Anesthesia Math

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Questions and Answers

How would you convert the ratio 1:10,000 to mg/ml?

Divide 1 by 10,000 and then multiply by 1000 (correct)

Multiply 1 by 10,000

Multiply 1 by 10,000 and then divide by 1000

Divide 1 by 10,000

What is the decimal equivalent of the fraction 1/2?

0.50 (correct)

0.30

0.75

0.25

What is the percentage expression of the decimal fraction 0.5?

500.0%

5.0%

50.0% (correct)

0.5%

How would you convert a percentage expression to mg/ml?

Multiply the percentage by 10 Signup and view all the answers

What is the ratio expression of the percentage 1%?

1:100 Signup and view all the answers

What is the principle behind Avogadro's hypothesis?

Equal volumes of all gases contain equal numbers of molecules Signup and view all the answers

What is the formula for calculating mEq?

mEq = mg/atomic weight * valence Signup and view all the answers

What does the unit 'mEq' represent?

Milliequivalents of a substance Signup and view all the answers

What is the relationship between the molecular weight of oxygen and the molecular weight of hydrogen?

The molecular weight of oxygen is 16 times the molecular weight of hydrogen Signup and view all the answers

According to Avogadro's hypothesis, what is the relationship between 1 mole of oxygen and 1 mole of carbon dioxide?

1 mole of oxygen is equal to 1 mole of carbon dioxide Signup and view all the answers

What is the primary function of a solvent in a solution?

To dissolve another substance Signup and view all the answers

What is the result of diluting a solution with more solvent?

The solution becomes less concentrated Signup and view all the answers

What is a stock solution?

A relatively concentrated solution that can be made weaker by diluting it Signup and view all the answers

What is the concentration of a 1:1 solution in the metric system?

1 gram per 1 ml Signup and view all the answers

What is the rate of acceleration of free-falling objects on Earth?

9.8 m/s/s Signup and view all the answers

What is the formula for pressure?

Pressure = force per unit area Signup and view all the answers

What is the purpose of the APL (Adjustable Pressure Limiting) valve?

To regulate pressure in the anesthesia circuit Signup and view all the answers

What is the equivalent water column supported by a pressure that supports a 7.5 mm column of Hg?

10.2 cm Signup and view all the answers

What is the correct formula for CPP?

CPP = MAP - ICP Signup and view all the answers

Why must a water manometer be held perpendicular to the plane of the floor?

To ensure accurate pressure readings Signup and view all the answers

What is the term for the work performed by the heart to pump blood?

Cardiac work Signup and view all the answers

What is the main difference between a solvent and a solute?

The solvent is the substance doing the dissolving, while the solute is the substance being dissolved. Signup and view all the answers

What does it mean to dilute a solution?

To decrease the concentration of a solution Signup and view all the answers

What is a stock solution in anesthesia?

A concentrated solution of a medication from which a weaker solution can be made by diluting it Signup and view all the answers

How many grams per milliliter (g/mL) are in a 1:1 solution?

1 Signup and view all the answers

What is the mathematical expression for pH?

-log[H+] Signup and view all the answers

What is the significance of the Henderson-Hasselbalch equation in anesthesia?

It helps calculate the pH based on the concentration of bicarbonate and carbonic acid Signup and view all the answers

What is the primary use of the Henderson-Hasselbach equation in anesthesia?

To estimate the pH of a solution containing a weak acid or its conjugate base Signup and view all the answers

What is a mole in chemistry?

A unit of measurement that represents 6.02214076 × 10^23 particles (atoms, subatomic particles, molecules, etc) Signup and view all the answers

How do you symbolize multiplication in SI?

· Signup and view all the answers

What is the equation for converting from Fahrenheit to Celsius?

°C = (°F - 32) × 5/9 Signup and view all the answers

What is the equation for converting centimeters (cm) to inches (in)?

1 in = 2.54 cm Signup and view all the answers

What is the equation for pressure in anesthesia?

Pressure = Force / Area Signup and view all the answers

What is a Torricelli tube?

A device used to measure gas pressure using mmHg Signup and view all the answers

You have an oxygen E cylinder with a pressure gauge that registers 0 psi. Is there oxygen in that cylinder?

Yes, there must be oxygen in the cylinder. Oxygen is at atmospheric pressure. Signup and view all the answers

What is a Bourdon gauge used for?

To measure the pressure of an oxygen cylinder Signup and view all the answers

7.5 mmHg equals how many cm of water pressure?

10.2 Signup and view all the answers

1 kPa equals how much mmHg?

7.5 mmHg Signup and view all the answers

14.7 psi is equivalent to how many mmHg?

760 Signup and view all the answers

What is the primary function of a water manometer in anesthesia?

To measure pressure in a circuit by holding perpendicular to floor Signup and view all the answers

What is the equation for work in anesthesia?

Force x Distance Signup and view all the answers

What is an alternate equation for work (cardiac and respiratory work)?

Pressure x Volume Signup and view all the answers

What is work measured in?

Joules Signup and view all the answers

How does the pressure-volume loop express respiratory work?

It illustrates the relationship between airway pressure and tidal volume Signup and view all the answers

What is power measured in?

Watts (rate of work) Signup and view all the answers

Match the base unit with the correct unit of measurement in SI

length = meter electric current = ampere thermodynamic temperature = kelvin mass = kilogram Signup and view all the answers

What is the MAC of sevoflurane?

