A nutritional formula calls for 500 g of dextrose in a total volume of 2000 ml. how many milliliters of a 70% w/v dextrose injection are needed to provide the required amount of dextrose?

This seems to be a dimensional analysis problem. We have:

500g/2000ml
70% w/v = 70 g dextrose/100 ml
Molecular Weight: 1 mmole/180 g dextrose

These are known, yet I am not sure of the set up.

I found out 2000 ml is not necessary knowledge to answer the equation. You simply do the following:

(500g dextrose) * (100 ml solution/70g dextrose) = 714.29 ml

500gm of Dextrose in 2000ml NS

makes it sol of D25%w conc. (25gm in 100ml)
Thus, to provide D70%
25gm =100ml
70= 100/25*70
= 280ml sol to be infused

To solve this problem, we need to find out how many milliliters of a 70% w/v dextrose injection are needed to provide 500 g of dextrose.

Let's set up the dimensional analysis as follows:

First, let's convert the grams of dextrose in the nutritional formula to millimoles:

500 g dextrose * (1 mmole/180 g) = 2.78 mmol dextrose

Next, let's convert the millimoles of dextrose to milliliters of 70% w/v dextrose solution:

2.78 mmol dextrose * (100 ml/70 g) = 3.97 ml of 70% w/v dextrose solution

Therefore, approximately 3.97 ml of a 70% w/v dextrose injection are needed to provide the required amount of dextrose.

To solve this problem using dimensional analysis, we need to set up the conversion factors correctly.

Given:
- Nutritional formula requires 500 g of dextrose in a total volume of 2000 ml.
- 70% w/v dextrose injection contains 70 g of dextrose per 100 ml.

First, let's convert the given requirement of 500 g of dextrose to millimoles (mmol).

1 mmole of dextrose = 180 g
500 g of dextrose * (1 mmole / 180 g) = 2.78 mmol of dextrose

Now, let's determine the volume of the 70% w/v dextrose injection needed to provide 2.78 mmol of dextrose.

Conversion factor: 70 g dextrose / 100 ml

2.78 mmol of dextrose * (100 ml / 70 g) = 3.97 ml

Therefore, approximately 3.97 milliliters of a 70% w/v dextrose injection are needed to provide the required amount of dextrose.