Math & More (ANA 901)

Unit Conversions: MG / G and ML / L

  • MG / G conversions
    • 1 mg=0.001 g1\ \mathrm{mg} = 0.001\ \mathrm{g}
    • 1 g=1000 mg1\ \mathrm{g} = 1000\ \mathrm{mg}
    • 1 mcg=0.001 mg1\ \mathrm{mcg} = 0.001\ \mathrm{mg}
    • 1 g=1,000,000 mcg1\ \mathrm{g} = 1{,}000{,}000\ \mathrm{mcg}
    • 1 mL=0.001 L1\ \mathrm{mL} = 0.001\ \mathrm{L}
    • 1 L=1000 mL1\ \mathrm{L} = 1000\ \mathrm{mL}
  • Important correction (error in the slide):
    • 1 mcg=0.001 mg1\ \mathrm{mcg} = 0.001\ \mathrm{mg} is correct (not 1000 mg).
  • ML / L conversions
    • 1 mL=0.001 L1\ \mathrm{mL} = 0.001\ \mathrm{L}
    • 1 L=1000 mL1\ \mathrm{L} = 1000\ \mathrm{mL}

Weight Conversions

  • Kg to Lb
    • lb=kg×2.2\text{lb} = \text{kg} \times 2.2
    • Examples:
    • 100 kg×2.2=220 lb100\ \text{kg} \times 2.2 = 220\ \text{lb}
    • 60 kg×2.2=132 lb60\ \text{kg} \times 2.2 = 132\ \text{lb}
  • Lb to Kg
    • kg=lb2.2\text{kg} = \frac{\text{lb}}{2.2}
    • Examples:
    • 220 lb/2.2=100 kg220\ \text{lb} / 2.2 = 100\ \text{kg}
    • 165 lb/2.2=75 kg165\ \text{lb} / 2.2 = 75\ \text{kg}
  • Short cut (approximate)
    • Subtract 10%, then divide by 2
    • Example: for 180 lb → (180−18)/2=162/2=81 kg(180 - 18)/2 = 162/2 = 81\ \text{kg}

Math Concentrations

  • Concentration (%) overview
    • Concentration is the weight of solute per volume, typically expressed as grams per 100 mL
    • Formula: Concentration (%)=m<em>soluteV</em>solution×100%\text{Concentration (\%)} = \frac{m<em>{\text{solute}}}{V</em>{\text{solution}}} \times 100\%
  • Examples
    • 50\% Dextrose = 50 \mathrm{g} per 100\mathrm{mL}
    • 5\% Glucose = 5 \mathrm{g} per 100\mathrm{mL}
    • 0.9\% Sodium Chloride = 0.9 \mathrm{g} per 100\mathrm{mL}
  • Summary statement
    • Concentration expresses how many grams are present per a fixed volume (mass per unit volume)

Math Conversions (detailed)

  • 1:1000 meaning
    • 1:!1000 means 1 g per 1000 mL1:!1000\ \text{means } 1\ \text{g per } 1000\ \text{mL}
    • 1 g1000 mL=1000 mg1000 mL=1 mg/mL\frac{1\ \mathrm{g}}{1000\ \mathrm{mL}} = \frac{1000\ \mathrm{mg}}{1000\ \mathrm{mL}} = 1\ \mathrm{mg/mL}
    • 0.1\% (equal to 1 mg/mL in this context)
  • 1:1000\text{, 1:100000, 1:200000, etc.} conversions to mg/mL and mcg/mL
    • 1:1000 → 1 mg/mL1\ \mathrm{mg/mL}; 0.1%0.1\%
    • 1:100{,}000 → 0.01 mg/mL0.01\ \mathrm{mg/mL}; 10 mcg/mL10\ \mathrm{mcg/mL}; 0.001%0.001\%
    • 1:200{,}000 → 0.005 mg/mL0.005\ \mathrm{mg/mL}; 5 mcg/mL5\ \mathrm{mcg/mL}; 0.0005%0.0005\%
    • 1:500{,}000 → 0.002 mg/mL0.002\ \mathrm{mg/mL}; 2 mcg/mL2\ \mathrm{mcg/mL}
  • Concentration (%) to mg/mL
    • Move one decimal place to the right
    • Examples:
    • 2% ⇒20 mg/mL2\%\ \Rightarrow 20\ \mathrm{mg/mL}
    • 0.9% ⇒9 mg/mL0.9\%\ \Rightarrow 9\ \mathrm{mg/mL}
  • Concentration ratio to mcg/mL
    • 1:!100,000⇒10 mcg/mL1:!100{,}000 \Rightarrow 10\ \mathrm{mcg/mL}
    • 1:!200,000⇒5 mcg/mL1:!200{,}000 \Rightarrow 5\ \mathrm{mcg/mL}
    • 1:!500,000⇒2 mcg/mL1:!500{,}000 \Rightarrow 2\ \mathrm{mcg/mL}

