Respiratory Care and Oxygen Therapy: cram pack

Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

1Formulas and methods

Oxygen therapy & respiratory calculations

Nasal cannula
FiO₂ ≈ 21% + 4% × L/min (1–6 L/min)
Cylinder duration
min = (psi − 200) × factor / (L/min); D 0.16, E 0.28, H 3.14 L/psi
Minute and alveolar ventilation
V̇E = VT·f, V̇A = (VT − VD)·f
Predicted body weight
men 50 + 0.91 × (cm − 152.4); women 45.5 + 0.91 × (cm − 152.4)
P/F ratio (Berlin, PEEP ≥ 5)
mild > 200–300, moderate > 100–200, severe ≤ 100 mmHg
Oxygen content
CaO₂ = 1.34·Hb·SaO₂ + 0.003·PaO₂
Oxygen delivery
DO₂ = CaO₂ × CO × 10
ROX index
(SpO₂/FiO₂)/RR

Method

  1. Put every value in the units of the formula: FiO₂ and SaO₂ as fractions, PaO₂ in mmHg, Hb in g/dL.
  2. For a cylinder, subtract the safe residual, multiply by the cylinder factor and divide by the flow.
  3. Round cylinder times and flows down, never up.
  4. For the P/F ratio, check the PEEP first, then divide PaO₂ by FiO₂ and compare with 300, 200 and 100 mmHg.
  5. For ventilation, subtract the dead space for alveolar ventilation and use the predicted body weight for tidal volumes.

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

Clinical assessment scores

Glasgow Coma Scale
GCS = E (1–4) + V (1–5) + M (1–6) = 3–15
APGAR
5 signs × 0–2 = 0–10; 7–10 reassuring, 4–6 moderately abnormal, 0–3 low
Braden scale
5 × (1–4) + 1 × (1–3) = 6–23; ≤ 18 at risk
Morse fall scale
falls 25, diagnosis 15, aid 15/30, IV 20, gait 10/20, mental status 15
NEWS2 risk
0–4 low; single 3 low–medium; 5–6 medium; ≥ 7 high
Mean arterial pressure
MAP = (SBP + 2·DBP)/3 = DBP + PP/3
Pulse pressure and shock index
PP = SBP − DBP, SI = HR/SBP
Body mass index
BMI = kg/m² = 703·lb/in²

Method

  1. Find the score sheet that the question uses and its range (GCS 3–15, APGAR 0–10, Braden 6–23, Morse 0–125).
  2. Score every item separately, matching the description to its level.
  3. Add the item scores and check that the total lies inside the range.
  4. Apply the cut-offs: for NEWS2 also look for any single parameter scoring 3.
  5. For derived values use MAP = (SBP + 2·DBP)/3, PP = SBP − DBP, SI = HR/SBP and BMI = kg/m².

Med-surg: cardiovascular & respiratory

Method

  1. Name the problem: pump failure, blocked artery, rhythm, clot, airway narrowing, infection or a device problem.
  2. Check the danger signs first: hypoxia, hypotension, chest pain, new confusion, a cold pulseless limb.
  3. Match the oxygen to the patient: 94–98% for most, 88–92% for those at risk of CO₂ retention.
  4. Link each drug to its test and its risk: warfarin and INR, heparin and aPTT and platelets, diuretics and potassium.
  5. Choose the safe first action, then escalate and reassess.

2Practice problems

1.Oxygen therapy & respiratory calculationsMedium
2000psiHf = 3.14 L/psi8 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 2000 psi and runs at 8 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

2000 psif = 3.14 L/psi8 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
2050psiDf = 0.16 L/psi45 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 45 minutes. The size D cylinder (factor 0.16 L/psi) reads 2050 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

45 min2050 psif = 0.16 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium
pH7.357.457.38PaCO₂mmHg354528HCO₃⁻mmol/L222616uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.38, PaCO₂ 28 mmHg (3.7 kPa) and HCO₃⁻ 16 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.38PaCO₂ 28 mmHg (3.7 kPa)HCO₃⁻ 16 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 42 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 42 mmol/L
PaCO₂ = mmHg
5.Clinical assessment scoresMedium
9954SBPDBPmmHgHR 78/min · SI = ?

Practice exercise (made-up values, not clinical guidance). A patient has a pulse of 78/min and a blood pressure of 99/54 mmHg. Find the shock index SI = HR/SBP. Round to two decimal places.

HR 78/minBP 99/54 mmHg
SI =
6.Clinical assessment scoresHard
3210123RR≤89–1112–2021–24≥25SpO₂≤9192–9394–95≥96air / O₂O₂airSBP≤9091–100101–110111–219≥220HR≤4041–5051–9091–110111–130≥131ACVPUAC, V, P, UT °C≤35.035.1–36.036.1–38.038.1–39.0≥39.1lowlow–mediummediumhigh

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 26/min, SpO₂ 96% on room air, blood pressure 130/78 mmHg, pulse 58/min, alert, temperature 37.1 °C. Which clinical risk group does the patient fall into? Click it.

