Problem 39 - Chemistry: Principles and Reactions

Question

An average adult has \(6.0 \mathrm{~L}\) of blood. The Red Cross usually takes 1 pint of blood from each donor at a donation. What percentage (by volume) of a person's blood does a blood donor give in one donation?

Step-by-Step Solution

Answer

Answer: A person donates approximately 7.9% of their total blood volume when they give 1 pint of blood.

Step 1: Convert the donated blood volume to liters

To convert the donated blood volume from pints to liters, we can use the conversion factor 1 pint = 0.473176 L. So, we have: 1 pint * 0.473176 L/pint = 0.473176 L

Step 2: Calculate the percentage of donated blood volume

Now, we will calculate the percentage of the total blood volume in the body that's been donated. We can do this by dividing the donated blood volume (in liters) by the total blood volume in the human body and multiply by 100 to get the percentage: Percentage = (Donated Blood Volume / Total Blood Volume) * 100 Percentage = (0.473176 L / 6.0 L) * 100

Step 3: Simplify the percentage

Now, we'll simplify the percentage calculation by completing the division and multiplication: Percentage ≈ (0.07886333) * 100 Percentage ≈ 7.886333 %

Step 4: Round the percentage to a reasonable value

Finally, we'll round the percentage to a more reasonable number. Percentage ≈ 7.9 % So, a blood donor gives approximately 7.9% of their total blood volume in one donation.

Key Concepts

Blood Donation

Blood donation is a generous act where a person voluntarily gives their blood for medical use. But what actually happens during a blood donation? Typically, this involves a quick and straightforward process:

• The person registering to donate.
• A brief health screening and blood test.
• The actual donation, where a specific amount of blood, often a pint, is collected.

For many, this pint doesn’t seem like much, but each donation can make a significant difference. Blood is needed for surgeries, injuries, chronic illnesses, and more. When you give blood, you play a vital role in saving lives and supporting medical treatments. Understanding the actual volume being donated can help make this vital process more transparent.

Volume Conversion

Volume conversion can often be confusing, but breaking it down makes it much simpler. In our original exercise, we were tasked with converting pints to liters. This is important because different countries use different volume units.

America commonly uses pints.

Many other countries use liters.

To convert, remember the key conversion factor: 1 pint equals approximately 0.473176 liters. By using this factor, we can easily find out how much volume a pint is in liters.
For instance, converting 1 pint of blood to liters would involve multiplying by this factor, resulting in 0.473176 liters. Understanding volume conversion enables you to seamlessly switch between measurement systems, enhancing your mathematical toolkit.

Percentage Calculation

Percentage calculation might seem tricky at first, but it follows a simple logical sequence. When calculating the percentage of something, you compare a part to a whole, then multiply by 100.
In the blood donation scenario, we discern how much of an adult's total blood is donated by using the formula:
\[\text{Percentage} = \left(\frac{\text{Donated Volume (L)}}{\text{Total Blood Volume (L)}}\right) \times 100\]
With this, you divide the donated volume of 0.473176 liters by the total blood volume, usually 6.0 liters for an adult. Multiplying the result by 100 gives approximately 7.9%, showing the fraction of the donated blood. Mastering percentage calculations enables ease in assessing proportions and changes, vital in both daily scenarios and complex academic exercises.