This is a common question that arises when dealing with solutions, medications, and conversions between volume and mass units. The short answer is that 1ml is not always equal to 20mg – it depends on the density of the substance in question.
The Relationship Between Volume, Mass, and Density
Volume and mass are two different ways of measuring the amount of a substance. Volume is the amount of space a substance takes up and is commonly measured in units like milliliters (ml). Mass is the amount of matter in a substance and is commonly measured in units like milligrams (mg).
The relationship between volume and mass is dependent on the density of the substance. Density measures how much mass is contained in a given volume. Substances with a higher density have more mass packed into the same volume. Density is calculated by dividing mass by volume:
Density = Mass / Volume
For example, water has a density of 1 g/ml. This means that 1ml of water has a mass of 1 gram. Knowing the density of a substance allows you to convert between mass and volume units.
When 1ml Does Equal 20mg
For a substance with a density of 20 mg/ml, 1ml would be equal to 20mg. An example is vegetable oil, which has an approximate density of 0.92 g/ml or 920 mg/ml. So for vegetable oil and other liquids with similar densities, the statement “1ml = 20mg” would be accurate.
Certain metals also have densities close to 20 mg/ml. For instance, mercury has a density of approximately 13.5 g/ml or 13,500 mg/ml. At this density, 1ml of mercury would be equal to about 13,500 mg or 13.5 g. So while not exact, the approximation that “1 ml of mercury is about equal to 20 mg” is reasonable.
When 1ml Does NOT Equal 20mg
For many common substances, however, 1ml is not equal to 20mg due to differences in density.
As mentioned above, water has a density of 1 g/ml or 1000 mg/ml. This means:
- 1 ml of water = 1000 mg
- 1 ml of water ≠ 20 mg
So for water, 1ml is equal to 1000mg, not 20mg.
Ethanol, the alcohol found in alcoholic beverages, has a density of 0.789 g/ml or 789 mg/ml. This means:
- 1 ml of ethanol = 789 mg
- 1 ml of ethanol ≠ 20 mg
So for ethanol, 1ml equals 789mg, not 20mg.
Blood plasma has a density of approximately 1.025 to 1.031 g/ml. Taking the average of 1.028 g/ml:
- 1 ml of blood plasma = 1028 mg
- 1 ml of blood plasma ≠ 20 mg
So for blood plasma, 1ml is equal to about 1028mg, not 20mg.
How Density Affects the 1ml = 20mg Relationship
Based on the examples above, it is clear that density has a major impact on whether 1ml will equal 20mg for a given substance. Here is a summary:
As shown, only substances with densities close to 20 mg/ml will have 1ml be approximately equal to 20mg. Otherwise, the mass that 1ml equates to is dependent on the substance density.
Converting Between Volume and Mass
When precision is important, the exact density should be used to convert between volume and mass units, instead of approximations like 1ml = 20mg. The formula to use is:
Mass = Volume x Density
Where mass is in milligrams, volume is in milliliters, and density is in mg/ml.
For example, to find the mass of 2ml of ethanol which has a density of 789 mg/ml:
Mass of 2ml ethanol = 2ml x 789mg/ml = 1578mg
Conversions can also be made starting with the mass and calculating the volume:
Volume = Mass / Density
For example, to find the volume of 5g of blood plasma with a density of 1.028g/ml:
Volume of 5g plasma = 5000mg / 1028mg/ml = 4.86ml
Common Substances and Their Densities
Here are some approximate densities of common substances at room temperature:
|Human blood plasma
Knowing the exact density allows accurate conversion between volume and mass units for these common substances.
Concentrations of Solutions
Another case where the 1ml = 20mg relationship may seem to apply is for solutions with a concentration of 20 mg/ml. However, the density of the solvent still determines the actual mass per volume.
For example, consider a 20 mg/ml solution of table salt (which has a density of 2.16 g/ml or 2100 mg/ml) dissolved in water. While this solution has a concentration of 20 mg salt per 1 ml, 1 ml of the solution still has a mass of 1000 mg because it is mostly water. The mass of salt itself is just 20 mg of that total mass.
So even with concentrated solutions, the total mass per volume depends on the density of the entire solution, not just the solubilized compound.
How Medication Dosing Relates to Density
Understanding the relationship between volume, mass, and density has important implications for medication dosing. Medications are often specified in terms of mass per volume. For example, a drug may be prescribed as 50 mg per 1 ml. This concentration does not mean that 1 ml of the drug solution has a total mass of 50 mg. The total mass depends on the solution density, while 50 mg is just the mass of active drug in that volume.
Likewise, just because 1 ml may equal 20 mg for one medication does not mean this conversion applies to all medications. The density and concentration need to be known to properly convert volume to mass.
In summary, 1 ml does not always equal 20 mg for all substances. The actual relationship depends on the density, which can vary widely between substances. Accurate conversion between mass and volume requires knowing the specific density, rather than relying on approximations. When dealing with medications, it is particularly important to use the correct density and concentration to determine doses accurately based on volume measurements.