Question

Thyroxine, an important hormone that controls the rate of metabolism in the body, can be isolated from the thyroid gland. When 0.455 g thyroxine is dissolved in 10.0 g benzene, the freezing point of the solution is depressed by \(0.300^{\circ} \mathrm{C}\) . What is the molar mass of thyroxine? See Table \(11.5 .\)

Short answer

The molar mass of thyroxine is approximately \(776 \: \text{g/mol}\).

Step-by-step solution

Calculate the molality (m) of the solution

To calculate the molality of the solution, we will use the formula ΔT = K_f * m, where ΔT is the freezing point depression, K_f is the freezing point depression constant (in °C/molal) for the solvent, and m is the molality of the solution. Given, ΔT = 0.300°C and for benzene, K_f = 5.12°C/molal (from Table 11.5). Rearrange the formula to solve for m: m = ΔT / K_f m = 0.300°C / 5.12°C/molal m = 0.0586 molal

Calculate the moles of thyroxine in the solution

Now we can calculate the moles of thyroxine in the solution using the formula molality = moles solute / mass of solvent in kg. Given, weight of thyroxine = 0.455 g and weight of benzene = 10.0 g. First, convert the mass of benzene to kg: 10.0 g = 0.010 kg Rearrange the formula to solve for moles of solute: moles solute = molality * mass of solvent in kg moles solute = 0.0586 molal * 0.010 kg moles solute = 0.000586 mol

Find the molar mass of thyroxine

Now that we have the moles of thyroxine, we can find its molar mass by using the formula molar mass = mass / moles. Molar mass of thyroxine = 0.455 g / 0.000586 mol Molar mass of thyroxine ≈ 776 g/mol Thus, the molar mass of thyroxine is approximately 776 g/mol.

Key concepts

Molality

Molality is a key concept in chemistry used to describe the concentration of a solution. Unlike molarity, which depends on volume, molality depends on the mass of the solvent. This makes it particularly useful in situations where temperature can change the density of a liquid, like when freezing point is involved.
To calculate molality:\[ m = \frac{\Delta T}{K_f} \]
Where:

• \( m \) is the molality in mol/kg.
• \( \Delta T \) is the change in freezing point (in °C).
• \( K_f \) is the freezing point depression constant specific to the solvent (in °C/molal).

In our example with benzene and thyroxine, we see that a known change in freezing point and a solvent's characteristic constant allows us to find the molality. This is the foundational step in predicting how much a solute, like thyroxine, will affect the freezing point of a liquid like benzene.

Thyroxine

Thyroxine is a crucial hormone involved in regulating metabolism. It's typically produced by the thyroid gland and helps control how the body's cells use energy. Understanding thyroxine's properties, including its molar mass, is vital in biology and pharmacology.
In experiments, isolating and studying thyroxine requires precise measurement methods. By knowing its molar mass, scientists can determine the exact amount to use in biological experiments or synthesize it for therapeutic purposes. The exercise of determining thyroxine's molar mass through freezing point depression is an excellent example of using chemistry to explore biological molecules.

Molar Mass Determination

Determining the molar mass of a compound is a fundamental practice in chemistry. In the context of freezing point depression, this is achieved by first finding out how many moles of solute are present in a given mass of solvent. Using the formula for molar mass:\[ \text{Molar Mass} = \frac{\text{mass of solute}}{\text{moles of solute}} \]
Here's how to do it step by step:

• Calculate molality using the adjusted freezing point and the solvent's constant.
• Determine the moles of solute by multiplying molality by the mass of the solvent (in kg).
• Divide the mass of the solute by the number of moles to find the molar mass.

In our exercise, after calculating the molality of the thyroxine-benzene solution, we use this value to find the moles of thyroxine. With the mass known, this lets us compute its molar mass, revealing crucial information about the compound's molecular weight.