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Chapter 9: Problem 53

A patient needs \(100 .\) g of glucose in the next 12 h. How many liters of a \(5 \%\) (m/v) glucose solution must be given?

Short Answer

Expert verified
2 liters of 5% glucose solution

Step by step solution

01

Understand the Problem

A patient requires 100 g of glucose, and the glucose solution available is 5% (mass/volume). Determine the volume of this solution needed to administer 100 g of glucose.
02

Write Down the Given Information

The problem provides the following data: - Concentration of glucose solution: 5% m/v - Required glucose: 100 g
03

Express the Concentration in Algebraic Form

The concentration of the solution is 5%, which means 5 g of glucose are present in 100 mL of the solution. Therefore, it can be written as \[ \text{Concentration} = \frac{5 \text{ g}}{100 \text{ mL}} \]
04

Set Up the Proportion

Let the required volume of the glucose solution be \( V \) mL. Using the concentration formula: \[ \frac{5 \text{ g}}{100 \text{ mL}} = \frac{100 \text{ g}}{V \text{ mL}} \]
05

Solve for Volume

Cross-multiply to find \( V \): \[ 5V = 100 \times 100 \] \[ 5V = 10000 \] \[ V = \frac{10000}{5} \] \[ V = 2000 \text{ mL} \]
06

Convert mL to Liters

Since there are 1000 mL in 1 liter, convert 2000 mL to liters: \[ V = \frac{2000 \text{ mL}}{1000} = 2 \text{ L} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

mass/volume percentage
Mass/volume percentage (m/v) is an important way to express concentration. It tells us the mass of solute in grams present in 100 mL of solution. If we have a 5% (m/v) glucose solution, it means there are 5 grams of glucose in every 100 mL of the solution.

Here are a few key things to remember:
  • The percentage always refers to grams of solute per 100 mL of solution.
  • This is a common concentration measure in medicine and biology.
  • Understanding this helps in preparing solutions with the right concentration.
In our exercise, the 5% (m/v) glucose solution is basically saying: for every 100 mL of this solution, there is 5 grams of glucose.
concentration
Concentration refers to the amount of a substance in a certain volume of a solution. It's crucial for accurately dosing chemicals, medicines, or nutrients.
The basics about concentration include:
  • It can be measured in different units like % (m/v), molarity (M), and ppm.
  • In a 5% (m/v) glucose solution, concentration is the mass of glucose over the volume of the solution, expressed as a percentage.
In our problem, the concentration 5% (m/v) means every 100 mL of the solution contains 5 grams of glucose. To find how much solution we need to provide 100 grams of glucose, we use this known concentration.
unit conversion
Unit conversion is converting one unit of measure to another. This is essential for ensuring all parts of your calculation use the same units.
To convert units:
  • Know the conversion factor, like 1000 mL in 1 liter.
  • Set up a proportion to solve for the desired unit.
In this example, after finding we need 2000 mL of solution, we convert it to liters because it's a more convenient measure. We use the fact that 1000 mL equals 1 liter. Thus, 2000 mL = 2 liters.
proportion
Proportion is a mathematical equation that states two ratios are equal. It's a handy way to solve problems involving direct relationships between quantities.
Here's how we used proportions in the exercise:
  • The ratio of glucose in the given solution (5 g in 100 mL) is equal to the ratio of required glucose to the total volume.
  • We set up the equation \( \frac{5 \, \text{g}}{100 \, \text{mL}} = \frac{100 \, \text{g}}{V \, \text{mL}} \).
  • By cross-multiplying and solving for V, we found the volume needed.
This method helps quickly find unknown values when dealing with similar ratios and direct relationships. In this case, it allowed us to determine the volume of the solution needed to provide a specific mass of glucose for the patient.

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Most popular questions from this chapter

Explain the following observations: a. An open can of soda loses its "fizz" faster at room temperature than in the refrigerator. b. Chlorine gas in tap water escapes as the sample warms to room temperature. c. Less sugar dissolves in iced coffee than in hot coffee.

If the solid \(\mathrm{NaCl}\) in a saturated solution of \(\mathrm{NaCl}\) continues to dissolve, why is there no change in the concentration of the \(\mathrm{NaCl}\) solution? (9.3)

Explain the following observations: a. More sugar dissolves in hot tea than in iced tea. b. Champagne in a warm room goes flat. c. A warm can of soda has more spray when opened than a cold one.

How many milliliters of a \(12 \%\) (v/v) propyl alcohol solution would you need to obtain \(4.5 \mathrm{~mL}\) of propyl alcohol? (9.4)

What is the difference between a \(5.00 \%(\mathrm{~m} / \mathrm{m})\) glucose solution and a \(5.00 \%(\mathrm{~m} / \mathrm{v})\) glucose solution?
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