2.0 Signup and view all the answers

What is the Minimum Alveolar Concentration (MAC) of isoflurane?

1.2% Signup and view all the answers

What is the MAC of desflurane?

6% Signup and view all the answers

What is the Minimum Alveolar Concentration (MAC) of nitrous oxide?

105% Signup and view all the answers

What is the blood:gas coefficient of sevoflurane?

0.65 Signup and view all the answers

What is the blood gas coefficient of desflurane?

0.45 Signup and view all the answers

What is the blood gas coefficient of isoflurane?

1.4 Signup and view all the answers

What is the blood gas coefficient of nitrous oxide?

0.47 Signup and view all the answers

What is the saturated vapor pressure of sevoflurane?

160 mmHg Signup and view all the answers

What is the saturated vapor pressure of desflurane in mmHg?

664 Signup and view all the answers

What is the saturated vapor pressure of isoflurane in mmHg?

250 mmHg Signup and view all the answers

What is the saturated vapor pressure of nitrous oxide at 20 degrees C?

None, it is a gas Signup and view all the answers

What is the term for the energy required for a liquid molecule to become vapour?

Latent heat of vaporization Signup and view all the answers

What is the term for when equilibrium exists between the rate of evaporation and condensation in a closed container?

Vapor pressure Signup and view all the answers

What does Dalton's Law state?

The total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas. Signup and view all the answers

What does Poisson's Law state?

Under isolated conditions, gas cools when expanded and warms when compressed due to adiabatic changes Signup and view all the answers

What does Henry's Law state?

The concentration of a gas in a liquid is directly proportional to the pressure of the gas. Signup and view all the answers

Study Notes

Ratios

A ratio is a means of expressing a relationship between quantities, using a different symbol than a fraction.
Example: Blood/gas coefficient for an anesthetic agent's solubility in blood compared to gas, expressed as 2.3:1 or 2.3/1.

Percent

Percent expressions represent a quantity in terms of parts per one hundred.
A percent number is a fraction whose numerator is verbalized and whose denominator is assumed to be one hundred.
Simple fractions can be converted to percent by first converting to a decimal fraction and then multiplying by 100.

Converting Percent to MG/ML

Multiply the percent by 10 to get mg/ml.
Examples: 0.25% * 10 = 2.5mg/ml, 5% * 10 = 50mg/ml.

Solute and Solvent

A solute is a substance dissolved in a solvent to make a solution.
A solvent is the component of a solution that is capable of dissolving another substance.
Solute may be in the form of solid, liquid, or gas.
Examples: pure drug or a concentrated solution.

Drug Calculations

Example: You have a 1% solution of phenylephrine and want to make a 500 cc (ml) bottle of 1:20,000 solution of phenylephrine in Lactated Ringer's.
Solution: Determine the mg/ml concentration of the final solution and then use the proportion method.

Metric Units of Weight and Volume

1 Kilogram = 1,000 grams
1 liter = 1,000 milliliters or cubic centimeters
1 Gram = 1,000 milligrams
1 milliliter = 1/1,000 liter

Metric Terms

Metric weight standard: 1 milliliter of pure water weighs 1 gram at 4 degrees centigrade.
1 gram of solute with sufficient solvent to make 1 gram per cc of a solution equals 100% solution or a 1:1 solution.

Units

1 gram/cc = 100% solution or a 1:1 solution
1,000 mg/cc = 100% solution or a 1:1 solution

Logarithm

The logarithm is the inverse operation to exponentiation.
The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.

Henderson-Hasselbalch Equation

pH can be calculated with bicarbonate and carbonic acid concentrations.

Avogadro's Hypothesis

Equal volumes of all gases contain equal numbers of molecules under conditions of fixed temperature and pressure.
1 mole of oxygen (with a molecular weight of 32) = 1 mole of hydrogen (m.w.= 2) = 1 mole water (m.w.= 18) = 1 mole carbon (m.w.= 12) = 1 mole carbon dioxide (m.w.= 44).

mEq

A liter of a particular intravenous solution contains 4.5 mEq · l-1 of potassium.
Formula: mEq= mg/atomic weight * valence

SI Prefixes

The Seven Base Units of the SI

Pressure

Pressure = force per unit area
1 newton will accelerate a 1 kilogram mass at 1 meter per second per second.

Force

The force of gravity: all free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s.

Inhaled Anesthetic Delivery Systems

Pressure sensor shut-off valve: the valve is open when the oxygen supply pressure is greater than the threshold value of 20 psig.

Pressure units

1 kPa = 7.5 mmHg = 10.2 cm H2O

Relevance

Cerebral perfusion pressure (CPP) formula: CPP = MAP - ICP
Importance of CPP in craniotomy surgery

Work

Work = F x D
Joule: the force of 1 N over 1 meter

Evaporation and Condensation

As a liquid evaporates into a space above it, the pressure of its vapour increases.
A point of equilibrium is reached when the rate of evaporation equals that of condensation, and the space becomes saturated.
At this point, the pressure is the saturated vapour pressure (SVP).

Energy Requirements

Liquid molecules require energy to become vapour, known as the latent heat of vaporization.
If this energy cannot be obtained from external sources, it is drawn from the liquid, causing it to cool.
This occurs in a vaporizer or when a nitrous oxide cylinder is used.

Condensation

When a vapour condenses, some of the latent heat of vaporization is returned as heat.

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