⚗️ Chemistry intermediate Lesson 5 of 5 4 min read

Solutions, Concentration & the Math Behind Dosing

How solutes dissolve in solvents, the concentration units used in medicine, the dilution formula, and worked examples of the arithmetic behind fluids and dosing.

Reading level

What you'll learn

  • Define solute, solvent, and solution, and describe factors that affect solubility.
  • Convert among common concentration units including percent, mg/mL, and molarity.
  • Use the dilution equation C1V1 = C2V2 to solve for an unknown volume or concentration.
  • Explain tonicity and predict how cells behave in isotonic, hypotonic, and hypertonic fluids.
  • Work through the arithmetic method used in dosage-style calculations.

Overview

Most chemistry in the body happens in solution, meaning substances dissolved in water. Understanding how solutions are described and measured lets you make sense of lab values, intravenous (IV) fluids, and the arithmetic behind medication amounts. This lesson builds from the basics of dissolving up to the calculation methods used in clinical settings, framed here as educational practice rather than as instructions for treating anyone.

Solute, Solvent, and Solubility

A solution has two parts: the solute (the substance being dissolved, present in the smaller amount) and the solvent (the dissolving medium, present in the larger amount). In the body, the solvent is almost always water, which is why water is called the universal biological solvent.

Solubility is the maximum amount of solute that will dissolve in a given amount of solvent at a specific temperature. Several factors influence it:

  • Temperature — most solids dissolve better in warm water; gases dissolve better in cold.
  • Polarity — “like dissolves like.” Polar and ionic solutes dissolve in polar solvents (water); nonpolar solutes dissolve in nonpolar solvents.
  • Pressure — mainly affects dissolved gases, such as oxygen and carbon dioxide in blood.

Ways to Express Concentration

Concentration tells you how much solute is present. Medicine uses several units, and being fluent in converting among them prevents errors.

UnitMeaningExample
Percent (% w/v)Grams of solute per 100 mL of solution0.9% saline = 0.9 g per 100 mL
mg/mLMilligrams of solute per milliliterA drug labeled 10 mg/mL
Molarity (M)Moles of solute per liter of solution1 M glucose = 180 g per liter
mEq/LMilliequivalents per liter (for ions)Serum sodium ~140 mEq/L

Note that a percent weight/volume figure is simply grams per 100 mL. This makes it quick to scale: 0.9% saline is 0.9 g per 100 mL, which is 9 g per liter.

Dilution: C1V1 = C2V2

Concentrated stock solutions are often diluted to a working strength. The relationship is:

C₁V₁ = C₂V₂

where C₁ and V₁ are the concentration and volume of the starting (stock) solution, and C₂ and V₂ are those of the final diluted solution. Because the amount of solute does not change when you add solvent, the products stay equal.

Worked example. How much 10% stock is needed to make 500 mL of 2% solution?

  • Solve for V₁: V₁ = (C₂ × V₂) / C₁
  • V₁ = (2% × 500 mL) / 10% = 100 mL

So you would measure 100 mL of stock and add solvent up to a total of 500 mL.

Dosage-Style Math (Educational Practice)

A common method for medication arithmetic is the “desired over have” approach:

Volume to give = (Desired dose ÷ Concentration on hand) × Volume of that concentration

Worked example. A practice problem asks: a solution is labeled 250 mg per 5 mL, and the ordered dose is 100 mg. How many milliliters contain 100 mg?

  • Concentration on hand = 250 mg per 5 mL = 50 mg/mL
  • Volume = 100 mg ÷ 50 mg/mL = 2 mL

Working through the units (dimensional analysis) is the safest habit: milligrams cancel, leaving milliliters.

Educational note: These calculations are provided to teach the underlying chemistry and arithmetic method only. They are not clinical orders or dosing guidance. Real medication administration is governed by professional training, verified references, and institutional protocols.

Tonicity and IV Fluids

Tonicity compares a solution’s effective solute concentration with the inside of a cell and predicts which way water will move by osmosis.

SolutionCompared to cellEffect on a red blood cell
IsotonicEqual soluteNo net water movement; cell stable
HypotonicLess soluteWater enters; cell swells, may burst
HypertonicMore soluteWater leaves; cell shrinks

0.9% sodium chloride, called normal saline, is isotonic with blood plasma, so it expands circulating volume without shifting water into or out of cells. This is why it is such a common IV fluid.

Clinical relevance

Concentration and tonicity are everyday concerns in patient care. Giving fluid that is accidentally hypotonic can drive water into cells and cause them to swell, while overly hypertonic fluid pulls water out and shrinks them; both can be harmful, which is why isotonic fluids like normal saline are the default for simple volume replacement. Lab reports express electrolytes such as sodium and potassium in concentration units (mEq/L), and interpreting whether a value is high or low depends on understanding what those units mean. Mastering the arithmetic of solutions, dilution, and unit conversion builds the numerical fluency that clinicians rely on to read labs, prepare fluids, and reason carefully about the substances moving through the body.

Going deeper advanced

Extra depth for when you're ready — expanded automatically in Advanced mode.

Osmolarity, osmolality, and colligative properties

Osmolarity is osmoles of solute per liter of solution, while osmolality is osmoles per kilogram of solvent; osmolality is preferred physiologically because it is independent of temperature and of the volume displaced by dissolved proteins and lipids. Both count dissociated particles, so 1 mole of NaCl contributes roughly 2 osmoles as it splits into Na+ and Cl-. This particle count drives the colligative properties, including the osmotic pressure that governs water movement across membranes and the freezing-point depression used by lab osmometers to measure it.

Why electrolytes are reported in mEq/L

Milliequivalents account for ionic charge, not just amount, so they capture the chemical combining capacity that matters for electroneutrality and membrane potentials. For a monovalent ion like sodium, mEq/L equals mmol/L, but for divalent calcium 1 mmol supplies 2 mEq, since each ion carries two charges. Reporting in mEq/L lets clinicians check that total cation and anion charges balance and reason about how ions substitute for one another across compartments.

Key terms

Solute
The substance that is dissolved in a solution, present in the smaller amount.
Solvent
The substance that does the dissolving, present in the larger amount; in the body this is water.
Solubility
The maximum amount of a solute that dissolves in a given amount of solvent at a set temperature.
Concentration
A measure of how much solute is present in a given amount of solution.
Molarity (M)
Concentration expressed as moles of solute per liter of solution.
Dilution
The process of lowering a solution's concentration by adding more solvent.
Tonicity
The relative solute concentration of a solution compared with the inside of a cell, which determines water movement.
Isotonic solution
A solution with the same effective solute concentration as the cell interior, causing no net water movement; 0.9 percent saline is an example.
Osmosis
The movement of water across a semipermeable membrane from lower to higher solute concentration.

Check your understanding

6 questions · answers reveal instantly.

  1. 1.In a solution of salt dissolved in water, the water is the:
  2. 2.Molarity is defined as:
  3. 3.Using C1V1 = C2V2, how much of a 10 percent stock solution is needed to make 500 mL of a 2 percent solution?
  4. 4.A red blood cell placed in a hypotonic solution will:
  5. 5.0.9 percent sodium chloride ('normal saline') is used clinically because it is:
  6. 6.A 0.9 percent saline solution contains how many grams of sodium chloride per 100 mL?

Citations & References

Links open publicly available educational and peer-reviewed sources.

  1. OpenStax. Chemistry 2e.
  2. OpenStax. Anatomy and Physiology 2e.
  3. MedlinePlus, U.S. National Library of Medicine.