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How many ml of diluent should be added to the medication to obtain a 1:4 concentration?

A loading dose of acetylcysteine 8 grams, which is available as a 20% solution (200 mg acetylcysteine per ml) is prescribed by nasogastric tube for a client with acetaminophen toxicity. How many ml of diluent should be added to the medication to obtain a 1:4 concentration? ( enter the numerical value only. If rounding is required, round to the whole number.)

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2 Answers

It would help to know what the ratio 1:4 is referring to.  If you want 1 acetylcysteine to 4 dilutent, then you're already too dilute because that would be a 25% solution.  If you want 1/4 the concentration of the 20% solution, then you can calculate dilutent (solvent) as follows.  You want 8 grams of medication which can be found by multiplying 8 by 1000 to get mg, then multiply it by the reciprocal of the medicine's concentration to get the mL of solution.  Then add three times the solution volume in dilutent to get the concentration to 1/4 of it's original strength.  That would work out to 120 mL of dilutent. 

This problem talks about a dilution ratio. This kind of ratio is very important for pharmacists and chemists,  so you'll probably be seeing a lot in your upper level science classes. The ratio indicates the amount of an active ingredient to the amount of inactive ingredients (the diluent) in a solution. For example, a 1:4 dilution ratio means that, out of 5 total parts, 1 part is active and 4 parts are inactive. Adding 4 parts water to 1 part sugar would provide a dilution ratio of 1:4.

In this case, the drug is already somewhat dilute at a 20% concentration. If you have 8 grams of the drug, at a concentration of 200 mg/ml, your dosage is 1600 mg/ml (1 g = 1 mL is generally the rule of thumb. It's actually only true of water @ room temperature because of its' density, so if this is for the MCATs like I think it is you might want to double check and see if they give you the actual density anywhere). To dilute that, just include four parts diluent. ~6400 mg/ml diluent in this case. Again, double check this.