Question

A patient receives \(250 \mathrm{~mL}\) of a \(4.0 \%(\mathrm{~m} / \mathrm{v})\) amino acid solution twice a day. a. How many grams of amino acids are in \(250 \mathrm{~mL}\) of solution? b. How many grams of amino acids does the patient receive in 1 day?

Short answer

a. 10 grams of amino acids b. 20 grams of amino acids

Step-by-step solution

Understanding the percentage concentration

Interpret the given concentration. A 4.0% (m/v) solution means there are 4 grams of amino acids in every 100 mL of solution.

Calculate grams of amino acids in 250 mL

Use the proportion to find the grams of amino acids in 250 mL: \ \[ \frac{4 \text{ g}}{100 \text{ mL}} = \frac{x}{250 \text{ mL}} \] Cross-multiply to find \(x\): \ \[ x = \frac{4 \text{ g} \times 250 \text{ mL}}{100 \text{ mL}} = 10 \text{ g} \]

Determine total daily intake

The patient receives the solution twice daily. Multiply the amount of amino acids in one dose by 2: \ \[ 10 \text{ g/dose} \times 2 = 20 \text{ g/day} \]

Key concepts

Percentage Concentration

Percentage concentration is an important concept in solution chemistry. It tells us how much solute (in this case, amino acids) is present in a given volume of solution. Specifically, percentage concentration can be written as \(\% (m/v)\), which stands for mass/volume percentage. This format indicates how many grams of solute are in every 100 milliliters of solution. For example, when we say a solution has a 4.0% (m/v) concentration, we mean there are 4 grams of solute in every 100 milliliters of solution.
Understanding this helps us calculate the amount of solute in different volumes of the solution using simple proportions.

Grams per Milliliter

Calculating the amount of a solute in a specific volume of solution requires understanding and using proportions. Given the relationship from the percentage concentration, you can set up a proportion to find out how much solute there is in a specific volume.
For instance, if we have a 4.0% amino acid solution, we know that:
\[ \frac{4 \text{ g}}{100 \text{ mL}} = \frac{x}{250 \text{ mL}} \]
Here, 'x' is the amount of amino acids in 250 mL. By cross-multiplying, we get:
\[ x = \frac{4 \text{ g} \times 250 \text{ mL}}{100 \text{ mL}} = 10 \text{ g} \]
This calculation shows that there are 10 grams of amino acids in 250 milliliters of solution.

Daily Dosage

Daily dosage refers to the total amount of a substance that a person takes in one day. In our example, the patient receives 250 mL of the amino acid solution twice a day. From our previous calculation, we know that each 250 mL dose contains 10 grams of amino acids.
To find the total daily intake, we simply need to multiply the amount of amino acids in one dose by the number of doses taken each day:
\[ 10 \text{ g/dose} \times 2 \text{ doses/day} = 20 \text{ g/day} \]
Therefore, the patient receives 20 grams of amino acids in a day.

• Calculating daily dosage helps ensure that patients receive the correct amount of medication or nutrients.
• It is a crucial step in settings such as hospitals, where dosages need to be clearly understood to avoid underdosing or overdosing.