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 patient with hyperkalemia is prescribed an oral potassium binder such as patiromer or sodium zirconium cyclosilicate. How does this drug lower potassium?
AIt binds potassium in the gut so it leaves in the stool
BIt moves potassium into cells in the next few minutes
CIt protects the heart muscle against high potassium levels
DIt stops the kidneys from absorbing water in the tubules
2.Lab values & electrolytesHard
A patient with long-term heavy alcohol use is admitted with alcohol withdrawal. Which group of electrolyte problems is most common?
ALow chloride, high bicarbonate and high calcium
BHigh magnesium, high phosphate and high potassium
CHigh sodium, high calcium and high glucose
DLow magnesium, low phosphate and low potassium
3.Arterial blood gas interpretationMedium
A practice gas shows a metabolic acidosis with HCO₃⁻ 12 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.
HCO₃⁻ 12 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
A practice gas shows a metabolic acidosis: pH 7.32, PaCO₂ 30 mmHg (4.0 kPa), HCO₃⁻ 15 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.
pH 7.32PaCO₂ 30 mmHg (4.0 kPa)HCO₃⁻ 15 mmol/L
1appropriate compensation
2added respiratory acidosis
3added respiratory alkalosis
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 8 mg/L at 1 h and 3.6 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.
C1 = 8 mg/L (1 h)C2 = 3.6 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3 L/h. Each dose is 750 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 3 L/hτ = 12 hS = 1F = 1D = 750 mg
Css,avg = mg/L
7.Clinical nursingMedium
A patient's low potassium does not improve despite potassium replacement. Which other electrolyte should be checked?
AChloride
BMagnesium
CSodium
DPhosphate
8.Clinical nursingHard
After a high spinal cord injury, a patient has low blood pressure with a slow heart rate and warm, dry skin. What is most likely?
AHypovolaemic shock
BSeptic shock
CNeurogenic shock
DCardiac tamponade
3Solutions
1.Lab values & electrolytes
Answer: A · It binds potassium in the gut so it leaves in the stool
Why this is the answer
Potassium binders exchange potassium in the gut for another ion, so potassium is removed from the body in the stool. They act over hours, so they are not used alone for emergencies; calcium protects the heart, and insulin with glucose shifts potassium into cells quickly.Checked against:High potassium level · MedlinePlus (NIH) (2025)
Answer
A · It binds potassium in the gut so it leaves in the stool
2.Lab values & electrolytes
Answer: D · Low magnesium, low phosphate and low potassium
Why this is the answer
Poor diet, vomiting, diarrhea and alcohol's effect on the kidneys commonly cause low magnesium, phosphate and potassium. These worsen arrhythmia and seizure risk, so they are checked and replaced, together with thiamine.
Answer
D · Low magnesium, low phosphate and low potassium
3.Arterial blood gas interpretation
Answer: PaCO₂ = 26 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.
Winter’s formula
PaCO₂ = 1.5·12 + 8 = 26 mmHg
range: 24–28 mmHg
Answer
PaCO₂ = 26 mmHg
4.Arterial blood gas interpretation
Answer: appropriate compensation
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
1.5·15 + 8 = 30.5 → 28.5–32.5 mmHg
Compare
measured: 30 mmHg → appropriate compensation
Answer
appropriate compensation
5.Clinical pharmacokinetics
Answer: t½ = 3.472 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(8/3.6)/4 = 0.7985/4 = 0.1996 h⁻¹
Half-life
t½ = 0.693/0.1996 = 3.472 h
Answer
t½ = 3.472 h
6.Clinical pharmacokinetics
Answer: Css,avg = 20.83 mg/L
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.
Hypomagnesaemia increases renal potassium loss and makes hypokalaemia hard to correct. Magnesium must be replaced as well.
Answer
B · Magnesium
8.Clinical nursing
Answer: C · Neurogenic shock
Why this is the answer
Neurogenic shock from cervical or high thoracic injury causes vasodilation and bradycardia because sympathetic outflow is lost. Hypovolaemic shock usually causes tachycardia and cool, pale skin.