Question

A patient received \(2.0 \mathrm{~g}\) of \(\mathrm{NaCl}\) in \(8 \mathrm{~h}\). How many milliliters of a \(0.90 \%(\mathrm{~m} / \mathrm{v}) \mathrm{NaCl}\) (saline) solution were delivered?

Short answer

222.22 mL

Step-by-step solution

- Understand the concentration of the solution

The concentration of the saline solution is given as 0.90% (m/v). This means that there are 0.90 grams of NaCl in 100 milliliters of solution.

- Set up the proportion

To find the volume of the saline solution needed to deliver 2.0 grams of NaCl, set up a proportion based on the concentration: 0.90 grams NaCl / 100 mL solution = 2.0 grams NaCl / X mL solution.

- Solve for X

Cross-multiply and solve for X: \[ 0.90 \times X = 2.0 \times 100 \] \[ 0.90X = 200 \] \[ X = \frac{200}{0.90} \] \[ X \approx 222.22 \text{ mL} \]

- Conclusion

Therefore, the patient received approximately 222.22 milliliters of the 0.90% (m/v) NaCl solution.

Key concepts

solution concentration

Solution concentration is an important concept in chemistry and medicine. It tells us how much of a substance (solute) is present in a specific amount of solution.
In the exercise, the solution concentration is given as 0.90% (m/v) NaCl. This means there are 0.90 grams of salt (NaCl) in every 100 milliliters of the solution.
Understanding concentrations is vital because it ensures that patients receive the right amount of medication or treatment.

• For example, too much salt can increase blood pressure, while too little can cause dehydration.
• Concentrations can be expressed in different ways, such as mass/volume (m/v) which was used here.

proportion calculation

Proportion calculation helps us compare two different ratios to find unknown values. In this exercise, we need to find out how much of a 0.90% NaCl solution is required to give a patient 2.0 grams of NaCl.
We start by setting up a proportion based on the given concentration: \( \frac{0.90 \text{ grams NaCl}}{100 \text{ mL solution}} = \frac{2.0 \text{ grams NaCl}}{X \text{ mL solution}} \).
This proportion tells us that 0.90 grams of salt is to 100 mL of solution as 2.0 grams of salt is to X mL of solution.

• Proportions are especially useful in recipes, medication dosages, and any scenario where scaling up or down is required.

cross-multiplication

Cross-multiplication is a method used to solve proportions. By cross-multiplying, we eliminate the fraction, making it easier to solve for the unknown variable.
In our problem, we set up the equation: 0.90 grams of NaCl / 100 mL solution = 2.0 grams of NaCl / X mL solution.

• To solve, we cross-multiply: \( 0.90 \times X = 2.0 \times 100 \)
• This gives us: \( 0.90X = 200 \)
• Solving for X, we get: \( X = \frac{200}{0.90} \)
• Finally, we find: \( X \thickapprox 222.22 \text{ mL} \)

Thus, cross-multiplication helps simplify complex proportions into solvable equations.

NaCl solution

A NaCl solution, commonly known as saline solution, consists of sodium chloride (salt) dissolved in water.
Saline solutions are used in medicine for dehydration, cleaning wounds, and intravenous therapy.
In our exercise, we are dealing with a 0.90% NaCl solution, meaning there are 0.90 grams of salt in every 100 mL of solution.

• It's crucial to know the exact concentration for medical purposes to ensure proper patient care.
• Different concentrations of NaCl solutions serve various medical applications, making understanding them vital for health professionals.

In conclusion, knowing how to determine the correct volume of a specific concentration ensures the patient safely and effectively receives their treatment.