Epinephrine Solutions

  • Labeled by concentration ratio per mL
    • 1:!1000⇒1000 mg/100,000 mL=0.01 mg/mL1:!1000 \Rightarrow 1000\ \mathrm{mg}/\text{100{,}000\,mL} = 0.01\ \mathrm{mg/mL}
    • Corresponding percent values shown:
    • 1:!1000⇒1 mg/mL0.1%1:!1000 \Rightarrow 1\ \mathrm{mg/mL} \quad 0.1\%
    • 1:!100,000⇒0.01 mg/mL0.001%1:!100{,}000 \Rightarrow 0.01\ \mathrm{mg/mL} \quad 0.001\%
    • 1:!200,000⇒0.005 mg/mL0.0005%1:!200{,}000 \Rightarrow 0.005\ \mathrm{mg/mL} \quad 0.0005\%

Dalton's Law (Partial Pressures)

  • Statement
    • The total pressure of a gas mixture equals the sum of the partial pressures of each gas
    • P<em>t=P</em>1+P<em>2+P</em>3+P<em>4+P</em>5P<em>t = P</em>1 + P<em>2 + P</em>3 + P<em>4 + P</em>5
  • Example (air at sea level)
    • Mixture components (typical approximate values):
    • P<em>N</em>2≈78.1 kPaP<em>{N</em>2} \approx 78.1\ \text{kPa}
    • P<em>O</em>2≈20.9 kPaP<em>{O</em>2} \approx 20.9\ \text{kPa}
    • PAr≈0.97 kPaP_{Ar} \approx 0.97\ \text{kPa}
    • P<em>H</em>2O≈1.28 kPaP<em>{H</em>2O} \approx 1.28\ \text{kPa}
    • P<em>CO</em>2≈0.05 kPaP<em>{CO</em>2} \approx 0.05\ \text{kPa}
    • Sum (air): Pt≈101.3 kPaP_t \approx 101.3\ \text{kPa}
    • Visual: illustrates that all partial pressures contribute to the total pressure

Oxygen Tank calculations

  • E cylinder (approximately):
    • Rated to about 2200 psi2200\ \text{psi} and contains roughly 660 L O2660\ \mathrm{L}\,\mathrm{O_2}
    • Flow assumptions:
    • 1 L/min⇒660 min1\ \mathrm{L/min} \Rightarrow 660\ \mathrm{min} (≈ 11 hours11\ \mathrm{hours})
    • 4 L/min⇒165 min4\ \mathrm{L/min} \Rightarrow 165\ \mathrm{min} (≈ 2 h 45 min2\ \mathrm{h}\ 45\ \mathrm{min})
  • H cylinder (approximately):
    • Roughly 7000 L O27000\ \mathrm{L}\,\mathrm{O_2}
    • Flow assumptions (as given):
    • 1 L/min⇒2200 min1\ \mathrm{L/min} \Rightarrow 2200\ \mathrm{min} (≈ 36 h 40 m36\ \mathrm{h}\ 40\ \mathrm{m})
    • 4 L/min⇒1750 min4\ \mathrm{L/min} \Rightarrow 1750\ \mathrm{min} (≈ 29 h 10 m29\ \mathrm{h}\ 10\ \mathrm{m})
  • NOTE on data consistency
    • The slide also states: “Half of the pressure (1100 psi) would have half the volume” (illustrating Boyle-type intuition)
    • In practice, cylinder volumes and durations depend on regulator settings and cylinder size; numbers above reflect the provided transcript and may vary in real-world specs

Time measurement in Anesthesia

  • Time conventions
    • All time is in military time
    • Documenting surgical minutes is important; concurrency is illegal to document
    • Billing increments
    • Time is billed in 15-minute units
    • Buckets: 0${-}15, 16{-}30, 31{-}45, 46{-}60 represent one unit

