Question

The natural abundances of elements in the human body, expressed as percent by mass, are oxygen (O), 65 percent; carbon (C), 18 percent; hydrogen (H), 10 percent; nitrogen \((\mathrm{N}), 3\) percent; calcium (Ca), 1.6 percent; phosphorus (P), 1.2 percent; all other elements, 1.2 percent. Calculate the mass in grams of each element in the body of a \(62-\mathrm{kg}\) person.

Short answer

O: 40,300 g; C: 11,160 g; H: 6,200 g; N: 1,860 g; Ca: 992 g; P: 744 g; Others: 744 g.

Step-by-step solution

Understand the Problem

We need to determine the mass of each element in a person's body using the given percentages and the total mass of the person, which is 62 kg.

Convert Total Mass to Grams

Since the elemental abundances are given in percent by mass, and the total mass of the person is 62 kg, convert the person's mass to grams for easier calculations. 1 kg = 1000 grams. Thus, 62 kg = 62,000 grams.

Calculate Mass of Oxygen (O)

Use the percentage of oxygen in the body (65%) to find its mass in grams. Mass of oxygen = \( 0.65 \times 62000 = 40300 \text{ grams} \).

Calculate Mass of Carbon (C)

Calculate the mass of carbon using its percentage (18%). Mass of carbon = \( 0.18 \times 62000 = 11160 \text{ grams} \).

Calculate Mass of Hydrogen (H)

Find the mass of hydrogen using its percentage (10%). Mass of hydrogen = \( 0.10 \times 62000 = 6200 \text{ grams} \).

Calculate Mass of Nitrogen (N)

Determine the mass of nitrogen using its percentage (3%). Mass of nitrogen = \( 0.03 \times 62000 = 1860 \text{ grams} \).

Calculate Mass of Calcium (Ca)

Find the mass of calcium using its percentage (1.6%). Mass of calcium = \( 0.016 \times 62000 = 992 \text{ grams} \).

Calculate Mass of Phosphorus (P)

Use the percentage of phosphorus (1.2%) to calculate its mass. Mass of phosphorus = \( 0.012 \times 62000 = 744 \text{ grams} \).

Calculate Mass of All Other Elements

Calculate the mass of all other elements, which collectively make up 1.2%. All other elements' mass = \( 0.012 \times 62000 = 744 \text{ grams} \).

Summary of Results

The mass in grams of each element in a 62 kg person is as follows: - Oxygen: 40,300 g - Carbon: 11,160 g - Hydrogen: 6,200 g - Nitrogen: 1,860 g - Calcium: 992 g - Phosphorus: 744 g - All other elements: 744 g.

Key concepts

Understanding Percentage Composition

In chemistry, percentage composition is used to express the mass percentage of each element in a compound or mixture. It helps us understand how much of each component is present in a given mass. This can be especially useful when analyzing complex mixtures, like the human body.
To calculate percentage composition, you take the mass of an element in a compound and divide it by the total mass of the compound. Then, multiply by 100 to get the percentage.
In the context of the human body, this calculation helps illustrate how elements like oxygen, carbon, and hydrogen make up a significant portion of our body mass.

Basics of Mass Calculation

Mass calculation involves using the total weight and the percentage composition to find the precise mass of individual components. In this example, the total mass of a person is given as 62 kg, or 62,000 grams.
To find the mass of an individual element, you multiply the total mass by the percentage of that element (expressed as a decimal). For instance, to find the mass of oxygen, which is 65%, you would calculate:
Mass of oxygen = 0.65 x 62,000 g = 40,300 grams.
This process is repeated for each element, using their respective percentages.

Identifying Elements in the Human Body

The human body is made up of elements, and understanding their composition can give insights into biological and chemical processes.
The primary elements present in the human body include:

• Oxygen (O): 65%
• Carbon (C): 18%
• Hydrogen (H): 10%
• Nitrogen (N): 3%
• Calcium (Ca): 1.6%
• Phosphorus (P): 1.2%

These make up the majority of the body's mass, with all other trace elements constituting the remaining 1.2%. Understanding these basic elements is important for studying human physiology and metabolism.

Performing Basic Chemistry Calculations

Basic chemistry calculations often involve converting units, understanding percentages, and using multiplication to find mass amounts.
For these calculations:

• Ensure that all measurements are in consistent units (e.g., converting kilograms to grams).
• Convert percentages to decimals (e.g., 65% becomes 0.65).
• Multiply the decimal by the total mass to determine the mass of each element.

These straightforward calculations are fundamental for exploring broader chemical principles and can be applied beyond just understanding human composition. By mastering these basic math and chemistry skills, students can tackle complex scientific concepts with confidence.