Problem 79 - Chemistry The Central Science

Question

Adrenaline is the hormone that triggers the release of extra glucose molecules in times of stress or emergency. A solution of 0.64 g of adrenaline in 36.0 g of \(\mathrm{CCl}_{4}\) elevates the boiling point by \(0.49^{\circ} \mathrm{C}\) Calculate the approximate molar mass of adrenaline from this data.

Step-by-Step Solution

Answer

The approximate molar mass of adrenaline is calculated using boiling point elevation and given data, resulting in a molar mass of 95 g/mol.

Step 1: Find the molality of the solution

Since we know the mass of adrenaline, solvent, and the change in boiling point, we can find the molality of the solution using the boiling point elevation equation: ΔTb = Kb × molality × i We are given that ΔTb = 0.49ºC and i = 1. Therefore: molality = ΔTb / Kb Before moving on to Step 2, let's convert the mass of adrenaline and solvent into kg: 0.64 g adrenaline = 0.00064 kg adrenaline 36.0 g CCl4 = 0.036 kg CCl4

Step 2: Calculate the boiling point elevation constant (Kb)

To find Kb, we need to rearrange the boiling point elevation equation: Kb = ΔTb / (molality × i) In this problem, we are not given Kb. However, since ΔTb and i are known, we can express Kb in terms of molality: Kb = 0.49 / molality

Step 3: Calculate the moles of adrenaline

Using the molality (moles solute/kg solvent), we can find the moles of adrenaline: moles adrenaline = molality × 0.036 kg CCl4

Step 4: Calculate the molar mass of adrenaline

Finally, we can calculate the molar mass of adrenaline using the formula: molar mass = mass of adrenaline / moles of adrenaline 0.00064 kg adrenaline / (molality × 0.036 kg CCl4) = molar mass of adrenaline Now we can substitute the expression for Kb from Step 2: (0.00064 kg adrenaline / (0.49 / Kb × 0.036 kg CCl4)) = molar mass of adrenaline And solve for Kb: Kb = 0.49 × (0.49 / 0.00064) × (0.036/0.49) = 2.62 K kg/mol Now we can substitute Kb back into the equation for molality: molality = ΔTb / Kb = 0.49 / 2.62 = 0.187 mol/kg Plugging this value into the equation for moles adrenaline: moles adrenaline = 0.187 mol/kg × 0.036 kg CCl4 = 0.00672 mol Finally, we can calculate the molar mass of adrenaline: molar mass = 0.00064 kg adrenaline / 0.00672 mol = 0.095 kg/mol The approximate molar mass of adrenaline is 95 g/mol.

Key Concepts

Molar Mass Calculation

Calculating the molar mass of a substance is a fundamental skill in chemistry. It involves determining the mass of one mole of a substance, which is often expressed in grams per mole (g/mol). This concept is critical not only for identifying unknown substances, like adrenaline in our example, but also for understanding how substances behave in various chemical reactions.

To calculate the molar mass, you'll typically need to know the mass of the substance in question and the amount of substance, measured in moles. In the context of solution chemistry, you often find the amount in moles by using the concentration of the solution, such as molality or molarity.

• For adrenaline, the molality was calculated by identifying the boiling point elevation.
• Once you determine the moles of adrenaline, the molar mass is found by dividing the mass of adrenaline by the number of moles.

Whether working on an exam or a lab project, mastering molar mass calculations helps in predicting how much of a chemical is necessary for a reaction or to understand the properties of the solution.

Solution Chemistry

Solution chemistry explores how substances dissolve and interact within solutions. It's a key topic in chemistry that explains essential phenomena, from how our bellies digest food to industrial chemical processes.

In simple terms, a solution is a homogeneous mixture composed of two or more substances. It's mainly characterized by its solute and solvent:

• The solute is the substance that dissolves, like adrenaline in the given exercise.
• The solvent is the substance in which the solute dissolves, such as Carbon Tetrachloride ( CCl_4 ) in our case.
• Solution properties include concentration, boiling point elevation, and freezing point depression, helping identify the solution's chemical composition and its behavior under different conditions.

Understanding solution chemistry is vital whether you're calculating the effects of a diet program or creating a new cleaning product. Notably, in the exercise, the adrenaline-solution's boiling point elevation helps infer its concentration and molar mass.

Hormones and Molecular Mass

Hormones are biological molecules that play critical roles in regulating physiological processes. An understanding of their molecular mass is important, given their impact on the body. For instance, adrenaline, often dubbed the "fight or flight" hormone, is pivotal in stress responses.

Molecular mass affects how hormones function and interact in the body.

• A hormone like adrenaline must be understood not only chemically but also in terms of its effect on the human body.
• Knowing its molecular mass allows scientists to synthesize it effectively and accurately for medical uses.

The molar mass of adrenaline can affect everything from how quickly it's distributed in the bloodstream to how it binds to different receptors in cells. Understanding the molecular mass of hormones is essential not only for practical applications in medicine but also to unravel the complex network of biological interactions they partake in.