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
Which instruction is correct for a patient starting oral iron tablets?
AYour urine will turn bright orange while you take it
BTake the tablet with an antacid to improve absorption
CTake each tablet with milk to protect the stomach
DYour stools may turn dark green or black
2.Lab values & electrolytesHard
After surgery, a patient receiving large volumes of hypotonic IV fluid develops headache, nausea and confusion. Which result best explains this?
AA potassium of 4.2 mEq/L
BA calcium of 9.4 mg/dL (2.35 mmol/L)
CA glucose of 110 mg/dL (6.1 mmol/L)
DA sodium of 126 mEq/L
3.Arterial blood gas interpretationMedium
A practice gas shows a metabolic acidosis with HCO₃⁻ 14 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.
HCO₃⁻ 14 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
A practice gas shows a metabolic alkalosis with HCO₃⁻ 43 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.
HCO₃⁻ 43 mmol/L
PaCO₂ = mmHg
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 98 kg patient receives a theophylline infusion. The clearance is 0.045 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 10 mg/L?
98 kgCL = 0.045 L/kg/hCss = 10 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 25 mg/h with no loading dose. The patient's clearance is 2.5 L/h and the half-life is 8 h. What is the level C after 13 h?
R = 25 mg/hCL = 2.5 L/ht½ = 8 ht = 13 h
C = mg/L
7.Clinical nursingMedium
Which side effect is associated with SGLT2 inhibitors such as dapagliflozin?
AGenital fungal infections
BBradycardia
CHair loss
DSevere weight gain and fluid retention
8.Clinical nursingHard
A patient with back pain develops numbness around the anus and genitals and new difficulty passing urine. Which condition should be suspected?
ACauda equina syndrome
BKidney stones
CSimple muscle strain
DConstipation
3Solutions
1.Lab values & electrolytes
Answer: D · Your stools may turn dark green or black
Why this is the answer
Oral iron commonly darkens the stools, which is harmless, but black tarry stools with abdominal pain should be reported. Milk, antacids and tea reduce absorption; vitamin C or orange juice can improve it.Checked against:Ferrograd C patient information leaflet (ferrous sulfate + vitamin C) · electronic medicines compendium (eMC), UK (2018)
Answer
D · Your stools may turn dark green or black
2.Lab values & electrolytes
Answer: D · A sodium of 126 mEq/L
Why this is the answer
Surgical stress raises antidiuretic hormone, and hypotonic fluids add free water, so sodium falls. Hyponatremia causes headache, nausea and confusion. The other values are normal.Checked against:Low blood sodium · MedlinePlus (NIH) (2025); Syndrome of inappropriate antidiuretic hormone secretion · MedlinePlus (NIH) (2025); Hyponatremia · StatPearls (NCBI Bookshelf)
Answer
D · A sodium of 126 mEq/L
3.Arterial blood gas interpretation
Answer: PaCO₂ = 29 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 = 1.5·14 + 8 = 29 mmHg
range: 27–31 mmHg
Answer
PaCO₂ = 29 mmHg
4.Arterial blood gas interpretation
Answer: PaCO₂ = 51.1 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
0.7·43 + 21 = 51.1 mmHg
Answer
PaCO₂ = 51.1 mmHg
The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.
5.Clinical pharmacokinetics
Answer: R = 44.1 mg/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.
Clearance
CL = 0.045·98 = 4.41 L/h
Infusion rate
R = 4.41·10 = 44.1 mg/h
Answer
R = 44.1 mg/h
6.Clinical pharmacokinetics
Answer: C = 6.758 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.
Steady-state level
Css = 25/2.5 = 10 mg/L
Rate constant
k = 0.693/8 = 0.08664 h⁻¹
Level after the given time
C = 10·(1 − e−0.08664·13) = 6.758 mg/L
Answer
C = 6.758 mg/L
7.Clinical nursing
Answer: A · Genital fungal infections
Why this is the answer
SGLT2 inhibitors cause glycosuria, which increases the risk of genital thrush and urinary infections. They can also rarely cause DKA with only modestly raised glucose.
Answer
A · Genital fungal infections
8.Clinical nursing
Answer: A · Cauda equina syndrome
Why this is the answer
Saddle anaesthesia, bladder or bowel dysfunction and leg symptoms with back pain suggest cauda equina syndrome. It needs an emergency MRI and surgical review to prevent permanent loss of function.