Question

This year, like many past years, you begin to feel very sleepy after eating a large helping of Thanksgiving turkey. Some people attribute this sleepiness to the presence of the amino acid tryptophan in turkey. Tryptophan can be used by the body to produce serotonin, which can calm the brain's activity and help to bring on sleep. a. What mass in grams of tryptophan is in a \(0.25\) -lb serving of turkey? (Assume tryptophan accounts for \(1.0 \%\) of the turkey mass.) b. What mass in grams of tryptophan is in \(0.25\) quart of milk? (Assume tryptophan accounts for \(2.0 \%\) of milk by mass and that the density of milk is \(1.04 \mathrm{~kg} / \mathrm{L}\).)

Short answer

a. The mass of tryptophan in a 0.25-lb serving of turkey is \(0.25 \times 453.592 \times 0.01 \mathrm{~g} = 1.13448 \mathrm{~g}\). b. The mass of tryptophan in a 0.25-quart serving of milk is \((0.25 \times 0.946353 \times 1.04 \mathrm{~kg}) \times 0.02 \mathrm{~g} = 4.93096 \mathrm{~g}\).

Step-by-step solution

Convert pounds to grams

We are given a 0.25-lb serving of turkey. To convert this to grams, we use the conversion factor: \(1 \mathrm{~lb} = 453.592 \mathrm{~g}\). So the mass of turkey in grams is: \(0.25 \times 453.592 \mathrm{~g}\).

Calculate the mass of tryptophan

We are given that tryptophan accounts for 1.0% of the turkey mass. Therefore, the mass of tryptophan in the 0.25-lb serving of turkey is: \(0.25 \times 453.592 \times 0.01 \mathrm{~g}\). #b. Mass of tryptophan in milk#

Convert quarts to grams

We are given a 0.25-quart serving of milk. To convert this to grams, we first need to convert quarts to liters using the conversion factor: \(1 \mathrm{~quart} = 0.946353 \mathrm{~L}\). Then, we use the given density of milk to convert liters to grams: \((0.25 \times 0.946353 \mathrm{~L}) \times (1.04 \mathrm{~kg} / \mathrm{L})\).

Calculate the mass of tryptophan

We are given that tryptophan accounts for 2.0% of the milk mass. Therefore, the mass of tryptophan in the 0.25-quart serving of milk is: \((0.25 \times 0.946353 \times 1.04 \mathrm{~kg}) \times 0.02 \mathrm{~g}\).

Key concepts

Chemical Calculations

Chemical calculations help us determine the amount of a specific substance within a larger mixture. In our exercise, we're interested in finding how much tryptophan is present in turkey and milk. To do this, we first need to know how much these items weigh in total, and what percentage of them is made up of tryptophan. For turkey, we know that tryptophan forms 1% of the turkey's mass. To find the mass of tryptophan, we multiply the total mass of turkey by 0.01. For milk, tryptophan is 2% of the total milk mass, so we multiply the total mass of milk by 0.02. By applying this method, we can accurately calculate the precise amount of tryptophan present in both these sources. These calculations are essential in nutritional science to assess dietary components and their impacts.

Unit Conversions

Unit conversions are a vital skill to have when working with any kind of measurements, especially in chemistry-related problems. In this exercise, we use conversions to determine the correct weight of the turkey and milk servings before calculating tryptophan content. For the turkey, we start with the weight given in pounds. Since 1 pound equals 453.592 grams, we compute the total gram weight by multiplying the pounds by this conversion factor. Similarly, for milk, it's initially measured in quarts. We convert quarts to liters, knowing 1 quart is approximately 0.946353 liters. With the volume in liters, we then convert it to grams using the density of milk. Unit conversions ensure measurements are in a standard format, making further calculations accurate and reliable.

Density

Density is a physical property defined as mass per unit volume, often expressed in units like kg/L or g/cm³. It plays a crucial role in our calculations for milk, where it helps convert volume to mass.In this exercise, we use the given density of milk (\(1.04 \, \text{kg/L}\)) to translate the volume into mass. First, we convert the volume of milk from quarts to liters, then multiply by the density to find the mass in kilograms. Since grams are more suited for this calculation, we convert kilograms to grams by multiplying by 1000.Knowing the density allows us to bridge the gap between how much space a substance occupies and how much it weighs, which is particularly useful when dealing with liquids like milk.