Question

Potency of Hormones Under normal conditions, the human adrenal medulla secretes epinephrine \(\left(\mathrm{C}_{9} \mathrm{H}_{13} \mathrm{NO}_{3}\right)\) at a rate sufficient to maintain a concentration of \(10^{-10} \mathrm{M}\) in circulating blood. To appreciate what that concentration means, calculate the volume of water that you would need to dissolve \(1.0 \mathrm{~g}\) (about 1 teaspoon) of epinephrine to a concentration equal to that in blood.

Short answer

Approximately 54.6 million liters of water are needed.

Step-by-step solution

Calculate the Moles of Epinephrine

First, we need to find out how many moles are in 1.0 g of epinephrine. Use the molar mass of epinephrine, which is approximately 183.21 g/mol. Calculate the moles using the formula:\[moles = \frac{mass}{molar\ mass} = \frac{1.0 \ g}{183.21 \ g/mol}\approx 0.00546 \ mol\]

Determine the Total Volume Needed

To find the volume that would result in the same concentration as in blood (\(10^{-10}\ M\), which is mol/L), rearrange the formula for concentration:\[volume = \frac{moles}{concentration} = \frac{0.00546 \ mol}{10^{-10} \ mol/L} = 5.46 \times 10^7 \ L\]

Verification of Results

It may seem like a large volume, but due to the extremely low concentration in blood, this check confirms the results. Therefore, you would need approximately 54.6 million liters of water to dissolve 1 g of epinephrine to achieve the same concentration as in blood.

Key concepts

Hormone Concentration

Hormones play a crucial role in regulating bodily functions, often doing so through incredibly low concentrations, especially in the case of blood circulation. Understanding hormone concentration is fundamental in biochemistry because it helps us comprehend how even minute amounts of a substance can significantly impact biological processes. In this exercise, the hormone epinephrine is maintained at a very low concentration of \(10^{-10} \ M\) in human blood. This highlights how our bodies require only trace amounts of epinephrine to properly carry out its functions, such as increasing heart rate and boosting energy levels during stress.The concept of hormone concentration is tied to how these molecules interact with receptors on cells, mainly due to their specific and potent effects. It also showcases why precise hormonal balance is vital for proper physiological function. Even slight deviations in hormone levels can lead to significant changes in how our body operates. Understanding this concentration helps us appreciate how sensitive our body systems are to these biochemicals.

Epinephrine Calculations

Calculating the amount of a hormone like epinephrine needed to achieve specific concentrations involves understanding the mass-to-mole conversion and how it pertains to solutions in biochemistry. We start by determining the number of moles in a given mass of a substance. Using the molar mass of epinephrine, 183.21 g/mol, we find the moles in 1 g. This represents the basic stoichiometric calculation which underpins much of biochemistry.In practice, to achieve the concentration of \(10^{-10} \ M\), the calculations reveal that dissolving 1 g of epinephrine requires a surprisingly large volume of water, approximately 54.6 million liters. It underscores just how potent hormones are, as such a tiny mass translates into a vast volume when diluted to physiological concentrations. These calculations are critical for research and development in pharmaceuticals and therapies where precision is paramount.

Molarity in Biochemistry

Molarity is a central concept in biochemistry, defining the concentration of a solute in a solution in terms of moles per liter (mol/L). This unit is pivotal because it provides a way to describe how substances interact in a biological context, especially given the vast differences in concentration required for ordinary biochemical processes.When working with substances like hormones, understanding molarity becomes extremely crucial due to the often minuscule amounts needed to effect change. For instance, when calculating how much water is necessary to achieve a \(10^{-10} \ M\) concentration of epinephrine, it becomes evident how significant smallness plays a role. Molarity lets scientists and students discern how concentrated or dilute a solution is, thereby informing experimental design, hypothesis testing, and biochemical analysis.By mastering molarity, students can better predict how molecules will behave in solution, how they will interact, and the extent of their biological effects, given different parameters.