Percent strength and dilution for the PTCB exam

The one anchor that makes concentration questions quick (1% = 10 mg/mL), plus ratio strength, mg%, parts per million, specific gravity, milliequivalents and the dilution equation worked so you answer the question actually asked.

Concentration, Strength, and Dilution

Three percentage formats

• w/w — grams of drug per 100 g of final mixture. Creams, ointments.
• v/v — mL of ingredient per 100 mL of final mixture. Alcohol solutions.
• w/v — grams of ingredient per 100 mL of solution. Most IV bags and pharmacy solutions.

Worked example — D10W

How many grams of dextrose are in 1 L of D10W?

• D10W = 10% dextrose = 10 g / 100 mL.
• 10 g / 100 mL = x g / 1,000 mL.
• x = (10 × 1,000) / 100 = 100 g dextrose.

Safety Rule — Units: Spell unit out. The abbreviation U is on the ISMP Do-Not-Use list because it looks like 0, 4, or cc.

Worked example — penicillin units

5,000,000 units of aqueous penicillin are ordered; stock is 500,000 units/mL.

• 500,000 units / 1 mL = 5,000,000 units / x mL.
• x = (5,000,000 × 1) / 500,000 = 10 mL.

Worked example — gentamicin IV push volume

Gentamicin 120 mg in 100 mL NS. Stock gentamicin = 40 mg/mL.

• 120 mg × (1 mL / 40 mg) = 3 mL gentamicin.
• Draw up 3 mL; add to a 100 mL NS minibag.

Ratio Strength

Very dilute preparations may be written 1:something, which is g/mL, g/g, or mL/mL depending on the product. 1:1,000 means 1 g of solute in 1,000 mL of solution.

Worked example — lidocaine/epinephrine

Lidocaine 2% with epinephrine 1:100,000. How many mg of epinephrine per 1 mL?

• 1:100,000 = 1 g / 100,000 mL = 1,000 mg / 100,000 mL.
• 1,000 mg / 100,000 mL = x mg / 1 mL. x = 0.01 mg.

Worked example — epinephrine 1:10,000

• 1 mg / 10 mL = x mg / 1 mL. x = 0.1 mg/mL.

Since 2016, the FDA has required that single-entity injectable drug products remove ratio expressions from labeling (affects epinephrine, isoproterenol, neostigmine). You will still see ratios on legacy references and on exam questions.

C₁V₁ = C₂V₂ (Dilution)

• C is concentration, V is volume. Subscripts separate starting solution from target solution.
• A plain diluent without active drug is 0%.
• An undiluted active ingredient is 100%.

Worked example — ethanol

Order: 20 mL of 49% ethanol. On hand: 98% ethanol.

• C₁V₁ = C₂V₂
• 98% × x mL = 49% × 20 mL
• x = (49 × 20) / 98 = 10 mL of 98% ethanol
• Add 10 mL of 98% ethanol to 10 mL sterile water = 20 mL of 49%.

Milligram Percent (mg%)

• mg% = mg per 100 mL = mg/dL (a deciliter is 100 mL).
• Used mostly for lab values — glucose, creatinine, cholesterol, blood alcohol.
• Conversion: 1 mg/dL = 0.001% (w/v).

Worked example — glucose

A patient's serum glucose is 140 mg/dL.

• 140 mg/dL = 140 mg/100 mL = 140 mg% — a deciliter is 100 mL, so mg/dL and mg% are numerically identical.
• 140 mg = 0.14 g, so 140 mg / 100 mL = 0.14 g / 100 mL = 0.14% (w/v).

Worked example — blood alcohol

A legally drunk blood alcohol level is 0.08% (w/v). Express as mg%.

• 0.08 g / 100 mL = 80 mg / 100 mL = 80 mg/dL = 80 mg%.

Parts Per Million (ppm)

• ppm = parts per 1,000,000 of the same unit (g/g, mL/mL, mg/kg).
• Equivalence: 1 ppm = 1:1,000,000 = 0.0001%.
• Used for very dilute concentrations — fluoride in drinking water, trace contaminants.

Worked example — fluoride

Drinking water contains 2 ppm fluoride. Express as ratio strength, percent, and g/L.

• 2 ppm = 2 g / 1,000,000 mL = 2:1,000,000 = 1:500,000.
• As percent: (2 / 1,000,000) × 100 = 0.0002% (w/v).
• Per liter: 2 g / 1,000,000 mL = x g / 1,000 mL; x = 0.002 g = 2 mg/L.

Worked example — scaling ppm

How many grams of sodium fluoride prepare 1,000 gallons of 1 ppm water? (1 gal = 3,785 mL)

• Total volume: 1,000 × 3,785 = 3,785,000 mL.
• 1 ppm = 1 g / 1,000,000 mL, so (1 / 1,000,000) × 3,785,000 = 3.785 g.

Specific Gravity (SG)

• SG is the ratio of a substance's weight to the weight of an equal volume of water at standard temperature.
• Water = 1.0 (since 1 mL water = 1 g).
• SG converts weight and volume for non-water liquids — glycerin (SG 1.25), sorbitol (SG 1.29), chloroform (SG 1.48).

Formulas:

weight (g) = volume (mL) × SG

volume (mL) = weight (g) / SG

Worked example — chloroform

How many grams does a pint (480 mL) of chloroform (SG 1.48) weigh?

• 480 × 1.48 = 710.4 g.

Worked example — glycerin

What volume does 8 lb of glycerin (SG 1.25) occupy?

• Convert: 8 lb × 454 g/lb = 3,632 g.
• Divide by SG: 3,632 / 1.25 = 2,906 mL.
• Convert: 2,906 mL = 2.906 L.

Milliequivalents (mEq) and Millimoles (mmol)

• A milliequivalent (mEq) measures chemical activity of an electrolyte and accounts for both molecular weight and ionic charge (valence).
• A millimole (mmol) measures amount — 1 mmol = 1/1,000 of a mole = molecular weight in milligrams.
• In TPN orders, sodium, potassium, and calcium are ordered in mEq; phosphate is ordered in mmol because its charge varies with pH.

Core formulas

mEq = (mg × valence) / MW

mmol = mg / MW

mg = (mEq × MW) / valence

Common atomic weights and valences

Worked example — sodium

How many mg are in 1 mEq of sodium?

• Na AW = 23; valence = 1. 1 mEq = 23 / 1 = 23 mg.

Worked example — KCl

How many mg per mEq of potassium chloride?

• MW = 39 + 35.5 = 74.5; highest valence = 1. 1 mEq KCl = 74.5 mg.

Worked example — CaCl₂

• MW = 40 + (35.5 × 2) = 111; highest valence = 2. 1 mEq CaCl₂ = 111 / 2 = 55.5 mg.

Worked example — potassium acetate stock

Stock: potassium acetate 40 mEq / 20 mL. Order: 10 mEq IV. What volume?

• 40 mEq / 20 mL = 10 mEq / x. x = (10 × 20) / 40 = 5 mL.

Worked example — TPN potassium phosphate (mmol)

Order: 30 mmol potassium phosphate. Stock: 45 mmol / 15 mL.

• 45 mmol / 15 mL = 30 mmol / x. x = (30 × 15) / 45 = 10 mL.

Related

All Order Entry and Processing guides · What is on the PTCE and how it is weighted · The Federal Requirements domain