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 starts high-dose prednisone. Which laboratory change should the nurse expect?
AA rise in serum potassium
BA fall in the white cell count
CA rise in blood glucose
DA fall in serum sodium
2.Lab values & electrolytesHard
A patient on warfarin with an INR of 3.6 fell and hit their head an hour ago. They now report a worsening headache and drowsiness. What is the priority?
AGive acetaminophen (paracetamol) and recheck the INR tomorrow
BReport urgently for imaging and possible reversal
CEncourage rest in a dark room to settle the pain
DHold warfarin for one dose and observe at home
3.Arterial blood gas interpretationMedium
Practice values: Na⁺ 150 mmol/L, glucose 20.7 mmol/L and urea 7.5 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.
Na⁺ 150 mmol/Lglucose 20.7 mmol/Lurea 7.5 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard
At sea level, a practice gas taken on 30% oxygen shows PaO₂ 54 mmHg (7.2 kPa) and PaCO₂ 36 mmHg (4.8 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 230 mg of tobramycin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2 h. Find the volume of distribution Vd.
D = 230 mgC₀ = 10 mg/Lt½ = 2 h
Vd = L
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 92 kg patient has a digoxin level of 0.6 mcg/L; the target is 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?
92 kgVd = 7 L/kgC = 0.6 → 1 mcg/LF = 0.7
LD = mcg
7.Clinical nursingMedium
A patient with liver cirrhosis becomes confused and drowsy, with a flapping tremor of the hands. Which complication is likely?
AHepatic encephalopathy
BStroke
CHypoglycaemia caused by insulin
DAlcohol intoxication only
8.Clinical nursingHard
Which ECG change is classically associated with severe hyperkalaemia?
ATall, peaked T waves
BA shortened PR interval
CProminent U waves
DST depression only
3Solutions
1.Lab values & electrolytes
Answer: C · A rise in blood glucose
Why this is the answer
Glucocorticoids raise blood glucose by increasing glucose production and reducing insulin sensitivity. They also tend to lower potassium, retain sodium and raise the white cell count by releasing neutrophils into the blood.Checked against:Blood Glucose Test · MedlinePlus (NIH) (2024)
Answer
C · A rise in blood glucose
2.Lab values & electrolytes
Answer: B · Report urgently for imaging and possible reversal
Why this is the answer
A head injury in an anticoagulated patient, with worsening headache and drowsiness, suggests intracranial bleeding. The provider is told at once, neurological checks are done often, urgent imaging is arranged, and warfarin reversal (vitamin K and a prothrombin complex concentrate) may be prescribed.Checked against:Taking warfarin (Coumadin, Jantoven) - what to ask your doctor · MedlinePlus (NIH) (2025); Prothrombin Time Test and INR (PT/INR) · MedlinePlus (NIH) (2024)
Answer
B · Report urgently for imaging and possible reversal
3.Arterial blood gas interpretation
Answer: Osm = 328 mOsm/kg
Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.
Calculated osmolality
Osm = 2·150 + 20.7 + 7.5 = 328.2 ≈ 328 mOsm/kg
Answer
Osm = 328 mOsm/kg
4.Arterial blood gas interpretation
Answer: A–a gradient = 114.9 mmHg
Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.
Alveolar oxygen
PAO₂ = 0.3·713 − 36/0.8 = 213.9 − 45 = 168.9 mmHg
Gradient
A–a = 168.9 − 54 = 114.9 mmHg
Answer
A–a gradient = 114.9 mmHg
5.Clinical pharmacokinetics
Answer: Vd = 23 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 = 230/10 = 23 L
Answer
Vd = 23 L
6.Clinical pharmacokinetics
Answer: LD = 368 mcg
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 = 7·92 = 644 L
Rise needed
1 − 0.6 = 0.4 mcg/L
Loading dose
LD = 644·0.4/(1·0.7) = 368 mcg
Answer
LD = 368 mcg
In practice the dose is rounded to a convenient amount.
7.Clinical nursing
Answer: A · Hepatic encephalopathy
Why this is the answer
Hepatic encephalopathy causes confusion and asterixis. Lactulose is commonly used to reduce ammonia absorption and treat precipitants such as infection or bleeding.
Answer
A · Hepatic encephalopathy
8.Clinical nursing
Answer: A · Tall, peaked T waves
Why this is the answer
Hyperkalaemia causes peaked T waves, then a widened QRS and possibly a sine-wave pattern and arrest. Hypokalaemia causes flat T waves and U waves.