RR 26SpO₂ 96%airSBP 130HR 58AT 37.1 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Why must intravenous potassium chloride never be given as a rapid push or undiluted?

  1. AIt immediately lowers the blood glucose to dangerous levels
  2. BIt turns into solid crystals inside the vein and blocks it
  3. CA sudden high potassium level can cause cardiac arrest
  4. DIt works only when given by mouth
8.Med-surg: cardiovascular & respiratoryHard

A patient with squamous cell lung cancer becomes confused, thirsty and constipated, with abdominal pain. Which electrolyte disturbance is most likely?

  1. AHyponatraemia
  2. BHypokalaemia
  3. CHypercalcaemia
  4. DHypomagnesaemia

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 706 min

Cylinder duration: usable litres = (gauge pressure − safe residual) × cylinder factor, with the safe residual usually 200 psi. Cylinder factors in L/psi: D 0.16, E 0.28, H (and K) 3.14. Duration (min) = usable litres/flow (L/min). Round a duration down, never up, so the cylinder is changed in time. In bar-based systems, the gas volume is the water capacity (L) × the pressure (bar).

Usable litres

(2000 − 200)·3.14 = 5652 L

Duration

5652/8 = 706.5 min → t = 706 min

Answer

t = 706 min

That is about 11 h 46 min.

2.Oxygen therapy & respiratory calculations

Answer: Q = 6 L/min

Cylinder duration: usable litres = (gauge pressure − safe residual) × cylinder factor, with the safe residual usually 200 psi. Cylinder factors in L/psi: D 0.16, E 0.28, H (and K) 3.14. Duration (min) = usable litres/flow (L/min). Round a duration down, never up, so the cylinder is changed in time. In bar-based systems, the gas volume is the water capacity (L) × the pressure (bar).

Usable litres

(2050 − 200)·0.16 = 296 L

Highest flow

296/45 = 6.578 L/min → Q = 6 L/min

Answer

Q = 6 L/min
3.Arterial blood gas interpretation

Answer: fully compensated

Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.

ROME, value by value

pH 7.38: within 7.35–7.45
PaCO₂ 28 mmHg: low (35–45)
HCO₃⁻ 16 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 30–34 mmHg, so the measured 28 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

fully compensated

Answer

fully compensated
4.Arterial blood gas interpretation

Answer: PaCO₂ = 50.4 mmHg

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Expected PaCO₂

0.7·42 + 21 = 50.4 mmHg

Answer

PaCO₂ = 50.4 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

5.Clinical assessment scores

Answer: SI = 0.79

Blood pressure values: pulse pressure PP = SBP − DBP. Mean arterial pressure MAP ≈ (SBP + 2·DBP)/3 = DBP + PP/3, an estimate based on the heart spending about two thirds of each beat in diastole at a normal heart rate (less accurate when the heart rate is fast); a MAP of at least about 65 mmHg is a common target for organ perfusion. The shock index SI = heart rate/SBP is normally about 0.5–0.7; a value above about 1 is a warning sign of shock.

Shock index

SI = 78/99 = 0.7879 ≈ 0.79

Answer

SI = 0.79

Above the usual 0.5–0.7.

6.Clinical assessment scores

Answer: low–medium

NEWS2 (National Early Warning Score 2, Royal College of Physicians 2017): score each of the seven parameters with the chart (respiration rate, SpO₂ on scale 1, air or supplemental oxygen, systolic blood pressure, pulse, consciousness on the ACVPU scale and temperature) and add the scores. Clinical risk: 0–4 low; a score of 3 in any single parameter low–medium; 5–6 medium; 7 or more high. A total of 5 or more needs an urgent response.

Score each parameter

RR 26/min → 3
SpO₂ 96% → 0
on air → 0
SBP 130 mmHg → 0
HR 58/min → 0
alert (A) → 0
T 37.1 °C → 0

Total and red scores

NEWS2 = 3 + 0 + 0 + 0 + 0 + 0 + 0 = 3
At least one parameter scores 3.

Risk group

low–medium

Answer

low–medium

A single score of 3 needs an urgent review even when the total is low.

7.Med-surg: cardiovascular & respiratory

Answer: C · A sudden high potassium level can cause cardiac arrest

Why this is the answer

Rapid or concentrated IV potassium can cause cardiac arrest. It is given diluted, by infusion, at controlled rates (often with a pump and ECG monitoring for higher rates). Concentrated ampoules are tightly controlled in hospitals because of fatal errors.

Answer

C · A sudden high potassium level can cause cardiac arrest
8.Med-surg: cardiovascular & respiratory

Answer: C · Hypercalcaemia

Why this is the answer

Squamous cell lung cancer can secrete PTH-related protein, and bone metastases can release calcium. Hypercalcaemia causes confusion, thirst, polyuria, constipation, abdominal pain and arrhythmias ("bones, stones, groans and psychiatric overtones"). Treatment includes IV fluids and bisphosphonates.

Answer

C · Hypercalcaemia

ExamProblems · examproblems.com/courses/respiratory-care-and-oxygen-therapy