Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
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.
In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.
Clinical pharmacokinetics
Rate constant and half-life
k = ln 2/t½ = 0.693/t½
First-order decay
C = C₀·e−kt = C₀·(1/2)t/t½
Two levels
k = ln(C₁/C₂)/Δt
Volume and clearance
Vd = dose/C₀, CL = k·Vd
Loading dose
LD = Vd·C/(S·F)
Maintenance rate
R = CL·Css/(S·F)
Average steady state
Css,avg = S·F·D/(CL·τ)
Steady state
1 − (1/2)ⁿ after n half-lives; ≈ 97% after 5
Infusion
C = (R/CL)(1 − e−kt)
Interval and dose from peak and trough
τ = ln(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
Cockcroft–Gault
CrCl = (140 − age) × kg/(72 × SCr mg/dL), × 0.85 for women
Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.
2Practice problems
1.Lab values & electrolytesMedium
A stool test for Clostridioides difficile is ordered. Which sample is appropriate?
AA rectal swab from a patient with constipation
BAn unformed (liquid or soft) stool
CA formed, hard stool sample
DAny stool after a laxative dose
2.Lab values & electrolytesHard
A patient on a heparin infusion has a platelet count that falls from 260 to 110 × 10³/µL on day 7. Which action is most appropriate?
AGive a platelet transfusion and continue the heparin
BTake no action, because the count is still just above 100 × 10³/µL
CReport it at once: heparin-induced thrombocytopenia is possible
DContinue the infusion and increase the rate as per protocol
3.Arterial blood gas interpretationMedium
A practice arterial blood gas shows pH 7.43, PaCO₂ 28 mmHg (3.7 kPa) and HCO₃⁻ 18 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.
pH 7.43PaCO₂ 28 mmHg (3.7 kPa)HCO₃⁻ 18 mmol/L
1uncompensated
2partially compensated
3fully compensated
4.Arterial blood gas interpretationHard
Practice values: Na⁺ 143, Cl⁻ 105 and HCO₃⁻ 18 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.
Na⁺ 143 mmol/LCl⁻ 105 mmol/LHCO₃⁻ 18 mmol/L
delta ratio =
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 25 mg/L at 1 h and 12.5 mg/L at 13 h. Assume first-order elimination. Find the half-life t½.
C1 = 25 mg/L (1 h)C2 = 12.5 mg/L (13 h)
t½ = h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 69 kg patient has a theophylline level of 6 mg/L; the target is 15 mg/L. The drug is given intravenously as aminophylline (S = 0.8), and the volume of distribution is 0.5 L/kg. What extra loading dose LD raises the level to the target?
69 kgVd = 0.5 L/kgC = 6 → 15 mg/LS = 0.8
LD = mg
7.Clinical nursingMedium
Which is a first-line nursing measure to help prevent constipation in hospital?
AGiving an enema to every patient on admission
BRestricting fluids to reduce urine output
CKeeping the patient in bed
DEncouraging fluids, fibre and mobility
8.Clinical nursingHard
A postoperative patient has a heart rate of 115/min, temperature 38.6 °C, respiratory rate 26/min and blood pressure 85/50 mmHg despite a fluid bolus. What does this most likely indicate?
AAnxiety about discharge
BMild dehydration only
CSeptic shock requiring urgent critical care review
DA normal inflammatory response in the first days after surgery
3Solutions
1.Lab values & electrolytes
Answer: B · An unformed (liquid or soft) stool
Why this is the answer
C. difficile testing is done on unformed stool from patients with diarrhea, because many people carry the organism without disease. Testing formed stool, or stool after laxatives, can lead to misdiagnosis.Checked against:C. diff Testing · MedlinePlus (NIH) (2026)
Answer
B · An unformed (liquid or soft) stool
2.Lab values & electrolytes
Answer: C · Report it at once: heparin-induced thrombocytopenia is possible
Why this is the answer
Heparin-induced thrombocytopenia causes a large fall in platelets (often more than half), usually 5–14 days after starting heparin, and carries a high risk of clots. The prescriber stops all heparin and starts a non-heparin anticoagulant if HIT is suspected.Checked against:Heparin-Induced Thrombocytopenia · StatPearls (NCBI Bookshelf) (2023)
Answer
C · Report it at once: heparin-induced thrombocytopenia is possible
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 7.43: within 7.35–7.45
PaCO₂ 28 mmHg: low (35–45)
HCO₃⁻ 18 mmol/L: low (22–26)
Compensation
fully compensated
Answer
fully compensated
4.Arterial blood gas interpretation
Answer: delta ratio = 1.333
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.
Anion gap
AG = 143 − (105 + 18) = 20
Delta ratio
(20 − 12)/(24 − 18) = 8/6 = 1.333
Answer
delta ratio = 1.333
Between 1 and 2: a pure high anion gap acidosis.
5.Clinical pharmacokinetics
Answer: t½ = 12 h
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Elimination rate constant
k = ln(25/12.5)/12 = 0.6931/12 = 0.05776 h⁻¹
Half-life
t½ = 0.693/0.05776 = 12 h
Answer
t½ = 12 h
6.Clinical pharmacokinetics
Answer: LD = 388.1 mg
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Volume of distribution
Vd = 0.5·69 = 34.5 L
Rise needed
15 − 6 = 9 mg/L
Loading dose
LD = 34.5·9/(0.8·1) = 388.1 mg
Answer
LD = 388.1 mg
In practice the dose is rounded to a convenient amount.
7.Clinical nursing
Answer: D · Encouraging fluids, fibre and mobility
Why this is the answer
Adequate fluids, a fibre-rich diet, mobility and privacy for toileting help prevent constipation. Laxatives are added if needed, especially with opioids.
Answer
D · Encouraging fluids, fibre and mobility
8.Clinical nursing
Answer: C · Septic shock requiring urgent critical care review
Why this is the answer
Infection signs with hypotension not responding to fluid suggest septic shock. Vasopressors and critical care input are likely needed, along with antibiotics and source control.
Answer
C · Septic shock requiring urgent critical care review