi-solid fats by adding hydrogen atoms to their molecular structures. This process improves the texture, shelf life, and flavor stability of foods. However, the introduction of trans fats into a diet has been associated with increased risks of heart disease, bad cholesterol (LDL) elevation, and a reduction in good cholesterol (HDL).

The health risks stem from the trans fat's unique configuration. Unlike the natural cis configuration of unsaturated fats, where hydrogen atoms are on the same side of the double bond, trans fats have their hydrogen atoms on opposite sides. This slight difference in structure significantly affects how the fats are processed in the body and their impact on health.

Recognizing these risks, many food manufacturers and regulatory agencies have taken steps to reduce or eliminate trans fats from their products. Nevertheless, it's crucial for consumers to check food labels and make informed choices to minimize their intake of trans fats.

Hydrogenation Process

The hydrogenation process is a chemical reaction that alters the nature of oils. It involves the addition of hydrogen atoms to unsaturated fats, usually in the presence of a catalyst such as nickel, to convert them to saturated fats or trans unsaturated fats. This is typically done by exposing the oil to hydrogen gas at high temperatures and pressures.

The primary reason for hydrogenating oils is to change their physical properties. Oils that are fully hydrogenated become solid and can be turned into margarine or shortening which are more shelf-stable and spreadable. Partial hydrogenation, which stops short of full saturation, is what leads to the creation of trans fats. A delicate balance is required during the process, as over-hydrogenation leads to a completely solid fat, while under-hydrogenation may not yield the desired stability and texture.

Moreover, the hydrogenation process is reversible—once the catalyst is removed and the oil is exposed to less hydrogen-rich conditions, it may return to its original state, a principle that is closely tied to the concept of chemical equilibrium.

Equilibrium Constant

The equilibrium constant (K) is a fundamental component in understanding chemical reactions that reach a state of balance where reactants and products are present at constant concentrations that no longer change with time, despite the ongoing process of the reaction. In the context of the hydrogenation process, the equilibrium constant quantifies the ratio of trans fats to the product of the concentrations of the reactants (cis fats and hydrogen) when the reaction is at equilibrium.

Mathematically, it is represented as:\[ K = \frac{[Trans\ fat]}{[Cis\ fat][H_2]} \] where the square brackets indicate the concentration of each component. A high value of K suggests a reaction that favors the formation of products (trans fats in this case), while a low value indicates a reaction that favors the reactants (cis fats and hydrogen).

The equilibrium constant is intrinsic to a given reaction at a specific temperature. Changing conditions such as temperature, or adding a catalyst, can shift the equilibrium position but does not change the value of K for a given reaction under the same conditions. In homework exercises, students use the K value to calculate the concentrations of reactants and products at equilibrium, providing crucial insight into the extent of the reaction.