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 type 1 diabetes has the flu, is eating little and has a glucose of 290 mg/dL (16.1 mmol/L). Which advice is correct?
AStop all insulin until you are eating normally again
BKeep taking insulin and check blood or urine ketones
CWait 3 days before checking the glucose again
DDrink only water and avoid all carbohydrate foods
2.Lab values & electrolytesHard
A patient in DKA is receiving IV fluids and insulin. The glucose has fallen to about 220 mg/dL (12.2 mmol/L), but the anion gap is still high. What change would the nurse expect?
AGive an IV bolus of sodium bicarbonate at once
BStop the insulin infusion because the glucose is near normal
CAdd dextrose to the IV fluids and continue the insulin
DStop the IV fluids and start oral fluids only
3.Arterial blood gas interpretationMedium
A practice gas shows PaCO₂ 22 mmHg (2.9 kPa). Use the rule that in acute respiratory alkalosis HCO₃⁻ falls by 2 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.
A practice gas shows pH 7.28, PaCO₂ 24 mmHg (3.2 kPa) and HCO₃⁻ 11 mmol/L, with Na⁺ 136 and Cl⁻ 91 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.
Practice exercise (made-up values, not clinical guidance). A 68 kg patient receives a theophylline infusion. The clearance is 0.04 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 12 mg/L?
68 kgCL = 0.04 L/kg/hCss = 12 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 82 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.03 L/kg/h. What dose D in mg gives an average steady-state level of 10 mg/L?
A patient's low potassium does not improve despite potassium replacement. Which other electrolyte should be checked?
APhosphate
BMagnesium
CSodium
DChloride
8.Clinical nursingHard
A patient taking dapagliflozin is vomiting and unwell, with high blood ketones and a blood glucose of only 11 mmol/L (198 mg/dL). What should be suspected?
ASimple gastroenteritis with no further concern
BHyperosmolar hyperglycaemic state
CEuglycaemic diabetic ketoacidosis
DHypoglycaemia
3Solutions
1.Lab values & electrolytes
Answer: B · Keep taking insulin and check blood or urine ketones
Why this is the answer
During illness, stress hormones raise glucose, so insulin is continued even when eating less. Glucose and ketones are checked often, fluids are taken, and the provider is contacted if ketones are moderate or high or vomiting prevents fluids.Checked against:Diabetes - when you are sick · MedlinePlus (NIH) (2026)
Answer
B · Keep taking insulin and check blood or urine ketones
2.Lab values & electrolytes
Answer: C · Add dextrose to the IV fluids and continue the insulin
Why this is the answer
The glucose usually falls before the ketoacidosis resolves. Dextrose is added so insulin can continue, clearing ketones without causing hypoglycemia, until the anion gap closes. Stopping insulin too early lets ketoacidosis return.
Answer
C · Add dextrose to the IV fluids and continue the insulin
3.Arterial blood gas interpretation
Answer: HCO₃⁻ = 20.4 mmol/L
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.
Change in PaCO₂
|22 − 40| = 18 mmHg → 1.8 × 10 mmHg
Expected HCO₃⁻
HCO₃⁻ = 24 − 2·1.8 = 20.4 mmol/L
Answer
HCO₃⁻ = 20.4 mmol/L
4.Arterial blood gas interpretation
Answer: pure high-gap acidosis
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 = 136 − (91 + 11) = 34
Delta ratio
(34 − 12)/(24 − 11) = 1.692
pure high-gap acidosis
Answer
pure high-gap acidosis
5.Clinical pharmacokinetics
Answer: R = 32.64 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 = 0.04·68 = 2.72 L/h
Infusion rate
R = 2.72·12 = 32.64 mg/h
Answer
R = 32.64 mg/h
6.Clinical pharmacokinetics
Answer: D = 196.8 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.
Clearance
CL = 0.03·82 = 2.46 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 10·2.46·8/(1·1) = 196.8 mg
Answer
D = 196.8 mg
7.Clinical nursing
Answer: B · Magnesium
Why this is the answer
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 · Euglycaemic diabetic ketoacidosis
Why this is the answer
SGLT2 inhibitors can cause DKA with near-normal or modestly raised glucose because glucose is lost in the urine. Ketones should be checked in unwell patients on these drugs.