It is claimed that beef can be stored for up to two years at \(-23^{\circ} \mathrm{C}\) but no more than one year at \(-12^{\circ} \mathrm{C}\). Is this claim reasonable? Explain.

When it comes to understanding how fast a chemical reaction can proceed, the reaction rate constant, denoted by the symbol k, is an essential quantity. The reaction rate constant is a measure of the speed at which reactants are converted into products under specific conditions, including temperature and pressure.

The value of k is not just a number to plug into equations; it encapsulates vital information about the reaction. For example, in a refrigeration scenario, the rate at which meat spoils is a reaction that we can describe using a rate constant. A higher reaction rate constant at a given temperature means that the spoilage reactions are happening faster. This constant is crucial for food industries where packaging, storage, and shelf life are tied closely to the speed of these reactions.

In the exercise, understanding k helps explain why beef may spoil slower at lower temperatures, indicating that k is lower when the beef is stored at -23°C compared to that at -12°C. It reflects the general rule that most chemical reactions, including spoilage, slow down as temperatures decrease.

The term activation energy, symbolized by the variable Ea, refers to the minimum amount of energy required to initiate a chemical reaction. Imagine it as a barrier that reactants must overcome to transform into products. A higher activation energy means that fewer molecules have the necessary energy to react at a given temperature, which slows down the reaction rate.

In the context of food preservation, activation energy is the 'hill' that spoilage-causing bacteria or reactions need to climb to make the beef go bad. Lower temperatures make this 'hill' even harder to surmount, as fewer bacteria or molecules have the required energy, resulting in longer preservation times. This concept explains why there's a difference in shelf life for beef stored at the temperatures provided in the exercise—beef has a longer shelf life at -23°C because the activation energy barrier is more difficult to overcome at this lower temperature, leading to slower spoilage rates.

The exercise provided us with temperatures in degrees Celsius, but in order to apply them in the Arrhenius equation, we must perform a temperature conversion to Kelvin. This is necessary because Kelvin is the standard unit of temperature in the scientific community, particularly in thermodynamics and kinetics calculations.

To convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature. This conversion is based on the fact that 0 K, or absolute zero, is the point where molecules theoretically stop moving and is equivalent to -273.15°C. So, for the exercise, -23°C becomes 250.15 K and -12°C becomes 261.15 K. These Kelvin temperatures can then be used to calculate how the reaction rate constant changes with temperature, which is central to the question posed about the storage duration of beef at different temperatures. This calculation underscores the importance of precision in scientific measurements and translations between temperature scales.