Practice Questions

  • Question 1
    • A 1:200{,}000 concentration of epinephrine is how many mcg/mL\text{mcg/mL}?
    • What about mg/mL\text{mg/mL}?
    • Answer:
    • mcg/mL=5 mcg/mL\text{mcg/mL} = 5\ \text{mcg/mL}
    • mg/mL=0.005 mg/mL\text{mg/mL} = 0.005\ \mathrm{mg/mL}
  • Question 2
    • Three mL of a 1:100{,}000 concentration of epinephrine contains how many mcg\text{mcg}?
    • Answer:
    • 1:100{,}000 corresponds to 10 mcg/mL10\ \mathrm{mcg/mL}
    • Amount in 3 mL: 3×10=30 mcg3 \times 10 = 30\ \mathrm{mcg}
  • Question 3
    • How many mg of epinephrine are required to make 50 mL50\ \mathrm{mL} of a 1:200,0001:200{,}000 solution?
    • Answer:
    • 0.005 mg/mL×50 mL=0.25 mg0.005\ \mathrm{mg/mL} \times 50\ \mathrm{mL} = 0.25\ \mathrm{mg}
  • Question 4
    • If you take 1 g of a drug and put it in 500 mL of water, what is its final concentration in %? What about mg/mL?
    • Answer:
    • Total drug = 1 g = 1000 mg in 500 mL
    • mg/mL = 1000 mg500 mL=2 mg/mL\frac{1000\ \mathrm{mg}}{500\ \mathrm{mL}} = 2\ \mathrm{mg/mL}
    • % (w/v) = 2 mg/mL×100 mL1000 mg=0.2%\frac{2\ \mathrm{mg/mL} \times 100\ \mathrm{mL}}{1000\ \mathrm{mg}} = 0.2\%
  • Question 5
    • How many mg are in 5 mL5\ \mathrm{mL} of a 4%4\% cocaine solution?
    • Answer:
    • 4\% w/v = 4\ g per 100 mL = 40\ mg/mL
    • In 5 mL: 5×40=200 mg5 \times 40 = 200\ \mathrm{mg}
  • Question 6
    • You are given a 25 mL25\ \mathrm{mL} vial of 1% lidocaine1\%\text{ lidocaine} with 1:500,000 epinephrine1:500{,}000\text{ epinephrine}, calculate the number of mg of each drug.
    • Answer:
    • Lidocaine: 1\% w/v = 10 mg/mL → 25 mL×10 mg/mL=250 mg25\ \mathrm{mL} \times 10\ \mathrm{mg/mL} = 250\ \mathrm{mg}
    • Epinephrine: 1:500{,}000 ≡ 0.002\ \mathrm{mg/mL} = 2\ \mathrm{mcg/mL}
      → 25 mL×0.002 mg/mL=0.05 mg=50 μg25\ \mathrm{mL} \times 0.002\ \mathrm{mg/mL} = 0.05\ \mathrm{mg} = 50\ \mu\mathrm{g}
  • Question 7
    • What volume should be taken from a 5\% solution to make 10 mL of a 2\% solution?
    • Answer:
    • Stock 5\%: 50 mg/mL; Target 2\%: 20 mg/mL
    • Required drug for 10 mL of 2\%: 10 mL×20 mg/mL=200 mg10\ \mathrm{mL} \times 20\ \mathrm{mg/mL} = 200\ \mathrm{mg}
    • Volume of stock needed: 200 mg/50 mg/mL=4 mL200\ \mathrm{mg} / 50\ \mathrm{mg/mL} = 4\ \mathrm{mL}
    • So, take 4 mL4\ \mathrm{mL} of 5\% solution and dilute to a total volume of 10 mL (with diluent) to obtain 2\% solution.

Quick reference formulas (summary)

  • Mass-concentration relationships
    • mg/mL=m<em>solV\text{mg/mL} = \dfrac{m<em>{\text{sol}}{}}{V} where msol is mass of solute in mg and V is volume in mL
    • %=m<em>solV×100%\% = \dfrac{m<em>{\text{sol}}}{V} \times 100\% when msol is in g and V is in mL (w/v)
  • Unit conversions
    • 1 mg=0.001 g1\ \mathrm{mg} = 0.001\ \mathrm{g}
    • 1 g=1000 mg1\ \mathrm{g} = 1000\ \mathrm{mg}
    • 1 mcg=0.001 mg1\ \mathrm{mcg} = 0.001\ \mathrm{mg} (note: cognition-check correct relation)
    • 1 L=1000 mL1\ \mathrm{L} = 1000\ \mathrm{mL}
  • Dalton’s Law (summary)
    • P<em>t=∑</em>iPiP<em>t = \sum</em>i P_i