Drug Dilutions, Clearly Explained

Pharmacy and Therapeutics

You will be able to answer the following questions and more after reading the following material.

  • What does Lidocaine 1% or 2% mean?
  • What is the difference between “%” solutions and dilutions, e.g. “1:1000” dilution?
  • To make lidocaine 1%, what is lidocaine mixed it?
  • How many milligrams of lidocaine are there in 5ml of a lidocaine 1% solution?
  • Why do diluted drugs like epinephrine have different concentrations?
  • 2 ml of Lidocaine 1% with 1:100,000 epinephrine has how many mg of lidocaine and how many mg of epinephrine?

Basic Chemistry

In chemistry, weights, instead of volumes are usually used to refer to chemical substances. In medicine, we often work with weights also. Drugs that come in pill form are often prescribed in units of weight. For example, Aspirin 325mg; Acetaminophen 325mg, etc.

But using the weight of a drug that is diluted can be confusing because diluted drugs often have different concentrations.

To understand how dilutions work, certain basic assumptions for the properties of fluids such as water must be made. The main assumption is:

1 cm3 (i.e. 1ml) of water weighs 1 gram at 4 degrees Celcius.

Gram per cubic centimeter is a unit of density in the Centimeter-Gram-Second (GCS)  system, commonly used in chemistry, defined as the mass in grams divided by volume in cubic centimeters. The official SI symbols are g/cm3. It is equivalent to the units gram per milliliter (g/mL) and kilogram per liter (kg/L). The density of water is about 1 g/cm3 or 1000 kg/m3 since the gram was originally defined as the mass of one cubic centimeter of water at its maximum density at 4 °C. As water cools down, it’s maximum density of water occurs at 4 degrees.  After that, it decreases. That’s why ice floats.

1ml of water = 1 gram at 4 degrees Celsius.

It means that 100ml of water has a weight of 100 g (at 4 Degrees Celsius).

For our purposes,  the difference between 4 degrees and room temperature where drugs are stored is negligible.

As such, we can say that a 100% solution would be 1 gram of drug in 1ml of volume.

Drug Dilutions, Explained Clearly

What does 1 percent, 1:1000 and 1:10000 refer to?

1 percent, 1:1000 and 1:10000 refers to the concentration of diluted drugs like epinephrine

  • 1 percent is the same as a 1:100 Solution
  • 1:1,000 is the same as 0.1% Solution
  • 1:10,000 is the same a 0.01% Solution
  • 1:100,000 is the same as 0.001 % solution.

Epinephrine dilutions can continue and there is 1:200,000 and up to 1: 1000,000 (i.e. 1: 1 million).

Even though percentages and dilutions (like 1:100) all refer to the same entity, i.e. the concentration of the diluted drugs people have tended to consistently use percentages when talking about drugs like lidocaine (1% or 2%) that aren’t as potent as epinephrine and so don’t require huge dilutions. To avoid saying epinephrine 0.001 %, people have preferred to use dilutions 1:100,000 to speak of epinephrine.

A key thing to remember is that:

  • Lidocaine 1% is the same thing as Lidocaine 1:100 dilution.
  • Epinephrine 0.1% is commonly known as 1:1000 dilution.

Another key thing to remember is that each of the volumes you will give has a certain number of milligrams of the drug that you will be administering to the patient. That’s what really is the active agent, not the volume of solution.

To make lidocaine 1%, what is lidocaine mixed it?

Lidocaine is mixed in water. However, other substances are added to it to make it isotonic and to make the PH  right for the body. Preservatives are also added as well. Sodium chloride is one of the substances added to make it isotonic. As such, in a sense, one could say normal saline is the solvent. But there are more substances than that, again for preservation as well as to create the ideal PH for the body and for isotonicity.

How many milligrams of lidocaine are there in 5ml of a lidocaine 1% solution?

Lidocaine 1% is commonly used for topical local anesthesia. A 1% solution literally means there is 1gram per 100mls. In terms of dilution, 1% is the same as a 1:100 solution dilution.

  • So, if there is 1g per 100mls there is also 1000mg per 100mls
  • If we divide this down there will be 10mg in 1ml
  • 5ml  of lidocaine will have 5 x 10mg = 50mg in a 5ml vial.

Why do diluted drugs like epinephrine have different concentrations?

1:1000 dilution  – When a low volume is needed, e.g. Anaphylaxis and Nebulized Epinephrine for severe asthma.

The 1:1000 is more concentrated and is good for situations where you want to give a good dose of medicine in a small volume. In anaphylactic shock, it’s better to give 0.5 ml (0.5mg of epinephrine) of the 1:1000 than 5mls of a more dilute solution. The 1:000 dilution of epinephrine is also useful for nebulized epinephrine in severe asthma exacerbation. You also don’t want to flood the patient’s lungs with a large volume of fluid to get the concentration of medicine that you want.

1:10,000 epinephrine – When a decent volume is needed as for IV Push during a cardiac arrest.

This is great for giving an IV push dose as during cardiac arrest.

 2 ml of Lidocaine 1% with 1:100,000 epinephrine has how many mg of lidocaine and how many mg of epinephrine?

When you have one bottle that has both lidocaine and epinephrine, you obviously have these two drugs diluted in the same solvent.

Lidocaine 1 % means a 1:100  dilution.
That is 1 g : 100ml;
That is 1000 mg : 100ml
That means 10 mg : 1ml.
2ml of the solution will contain 2 (10mg) = 20 mg of lidocaine.

Epinephrine 1:100,000 means
1g : 100, 000 ml
1000mg : 100,000 ml, or
1mg : 100ml
0.01mg : 1ml, or
2ml of the solution will contain 2 (0.01mg) = 0.02mg of epinephrine..

2ml of lidocaine 1% and Epinephrine 1:100,000 has 20mg of lidocaine and 0.002mg of epineprine.

Knowing this is very important because lidocaine has a maximum dose that can be injected into a patient. It is 4mg/kg/dose (up to 300mg per dose) without epinephrine and 7mg/kg/dose (up to 500mg per dose) with epinephrine. See here.

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Note 1ml = 1 cm3 , i.e. 1 milliliter equals 1 cubic centimeter. 

The density of water = 1g/cm3 = 1g/ml = 1kg/L

The CGS (centimeter–gram–second) system of units is a variant of the metric system based on the centimeter as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are derived from these three base units.

References

Am Fam Physician. 2014 Jun 15;89(12):956-962. Infiltrative Anesthesia in Office Practice.

https://emergencypedia.com/2014/01/07/the-solution-to-dilution/

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