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
1050psiEf = 0.28 L/psi10 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size E oxygen cylinder (factor 0.28 L/psi) reads 1050 psi and runs at 10 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1050 psif = 0.28 L/psi10 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 6.3 kPa · FiO₂ 0.5 · PEEP 10 cmH₂O0100200300400500P/F (mmHg)above 300mildmoderateseverenot gradable: PEEP below 5

Practice exercise (made-up values, not clinical guidance). A patient with acute hypoxaemia and bilateral opacities, not explained by heart failure, has PaO₂ 6.3 kPa on 50% oxygen with a PEEP of 10 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 6.3 kPaFiO₂ 50%PEEP 10 cmH₂O
  1. 1above 300
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 144 mmol/L, glucose 27.1 mmol/L and urea 15 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 144 mmol/Lglucose 27.1 mmol/Lurea 15 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 21% oxygen shows PaO₂ 77 mmHg (10.3 kPa) and PaCO₂ 31 mmHg (4.1 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 21%PaO₂ 77 mmHg (10.3 kPa)PaCO₂ 31 mmHg (4.1 kPa)
A–a gradient = mmHg
5.Clinical assessment scoresMedium
S? / 4+M? / 4+A? / 4+Mob? / 4+N? / 4+F? / 3Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Braden scale: sensory perception: completely limited; moisture: rarely moist; activity: walks occasionally; mobility: very limited; nutrition: probably inadequate; friction and shear: potential problem. Find the Braden total B.

6–23
B =
6.Clinical assessment scoresHard
low riskmoderate riskhigh risk

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Morse fall scale: history of falling in the last 3 months: no; secondary diagnosis: no; ambulatory aid: crutches, cane or walker; IV therapy or saline lock: no; gait: normal, bed rest or wheelchair; mental status: knows own limits. Using the cut-offs 0–24 low, 25–44 moderate and 45 or more high, click the fall-risk level.

  1. 1low risk
  2. 2moderate risk
  3. 3high risk
7.Med-surg: cardiovascular & respiratoryMedium

A patient with heart failure asks why salt is being limited. Which explanation is correct?

  1. ASodium stops the diuretic tablets from being absorbed properly
  2. BSodium makes the body retain water, which adds to congestion
  3. CSodium raises the heart rate during sleep
  4. DSodium directly weakens the contracting heart muscle
8.Med-surg: cardiovascular & respiratoryHard

Two days after a coronary stent, a patient on aspirin and ticagrelor has black, tarry stools and feels faint on standing. What should the nurse do?

  1. AGive a laxative and repeat the observations tomorrow
  2. BReassure the patient that iron tablets cause black stools
  3. CCheck vital signs, report urgently and anticipate a blood count
  4. DStop both antiplatelet drugs permanently on the nurse's own decision

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 23 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

(1050 − 200)·0.28 = 238 L

Duration

238/10 = 23.8 min → t = 23 min

Answer

t = 23 min
2.Oxygen therapy & respiratory calculations

Answer: severe

P/F ratio and ARDS (Berlin definition): P/F = PaO₂ (mmHg)/FiO₂ (as a fraction). With PEEP or CPAP of at least 5 cmH₂O, ARDS is graded mild for 200 < P/F ≤ 300, moderate for 100 < P/F ≤ 200 and severe for P/F ≤ 100 mmHg. The other Berlin criteria (onset within a week, bilateral opacities, not fully explained by heart failure) must also be met. PaO₂ in kPa × 7.5 gives mmHg. The ROX index (SpO₂/FiO₂)/respiratory rate is used to follow patients on high-flow nasal oxygen.

PEEP

PEEP 10 ≥ 5 cmH₂O

PaO₂ in mmHg

6.3·7.5 = 47.25 mmHg

P/F ratio

P/F = 47.25/0.5 = 94.5 mmHg

Berlin severity

severe

Answer

severe
3.Arterial blood gas interpretation

Answer: Osm = 330 mOsm/kg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Calculated osmolality

Osm = 2·144 + 27.1 + 15 = 330.1 ≈ 330 mOsm/kg

Answer

Osm = 330 mOsm/kg
4.Arterial blood gas interpretation

Answer: A–a gradient = 33.98 mmHg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Alveolar oxygen

PAO₂ = 0.21·713 − 31/0.8 = 149.7 − 38.75 = 111 mmHg

Gradient

A–a = 111 − 77 = 33.98 mmHg

Answer

A–a gradient = 33.98 mmHg
5.Clinical assessment scores

Answer: B = 14

Braden scale: six subscales for pressure-injury risk. Sensory perception, moisture, activity, mobility and nutrition score 1 to 4, from the worst level (1) to no problem (4); friction and shear scores 1 to 3. The total runs from 6 to 23, and a lower total means a higher risk. Common bands: 19–23 not at risk, 15–18 mild risk, 13–14 moderate risk, 10–12 high risk and 9 or below very high risk.

Score each subscale

sensory perception: completely limited → 1
moisture: rarely moist → 4
activity: walks occasionally → 3
mobility: very limited → 2
nutrition: probably inadequate → 2
friction and shear: potential problem → 2

Add

Braden total = 1 + 4 + 3 + 2 + 2 + 2 = 14

Answer

B = 14
6.Clinical assessment scores

Answer: low risk

Morse fall scale: six items. History of falling: no 0, yes 25. Secondary diagnosis: no 0, yes 15. Ambulatory aid: none, bed rest or nurse assistance 0; crutches, cane or walker 15; holding on to furniture 30. IV therapy or saline lock: no 0, yes 20. Gait: normal, bed rest or wheelchair 0; weak 10; impaired 20. Mental status: knows own limits 0; overestimates or forgets limits 15. The total runs from 0 to 125. Risk cut-offs differ between hospitals; a common set is 0–24 low, 25–44 moderate and 45 or more high.

Score each item

history of falling in the last 3 months: no → 0
secondary diagnosis: no → 0
ambulatory aid: crutches, cane or walker → 15
IV therapy or saline lock: no → 0
gait: normal, bed rest or wheelchair → 0
mental status: knows own limits → 0

Add

Morse total = 0 + 0 + 15 + 0 + 0 + 0 = 15

Risk level

15 → low risk

Answer

low risk
7.Med-surg: cardiovascular & respiratory

Answer: B · Sodium makes the body retain water, which adds to congestion

Why this is the answer

Sodium retention leads to water retention, increasing circulating volume, preload and congestion. Limiting sodium and, in some patients, fluid helps control oedema and breathlessness. The exact limits are set by the prescriber.

Answer

B · Sodium makes the body retain water, which adds to congestion
8.Med-surg: cardiovascular & respiratory

Answer: C · Check vital signs, report urgently and anticipate a blood count

Why this is the answer

Melaena with postural dizziness suggests upper gastrointestinal bleeding, a risk with dual antiplatelet therapy. The nurse assesses for shock, informs the team urgently and expects bloods, a group and save (type and screen) and possibly endoscopy. Stopping antiplatelets after a stent risks stent thrombosis, so the decision belongs to the medical and cardiology team.

Answer

C · Check vital signs, report urgently and anticipate a blood count

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