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 taking furosemide has a potassium of 2.9 mEq/L. Which finding would the nurse expect?
ATingling around the mouth with a positive Chvostek’s sign
BMuscle weakness and leg cramps
CTall, peaked T waves on the ECG
DDiarrhea and abdominal cramping from overactive bowels
2.Lab values & electrolytesHard
At the start of a shift, the nurse reviews four new results. Which patient needs attention first?
AGlucose 180 mg/dL (10 mmol/L) after a meal in a patient with diabetes
BHemoglobin 11.0 g/dL (110 g/L) in a patient with rheumatoid arthritis
CPotassium 5.2 mEq/L in a patient with stable chronic kidney disease
DSodium 119 mEq/L in a patient with new confusion and vomiting
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 alkalosis with HCO₃⁻ 33 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.
HCO₃⁻ 33 mmol/L
PaCO₂ = mmHg
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 140 mg of tobramycin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 3 h. Find the volume of distribution Vd.
D = 140 mgC₀ = 10 mg/Lt½ = 3 h
Vd = L
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 77 kg patient on regular gentamicin doses is at steady state. The target is a peak of 7 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
77 kgVd = 0.3 L/kgCpeak = 7 mg/LCtrough = 1 mg/L
D = mg
7.Clinical nursingMedium
Which finding with a groin hernia needs urgent surgical review?
AThe lump disappears completely when the patient lies down flat
BThe lump has become painful and tender and cannot be pushed back
CThe lump has been present for several years without pain
DThe lump gets bigger when the patient coughs
8.Clinical nursingHard
A potassium result of 6.9 mmol/L comes back on a well patient with a normal ECG, and the laboratory reports that the sample was haemolysed. What is the best action?
ARepeat the blood test promptly, as haemolysis can falsely raise potassium
BStart a potassium supplement
CIgnore the result because the patient looks well and the ECG is normal
DGive IV insulin and glucose straight away
3Solutions
1.Lab values & electrolytes
Answer: B · Muscle weakness and leg cramps
Why this is the answer
Low potassium causes muscle weakness, cramps, reduced bowel movement (constipation, even ileus) and arrhythmias. Peaked T waves are seen in hyperkalemia, and perioral tingling suggests low calcium.Checked against:Heart failure - fluids and diuretics · MedlinePlus (NIH); Low blood potassium · MedlinePlus (NIH) (2025)
Answer
B · Muscle weakness and leg cramps
2.Lab values & electrolytes
Answer: D · Sodium 119 mEq/L in a patient with new confusion and vomiting
Why this is the answer
Severe hyponatremia with confusion and vomiting suggests cerebral edema and can progress to seizures and coma. The other results are mildly abnormal and expected for those conditions, so they are less urgent.Checked against:Low blood sodium - Medical Encyclopedia · MedlinePlus (NIH) (2025); Sodium Blood Test · MedlinePlus (NIH) (2024)
Answer
D · Sodium 119 mEq/L in a patient with new confusion and vomiting
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: PaCO₂ = 44.1 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
0.7·33 + 21 = 44.1 mmHg
Answer
PaCO₂ = 44.1 mmHg
The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.
5.Clinical pharmacokinetics
Answer: Vd = 14 L
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.
Volume of distribution
Vd = 140/10 = 14 L
Answer
Vd = 14 L
6.Clinical pharmacokinetics
Answer: D = 138.6 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 = 0.3·77 = 23.1 L
Dose
D = 23.1·(7 − 1) = 138.6 mg
Answer
D = 138.6 mg
In practice the dose is rounded to a convenient amount.
7.Clinical nursing
Answer: B · The lump has become painful and tender and cannot be pushed back
Why this is the answer
An irreducible, painful, tender hernia, especially with vomiting, suggests incarceration or strangulation. This is a surgical emergency because the trapped bowel can become ischaemic.
Answer
B · The lump has become painful and tender and cannot be pushed back
8.Clinical nursing
Answer: A · Repeat the blood test promptly, as haemolysis can falsely raise potassium
Why this is the answer
Haemolysis in the tube releases intracellular potassium, giving a falsely high reading. The result still needs prompt repeating and review, because true hyperkalaemia cannot be excluded.
Answer
A · Repeat the blood test promptly, as haemolysis can falsely raise potassium